◉Et est ex 7 capitulis. Primum capitulum est proemium; Secundum de eis que debent proponi sermoni in deceptionibus visus; Tertium de causis quibus deceptio accidit visui; Quartum in distinguendo deceptiones visus; Quintum de qualitatibus deceptionum visus que fiunt solo sensu; Sextum de qualitatibus deceptionum visus que fiunt in cog nitione; Septimum de qualitatibus deceptionum visus que fiunt in ratione.

◉[This is the third book], and it consists of seven chapters. The first chapter comprises the prologue. The second [concerns certain] things that need to be set forth for the analysis of visual illusions. The third [concerns] the reasons why visual illusions occur. The fourth describes [the various kinds of] visual illusions. The fifth [deals with] the sorts of visual illusions that occur during brute sensation. The sixth [deals with] the sorts of visual illusions that occur during recognition. The seventh [deals with] the sorts of visual illusions that occur during judgment.

◉[Capitulum 1]

◉[Chapter 1]

1.1 ◉ Declaratum est in primo tractatu et secundo quomodo visus comprehendit visibilia secundum quod sunt si comprehensio eius fuerit recte, et quomodo certificat formam visi, et quomodo comprehendit unamquamque intentionum particularium secundum quod est, et quomodo certificat illam. Sed non omne comprehensibile a visu comprehenditur ab eo secundum quod est, nec omne quod videtur ab inspiciente ipsum comprehendi in rei veritate est recte comprehensum. Sed multotiens decipitur visus in multis eorum que comprehendit ex visibilibus, et comprehendit illa alio modo ab eo quo sunt. Et forte percipit suam deceptionem etiam cum decipitur, et forte non, sed reputat se bene comprehendere. Cum enim visus comprehendit aliquod visum per spatium remotum, tunc mensura eius videbitur minor quam vera mensura, et quando illud visum fuerit forte propinquum visui, comprehendet mensuram eius maiorem vera. Et amplius quando visus comprehenderit quadratum aut poligonium a remoto, comprehendet eum rotundum, si fuerit equalium dyametrorum, aut longum, si fuerit inequalium dyametrorum, et si comprehenderit speram a remotissimo, comprehendet eam planam. Et talia sunt multa et multimoda, et omnia que sunt comprehensa a visu tali modo sunt fallibilia.

1.1 ◉ It has been shown in the first and second books how sight perceives visible objects as they actually exist when they are perceived directly,⁑ and [it has been shown] how sight determines the form of the thing seen, how it perceives each particular [visible] attribute as it actually exists, and how it determines every such attribute. But not everything that is perceptible to sight is perceived by it as it actually exists, nor is everything that seems to the viewer to be perceived as it actually exists correctly perceived. On the contrary, sight is frequently deceived about many of the things it perceives about visible objects, and it perceives them other than they really are. Moreover, sight sometimes perceives that it is being deceived even as it is being deceived, but it sometimes does not, thinking, rather, that it is perceiving properly. For when sight perceives some visible object from a great distance, that object will look smaller than it really is, whereas when that [same] visible object lies quite near the eye, sight will perceive it as larger than it really is. Furthermore, when sight perceives a quadrilateral or polygon from a distance, it will perceive it as circular if its diagonals are equal, or oblong, if its diagonals are unequal, and if it perceives a sphere from a very great distance, it will perceive it as flat. Such cases are numerous and variegated, and everything that is perceived by sight in such a way is subject to deception.

1.2 ◉ Amplius quando visus inspexerit aliquam stellam, comprehendet eam quiescentem, licet stella tunc moveatur; et cum inspiciens revertatur ad scientiam sciet illam stellam moveri apud aspectum. Et cum inspiciens distinxerit illud, statim percipit se decipi in hoc quod comprehenderit de quiete stelle. Et cum aliquis inspexerit aliquod individuum super faciem terre a remotissimo, et illud individuum fuerit motum motu tardissimo et non diu duraverit aspectus, tunc in tali statu aspectus comprehendet ipsum quiescens. Et si aspiciens non perceperit ante motum illius individui, et non diu duraverit in eius oppositione, tunc non percipiet se esse deceptum in hoc quod comprehendit de quiete illius individui, et in comprehensione huiusmodi erit deceptus. Et cum hoc non percipiet se decipi. Accidet igitur visui deceptio in multis eorum que comprehendit, que forte percipitur ab eo, et forte non.

1.2 ◉ In addition, when sight looks at some star, it will perceive it to be immobile, even though the star actually moves at the time; but when the viewer thinks about it, he will realize that the star is moving while he looks at it. And when the viewer discerns this fact, he immediately realizes that he is being deceived in his perception that the star is immobile. Also, if someone stares at something standing on the ground extremely far away, and if that thing is moving quite slowly, then, if the observer does not look at it long [enough], he will perceive it as immobile. And if the viewer has not perceived that thing’s motion before and does not keep watching it for awhile, he will not perceive that he is deceived in perceiving that thing as immobile, so he will be deceived in this sort of perception. He will nonetheless not perceive that he is deceived. Sight may therefore happen to be deceived about many things it perceives, and sometimes it perceives [that it is deceived], and sometimes it does not.

1.3 ◉ Et cum in duobus tractatibus precedentibus sit declaratum quomodo visus comprehendit visibilia secundum quod sunt, in hoc autem capitulo declaratum est ex eis que diximus quod multotiens accidit visui deceptio in multis eorum que comprehendit, remanet declarandum quare deceptio accidit visui et quando et quomodo. Nos autem in hoc tractatu contenti sumus ex deceptionibus visus in eis que comprehendit recte, et declarabimus causam in hoc, et diversitates deceptionum, et quomodo accidit unaqueque deceptio.

1.3 ◉ Since it has been shown in the two previous books how sight perceives visible objects as they actually exist, whereas in this chapter it has been shown on the basis of what we have said that sight often happens to be deceived about many things it perceives, it remains for us to explain why, when, and how sight happens to be deceived. In this book, however, we limit ourselves to visual illusions regarding things that sight perceives directly, and we shall explain the reason for such [illusions], the different illusions [that can arise], and how each illusion occurs.

◉[Capitulum 2]

◉[Chapter 2]

2.1 ◉ Declaratum est in primo tractatu quod visus nichil comprehendit ex visibilibus nisi secundum verticationes linearum radialium et quod ordo visibilium et partium eorum non comprehenditur nisi ex ordinatione linearum radialium. Et dictum est etiam quod unum visum quod comprehenditur duobus oculis in simul non comprehenditur unum nisi quando positio eius in respectu duorum oculorum fuerit positio consimilis; et quod si positio fuerit diversa, tunc unum comprehendetur duo. Sed unumquodque visibilium assuetorum que semper comprehenduntur a duobus visibus semper comprehendetur unum. Unde oportet nos declarare quomodo unum visum comprehenditur a duobus visibus unum in maiori parte temporis et in pluribus positionibus, et quomodo positio unius visi ab ambobus oculis in maiori parte temporis et in pluribus erit consimilis. Et declarabimus etiam quomodo positio unius visi ab ambobus visibus erit positio diversa et quando accidit hoc. Et iam diximus hoc in primo tractatu, et declaravimus ipsum universaliter non determinate.

2.1 ◉ It was shown in the first book that sight perceives no visible object unless it does so along radial lines and that the arrangement of visible objects and their parts is perceived only according to the arrangement of the radial lines.⁑ And it was also pointed out that a single visible object perceived simultaneously by both eyes is perceived as single only when its situation with respect to both eyes is equivalent; if its situation is not equivalent, then a single object will be perceived as double.⁑ However, every familiar visible object that is continually perceived by both eyes will always be perceived as single. So we need to explain how a single visible object is generally perceived as single by both eyes in many [different] situations, as well as how the situation of a single visible object will generally be equivalent with respect to both eyes under various conditions. And we shall also explain how the situation of a single visible object may not be equivalent with respect to both eyes, as well as explaining the conditions under which this happens. We have already made this claim in the first book, but we explained it in a general rather than a definitive way.⁑

2.2 ◉ Dicamus quod quando inspiciens inspexerit aliquod visum, tunc uterque visus erit in oppositione illius visi, et cum inspiciens direxerit pupillam ad illud visum, tunc uterque diriget pupillam ad illud visum directione equali, et cum visus fuerit motus super rem visam, tunc uterque visus movebitur super illud.

2.2 ◉ We should point out that, when an observer looks at some visible object, each eye will face that visible object directly, so when the observer directs his gaze on that visible object, he will direct both eyes on that visible object in a corresponding way, and when his sight passes over the visible object, both eyes will pass [correspondingly] over it.

2.3 ◉ Et cum inspiciens direxerit pupillam ad rem visam, tunc axes duorum visuum congregabuntur in illa re visa et coniunguntur in aliquo puncto illius superficiei, et si inspiciens moverit visum per illam rem visam, tunc illi duo axes movebuntur simul super superficiem illius visi et per omnes partes eius. Et universaliter duo oculi sunt equales in omnibus suis dispositionibus, et virtus sensibilis que est in eis est eadem, et actio et passio eorum semper est equalis et consimilis. Et si alter visus fuerit motus ad videndum, statim reliquus movebitur ad illud visum illo eodem motu, et si alter visus quieverit, reliquus quiescet; et impossibile est ut alter visus moveatur ad videndum et reliquus quiescat nisi impediatur.

2.3 ◉ Moreover, when the observer directs his gaze on a visible object, the axes of both eyes will meet on that visible object and intersect at some point on its surface, so if the observer passes his sight over that visible object, those two axes will pass together over the surface of the visible object and will scan all of its parts.⁑ Generally, the two eyes correspond in all their dispositions, and the sensitive power in each of them is the same, so the way they act and are affected is invariably the same. And if either eye is moved for the sake of viewing [something], the other one will immediately move toward that object with a matching movement, whereas if either eye remains fixed, the other will remain fixed as well; and it is impossible for either eye to move for the sake of viewing [something] while the other remains fixed unless there is interference.

2.4 ◉ Et declaratum est in predictis quod inter quodlibet visum et centrum visus est piramis ymaginabilis apud visionem cuius conus est centrum visus et basis superficies visi quod visus comprehendit. Sed ista piramis continet omnes verticationes ex quibus comprehendit illam rem visam. Cum igitur duo axes amborum visuum fuerint coniuncti in aliquo puncto superficiei visi, tunc superficies visi erit basis communis ambabus piramidibus radialibus figuratis inter duo centra amborum visuum et illud visum, et tunc positio puncti in quo duo axes sunt coniuncti apud ambos visus est positio consimilis, quia est oppositus duobus mediis amborum visuum, et duo axes qui sunt inter illud et duos visus sunt perpendiculares super superficiem duorum visuum. Quod autem remanet ex superficie visi inter quodlibet punctum in eo et duo centra amborum visuum sunt due linee quarum positio in respectu duorum axium erit positio consimilis in parte—scilicet quoniam omnes due linee ymaginabiles inter duo centra duorum visuum et punctum superficiei visi in quo coniunguntur duo axes amborum visuum ambe erunt declinabiles a duobus axibus ad unam partem. Nam omnis punctus superficiei visi in quo duo axes coniunguntur declinabitur a puncto coniunctionis ad eandem partem; punctus autem coniunctionis est super utrumque axem. Remotiones autem istarum linearum a duobus axibus sunt equales, quoniam omnes due linee exeuntes a duobus centris duorum visuum ad quodlibet punctum punctorum valde propinquorum puncto coniunctionis equaliter distant a duobus axibus quantum ad sensum. Duo enim axes exeuntes ad punctum coniunctionis erunt equales, aut non erit inter illas diversitas sensibilis quando res visa non fuerit valde propinqua visui, et distantia eius a visu fuerit mediocris. Et similiter est dispositio cuiuslibet puncti multum propinqui puncto coniunctionis—scilicet quod omnes due linee exeuntes a duobus centris duorum visuum ad quodlibet punctum eorum fere non differunt in longitudine quantum ad sensum, et forte erunt equales. Quando autem due linee declinantes coniuncte fuerint in superficie in qua sunt duo axes, erunt inequales, nam linea que exit a puncto in quo duo axes coniunguntur ad punctum declinans ab illo continet cum duobus axibus angulos inequales. Et duo axes sunt equales, et linea copulans duo puncta est communis, quapropter due linee declinantes erunt inequales. Sed ista inequalitas non operatur in sensu si punctus declinans fuerit propinquus puncto coniunctionis. Si autem due linee declinantes fuerint sub axibus aut super illos, possunt esse equales, duo enim anguli quos continent duo axes cum linea continuante duo puncta possunt esse equales si punctus fuerit sub axibus aut super eos. Et in positionibus que sunt inter has duas positiones erit diversitas que est inter duas lineas declinantes minor quam diversitas que est inter duas lineas primas declinantes, et sic non erit inter eas differentia operans in sensum.

2.4 ◉ It has also been shown in an earlier discussion that, when vision occurs, a cone can be imagined [to extend] between any visible object and the center of the eye, the vertex [of that cone] being the center of sight and the base the surface of the visible object that sight perceives.⁑ But this cone contains all the radial lines according to which sight perceives that visible object. Thus, when the [visual] axes of both eyes intersect at some point on the surface of a visible object, the surface of the visible object will form a common base for both visual cones described between the centers of both eyes and the visible object, and thus the situation of the point where the two [visual] axes intersect is equivalent with respect to both eyes, since it faces the middle [of the surfaces] of both eyes, and the [visual] axes extending between the visible object and the two eyes are perpendicular to the surfaces of both eyes.⁑ For any [other] point on the surface of the visible object, there are two lines that can be drawn from it to the centers of both eyes so as to be equivalently situated with regard to the [visual] axes as far as direction is concerned—i.e., any two lines imagined [to extend] between the centers of both eyes and the point on the surface of the visible object where the [visual] axes of both eyes meet will incline toward the same side of the two [visual] axes. Now every point on the surface of the visible object upon which the two [visual] axes intersect will lie on the same side of the point where the axes intersect; but the point of intersection lies upon both [visual] axes. Moreover, these [two] lines are equidistant from the two [visual] axes, for any two lines extending from the centers of both eyes to any of the points quite near the point of intersection [of the visible axes] are equidistant from the two [visual] axes as far as sense is concerned. For the two [visual] axes extending to the point of intersection will be equal, or else there will not be a perceptible difference between them when the visible object is not too near the eye, but, rather, its distance from the eye is moderate. And the same applies to the situation of any point that is very near the point of intersection—i.e., any two lines extending from the centers of the two eyes to any point [on the visible surface] scarcely differ in length as far as sense is concerned, and sometimes they will actually be equal [as far as sense is concerned]. However, since the two lines that intersect [somewhere] beside [the point of intersection of the visual axis] lie on the plane of the two [visual] axes, they will be unequal [in length], for the line extending from the point where the two [visual] axes intersect to some point beside it forms unequal angles with the two [visual] axes. But the two axes are equal, while the line joining the two points is common, so the two lines to the side [of the visual axes] will be unequal. However, this difference in length does not affect the sense if the point beside the point where the visual axes intersect is near it. On the other hand, if the two lines lie below or above the [visual] axes, they can be equal, for the two angles formed by the two [visual] axes with the line extended between the two points [of intersection] can be equal if the [other] point lies below or above [the point of intersection of] the [visual] axes.⁑ Furthermore, in the situations lying between these two the difference between the two lines beside [the visual axes] will be less than the difference between the first [set of] lines beside [the visual axes], so there will be no effective difference between them as far as sense is concerned.

2.5 ◉ Ergo due linee exeuntes a duobus centris duorum visuum ad puncta propinqua puncto in quo coniunguntur duo axes non differunt fere in longitudine quantum ad sensum. Et duo axes sunt equales, et linea que copulat punctum coniunctionis cum puncto declinante ad quod exeunt due linee a duobus centris est communis duobus triangulis factis ex istis lineis. Ergo duo anguli qui sunt apud duo centra duorum visuum quibus subtenditur apud superficiem visi linea communis erunt equales, aut fere inter eas non erit diversitas sensibilis. Et isti duo anguli semper erunt minimi quando punctus fuerit propinquissimus multum coniunctioni duorum axium.

2.5 ◉ Hence the two lines extending from the centers of the two eyes to points near the point where the two [visual] axes intersect scarcely differ in length as far as sense is concerned. Moreover, the two [visual] axes are equal, and the line joining the point of [their] intersection with the point beside it to which the [other] two lines are extended from the two centers [of sight] is common to both triangles formed by these lines. Therefore, the two angles at the centers of both eyes subtended by that common line on the surface of the visible object will be equal, or else there will be scarcely any perceptible difference between them. And these two angles will always be minimal when the point is extremely close to the point where the two [visual] axes intersect.⁑

2.6 ◉ Et cum due linee que exeunt ad quodlibet punctum propinquum puncto coniunctionis contineant cum duobus axibus angulos equales, tunc remotio quarumlibet duarum linearum exeuntium ad eundum punctum punctorum propinquorum puncto coniunctionis a duobus axibus duorum visuum erit remotio equalis.

2.6 ◉ In addition, if the two lines extending to any point near the point of intersection [of the visual axes] form equal angles with the two [visual] axes, then the distance [from the two visual axes] of any of the two lines extending to the same point among the points that are near the point of intersection [of the two visual axes] will be equal.⁑

2.7 ◉ Ergo positio cuiuslibet puncti superficiei visi in quo coniunguntur duo axes visuum, si fuerit propinquus puncto coniunctionis in respectu duorum visuum, est positio consimilis in parte et in remotione a duobus axibus. Dispositio autem in punctis remotis a puncto coniunctionis declinantibus ad unam partem ab ambobus axibus est talis anguli qui sunt inter duas lineas exeuntes ad aliquem punctum eorum et inter duos axes fortasse differunt diversitate aliquanta, et positio omnium huiusmodi punctorum remotorum a puncto coniunctionis in respectu duorum visuum est positio consimilis in parte tantum sed non in remotione a duobus axibus. Visum igitur comprehensum ambobus visibus, cum fuerit alicuius quantitatis et propinquorum dyametrorum, positio cuiuslibet puncti apud duos visus est positio consimilis in parte et in remotione, quapropter forma eius statuetur in duobus visibus in duobus locis consimilis positionis a duobus visibus. Et cum visum comprehensum ambobus visibus fuerit maximorum dyametrorum, tunc positio eius puncti in quo coniunguntur duo axes erit positio consimilis apud duos visus, et quanto magis appropinquaverint illi puncta que sunt in superficie illius visi, tanto magis positio illorum apud duos visus erit consimilis in parte et in remotione in simul. Puncta autem que sunt in superficie illius visi remota a puncto coniunctionis et declinantia ab ambobus axibus ad unam partem habent positionem consimilem in parte apud duos visus, et in remotione forte consimilem et forte non. Forma igitur partis que est apud locum coniunctionis huius visi et eius que continet punctum coniunctionis et eius quod est illi propinquum, instituitur in duobus locis duorum visuum consimilis positionis in omnibus dispositionibus. Et instituentur forme partium residuarum remotarum a puncto coniunctionis circumdantium partem consimilis positionis continue cum forma partis consimilis positionis. Et sic universum duarum formarum instituitur in duobus locis duorum visuum inter que non est maxima differentia in positione. Sed si fuerit, erit inter extrema tantum, et erit modica propter continuationem extremorum cum duobus mediis que sunt consimilis positionis; et hoc erit dum duo visus fixi fuerint in oppositione visi et duo axes fuerint fixi in uno puncto eius. Cum autem duo visus fuerint moti super rem visam et duo axes fuerint translati ab illo puncto et fuerint moti in simul per superficiem illius visi, tunc positio cuiuslibet puncti illius visi et positio punctorum propinquorum illi in respectu duorum visuum apud coniunctionem duorum axium in ipso erit positio consimilis valde, et forma cuiuslibet partis visi apud motum duorum axium per superficiem erit in duobus locis positionis consimilis apud duos visus. Et sic forma omnium partium visi apud motum et intuitionem erit consimilis dispositionis apud ambos visus.

2.7 ◉ Hence the situation of every point on the surface of the visible object upon which the two visual axes intersect, assuming that it lies near the point of intersection [of those axes] with respect to both eyes, constitutes a corresponding situation in terms of direction and distance from the two [visual] axes. On the other hand, the situation in the case of points lying far to one side of the point of intersection of the two [visual] axes is such that the angles formed by the two lines extending to some point [on the visible surface] and the two [visual] axes may differ by a measurable amount, so all such points that are [significantly] distant from the point of intersection [of the visual axes] in respect to the eyes have a corresponding situation as far as direction alone is concerned, but not as far as the distance from both [visual] axes is concerned.⁑ Hence, as long as a visible object perceived by both eyes is of measurable size and its cross-sections are roughly equal in size, any point on it has a corresponding situation vis-à-vis the two eyes in terms of both direction and distance, so its form will occupy corresponding locations on each of the two eyes. But if the visible object perceived by both eyes is extremely large in cross-section, then the point on it where the two [visual] axes intersect will have a corresponding situation vis-à-vis the two eyes, and the closer to that point the [other] points are on the surface of that visible object, the more those points will have a corresponding situation vis-à-vis the eyes in terms of both direction and distance. However, points on the surface of that visible object that lie far away from the point of intersection and that lie on one side of the two [visual] axes have a corresponding situation vis-à-vis the two eyes in terms of direction, but as far as distance is concerned, they may or may not. Hence, the form of the area on such a visible object where the intersection [of the visual axes] occurs, as well as the form that includes the point of [that] intersection and everything surrounding it, is impressed at two areas on the two eyes that have a corresponding situation under all circumstances. Meanwhile the forms of the remaining parts that are distant from the point of intersection and that surround the area that has a corresponding situation [in each eye] are continuous with the form of the area that has a corresponding situation. Hence, every pair of forms is impressed on two areas on the two eyes that do not differ much in relative situation. And when there is difference, it will only be between the extremities, and it will be slight on account of the continuity of the extremities with the intermediate parts that are correspondingly situated; and this will be the case as long as the two eyes are focused on a directly facing visible object and the two axes remain focused on one of its points. Moreover, as the two eyes move over the visible object and the two [visual] axes are shifted from that point to move together over the surface of that visible object, the situation of every point on that visible object, as well as the situation of the points that are near it relative to the two eyes at the intersection of the two [visual] axes will be in nearly perfect correspondence, so the form of every part of the visible object as the two axes move over its surface will have a corresponding situation at two places on both the eyes. And thus, as movement and visual scrutiny continue, the form of all parts of the visible object will have a corresponding situation in both eyes.

2.8 ◉ Et similiter etiam quando visus comprehendit visibilia separata in eadem hora in simul, et duo axes fuerint coniuncti in aliquo eorum, et illud visum in quo sunt coniuncti duo axes fuerit propinquorum dyametrorum, tunc forma illius visi instituetur in duobus locis duorum visuum consimilis positionis. Et etiam forma eius quod propinquum est illi viso, si fuerit parve quantitatis, instituetur in duobus locis duorum visuum inter quorum positiones non erit differentia sensibilis. Forma autem visi remoti a viso in quo duo axes coniunguntur quando ambo visus comprehendunt illud visum, dum duo axes sunt fixi in illo viso, instituetur in duobus locis duorum visuum consimilis positionis in parte tantum et non in remotione; aut non omnes partes eorum erunt consimilis positionis in remotione a duobus axibus, nec forma erit certificata. Deinde si duo visus fuerint moti, et duo axes, et fuerint coniuncti in unoquoque visibilium comprehensorum in simul, tunc forma uniuscuiusque eorum instituetur in duobus locis consimilis positionis in respectu duorum visuum in parte et in remotione; et tunc certificabitur forma uniuscuiusque illorum visibilium.

2.8 ◉ So, too, when sight perceives separate visible objects together at the same time, and the two [visual] axes intersect on one of them, if the visible object on which the two [visual] axes intersect has nearly equal cross-sections, then the form of that visible object will be impressed on two correspondingly situated places on the two eyes. Moreover, the form of whatever lies near that visible object, if it is small, will be impressed on two places on the two eyes that do not differ perceptibly in relative situation. However, when both eyes perceive a visible object far from the one on which the two [visual] axes intersect, and if the two [visual] axes remain focused on the original object, the form of the far object will be impressed on two places on the two eyes that are correspondingly situated in terms of direction only, not in terms of distance; not all of its parts will be correspondingly situated with respect to the two [visual] axes as far as distance is concerned, nor will its form be determinate. If the two eyes are then moved along with the two [visual] axes so that they intersect on each of [the other] visible objects perceived at the same time, the form of each of them will be impressed on two places on the two eyes that are correspondingly situated in terms of both direction and distance; and in that case the form of each of those visible objects will be determinate.

2.9 ◉ Et multotiens coniunguntur duo axes amborum visuum in aliquo viso, et cum hoc duo visus comprehendent aliam rem visam cuius positio in respectu duorum visuum erit diversa in parte. Et hoc erit quando illud aliud visum fuerit propinquius ambobus visibus viso in quo coniunguntur duo axes, et fuerit cum hoc inter duos axes aut fuerit remotius ab ambobus visibus viso in quo coniunguntur duo axes, et fuerit etiam inter duos axes cum fuerimus ymaginati extensos post coniunctionem, et visum in quo coniunguntur duo axes non cooperiet visum quod est remotius ipso aut cooperiet quoddam illius.

2.9 ◉ Furthermore, the axes of both eyes often intersect on some visible object while the two eyes perceive another visible object that is not correspondingly situated with respect to the eyes in terms of direction. This will happen when that other visible object lies nearer both eyes than the visible object on which the two [visual] axes intersect and, moreover, falls between the two axes, or when it lies farther from both eyes than the visible object on which the two visual axes intersect but still falls between the two [visual] axes as we imagine them extended beyond their intersection, provided that the visible object on which the axes intersect does not block the visible object lying beyond it or [only] blocks part of that object.⁑

2.10 ◉ Hiis igitur modis fit comprehensio visibilium ambobus visibus.

2.10 ◉ In these ways, then, both eyes perceive visible objects.

2.11 ◉ Et etiam declaratum est in secundo tractatu quod axis radialis in utroque visu est eadem linea que non transmutatur, et quod pertransit centra omnium tunicarum visus et extenditur recte per centrum omnium tunicarum ad medium loci incurvationis ex concavo nervi super quem componitur oculus qui est apud foramen quod est in concavo ossis, et quod est inseparabilis ab omnibus centris, et quod positio eius apud omnes partes visus est positio semper eadem non transmutabilis apud motum visus nec apud quietem eius, et quod positio duorum axium apud duos visus est positio consimilis in respectu amborum visuum apud concavitatem nervi communis ex quo ultimum sentiens comprehendit formas visibilium. Ymaginemur igitur lineam rectam copulantem inter duo centra duorum foraminum que sunt in duabus concavitatibus duorum ossium continentium duos oculos, et ymaginemur duas lineas exeuntes a duobus centris duorum foraminum ossium extensas in duobus mediis duarum concavitatum nervorum. Hee igitur linee coniunguntur in medio concavitatis nervi communis, quia positio duorum nervorum in respectu concavitatis communis nervi est positio consimilis; et positio harum duarum linearum apud lineam copulantem inter duo centra duorum foraminum erit positio consimilis, quia duorum nervorum positiones in respectu duorum foraminum erit positio consimilis. Et sic duo anguli qui sunt inter has duas lineas et lineam copulantem inter duo centra duorum foraminum equales.

2.11 ◉ It was also shown in the second book that the visual axis in each eye constitues a unique and unchanging line, and that it passes through the centers of all the tunics of the eye and extends directly through the center of all the tunics to the middle of the place where the hollow of the nerve to which the eye is attached flexes, this place being at the opening in the eye socket,⁑ [and it was shown] that the visual axis is inseparable from all the [ocular] centerpoints, that its situation with respect to all parts of the eye is always the same, remaining unaffected by the motion or immobility of the eye,⁑ and that the two axes in the two eyes have a corresponding situation with respect to both eyes from the hollow of the common nerve where the final sensor perceives the forms of visible objects.⁑ Let us therefore imagine a straight line joining the centers of the two openings in the two sockets containing the eyes, and let us imagine two lines extending from the centers of both openings in the eyesockets through the middle of [each of] the two hollow nerves. These lines therefore intersect in the middle of the hollow of the common nerve, because both nerves are correspondingly situated with respect to the hollow of the common nerve; so these two lines will be correspondingly situated with respect to the line joining the centers of the two openings [in the eyesockets], because the two nerves will be correspondingly situated with respect to those two openings. Hence, the two angles formed by these two lines and the line joining the centers of the two openings [in the eyesockets] will be equal.

2.12 ◉ Et ymaginemur etiam lineam copulantem inter duo centra duorum foraminum divisam in duo equalia, et ymaginemur lineam exeuntem a puncto quod est in medio concavitatis nervi communis in quo due linee extense in concavitatibus duorum nervorum sunt coniuncte extensam ad punctum dividentem lineam copulantem duo centra duorum foraminum in duo equalia. Hec igitur linea erit perpendicularis super lineam copulantem duo centra duorum foraminum. Et ymaginemur istam perpendicularem extensam recte in partem oppositam visui; et sic ista linea erit fixa in eodem statu, et positio eius non transmutabitur, quia punctus qui est in medio concavitatis nervi communis in quo due linee extense in duobus mediis concavitatum duorum nervorum sunt coniuncte est unus non transmutabilis. Et punctus etiam qui dividit lineam copulantem duo centra duorum foraminum est etiam unus punctus non transmutabilis, quapropter positio linee recte transeuntis per illa est una positio non transmutabilis. Hec igitur linea vocetur axis communis.

2.12 ◉ Let us also imagine that the line joining the centers of the two openings [in the eye sockets] is bisected, and let us imagine a line extending from the midpoint of the hollow of the common nerve where the two lines passing through the hollows of the two nerves intersect so as to continue to the point where the line joining the centers of the two openings [in the eyesockets] is bisected. This line will therefore be perpendicular to the line joining the centers of the two openings [in the eye sockets]. Now let us imagine that this perpendicular line is extended straight outward from the eye[s]; and so this line will remain fixed, and its situation will not change, because the point at the middle of the hollow of the common nerve where the two lines passing through the middle of the hollows of the two nerves intersect is unique and invariant. In addition, the point where the line joining the centers of the two openings [in the eye sockets] is bisected is also unique and invariant, so the straight line passing through those [two unique and invariant] points has a unique and invariant situation as well. Accordingly, this line will be referred to as the »common axis.«⁑

2.13 ◉ Et ymaginemur apud punctum aliquem istius linee in parte opposita visui aliquod visum, et ymaginemur duos visus aspicere illud visum et duos axes in simul coniungi in puncto superficiei visi in quo axis communis occurrerit superficiei illius visi, et hoc quidem possibile est in omni viso cuius situs ex duobus visibus est situs consimilis. Cum igitur duo axes fuerint coniuncti in aliquo puncto axis communis, tunc duo axes, et axis communis, et linea que copulat duo centra foraminum duorum ossium, et due linee extense in concavitatibus duorum nervorum omnia erunt in una superficie. Duo enim axes transeunt per centra duorum foraminum, transeunt enim per duo media concavitatum duorum nervorum in loco piramidationis duorum nervorum. Cum igitur duo axes fuerint coniuncti in axe communi, erunt omnes in superficie in qua est axis communis, et linea secans ipsum que copulat centra foraminum duorum ossium. Et duo axes de loco centrorum duorum foraminum usque ad punctum coniunctionis qui est in axe communi erunt equales. Et positio eorum apud axem communem erit positio consimilis, et due partes duorum axium que sunt de centris duorum visuum usque ad punctum coniunctionis erunt equales, et remotio centrorum duorum visuum a foraminibus duorum ossium et a centris duorum foraminum est remotio equalis. Et etiam due partes duorum axium que sunt de superficiebus duorum visuum usque ad punctum coniunctionis etiam erunt equales. Nam due medietates dyametrorum sperarum duorum visuum sunt equales, et quia ita est, positio puncti superficiei visi in quo coniuncti sunt duo axes apud duo puncta per que transeunt duo axes erit positio consimilis, et remotio eius ab eis erit equalis. Et hec duo puncta superficierum visuum sunt illa in quibus infigitur forma puncti in quo coniuncti sunt duo axes.

2.13 ◉ Now let us imagine some visible object facing the eye at some point on this line, and let us imagine that the two eyes look at this object while the two [visual] axes intersect at the point on the surface of the visible object where the common axis meets that surface, which is certainly possible for any visible object that is correspondingly situated with respect to the two eyes. When the two [visual] axes intersect at some point on the common axis, then the two [visual] axes, the common axis, the line joining the centers of the two openings in the eye sockets, and the two lines passing through the hollows of the two nerves will all lie in the same plane. For the two [visual] axes pass through the centers of the two openings [in the eye- sockets], since they pass through the middle of the hollow of the two nerves where the two nerves funnel outward [toward the front of the eyeball]. Therefore, if the two [visual] axes intersect on the common axis, they will all lie on the same surface as the common axis and the line intersecting it that joins the centers of the openings in the two eye sockets. In addition, the two [visual] axes [extending] from the centers of both openings [in the eye sockets] to the point of intersection on the common axis will be equal. Also, they will be correspondingly situated with respect to the common axis, the two segments of the two [visual] axes [that extend] from the centers of the two eyes to the point of intersection will be equal, and the distance of the centers of both eyes from the openings in the two eye sockets as well as from the centers of those two openings is equal. Meanwhile, the two segments of the two [visual] axes extending from the surfaces of the two eyes to the point of intersection will also be equal. For the radii of the two ocular spheres are equal, and since that is so, the point on the surface of the visible object where the two [visual] axes meet will be correspondingly situated with respect to the two points through which the two [visual] axes pass [through the surfaces of the eye], so its distance from those [two points] will be equal. And these two points on the surfaces of the eyes are the ones upon which the form of the point where the two [visual] axes intersect is impressed.

2.14 ◉ Et etiam positio utriusque duorum punctorum que sunt in duobus axibus superficierum duorum visuum apud concavitatem nervi communis erit positio consimilis, et positio istorum duorum punctorum apud quodlibet punctum in axe communi est positio consimilis. Ergo positio duorum punctorum que sunt in duobus axibus superficierum duorum visuum apud punctum axis communis qui est in medio concavitatis nervi communis in quo sunt coniuncte due linee exeuntes a centris duorum foraminum est positio valde consimilis et equalis. Et ambe forme que instituuntur in duobus punctis superficierum duorum visuum que sunt in duobus axibus, cum pervenerint ad concavitatem nervi communis, infigentur in puncto qui est in axe communi quod est in medio concavitatis nervi communis in quo linee sunt coniuncte, et efficientur una forma.

2.14 ◉ Moreover, the two points on the surfaces of the two eyes that lie on the two [visual] axes will be correspondingly situated with respect to the hollow of the common nerve, and these two points will also be correspondingly situated with respect to any point on the common axis. Thus, the situation of the two points on the surfaces of the two eyes that lie on the two [visual] axes is perfectly uniform and equal with respect to the point on the common axis at the middle of the hollow of the common nerve where the two lines passing [inward] from the centers of the two openings [in the eye sockets] intersect. So when they reach the hollow of the common nerve, both forms that are impressed on the two points where the two [visual] axes intersect the surfaces of the two eyes will be impressed on the point of the common axis that lies in the middle of the hollow of the common nerve, where the lines intersect, so they will produce a single form.

2.15 ◉ Et cum due forme que sunt in duobus punctis que sunt in duobus axibus superficierum duorum visuum figuntur in puncto quod est in axe communi quod est in medio concavitatis nervi communis, forme que sunt in punctis circumdantibus utrumque duorum punctorum que sunt in duobus axibus superficierum duorum visuum infiguntur in concavitate communis nervi in punctis circumdantibus punctum quod est in axe communi. Et positio quorumlibet duorum punctorum superficierum duorum visuum quorum positio apud duo puncta posita in medio in duobus axibus duorum visuum est positio consimilis in parte et in remotione apud eundem punctum concavitatis nervi communis est positio consimilis. Et puncta quorum positio apud ipsa est positio consimilis erunt declinantia a puncto quod est in axe communi quod est in loco coniunctionis linearum ex concavitate nervi communis in parte ad quam ambo puncta que sunt in superficiebus duorum visuum sunt declinantia, et remotio eorum ab ipso erit secundum remotiones eorum a duobus axibus. Et due forme que infiguntur in duobus punctis que sunt consimilis positionis apud superficies duorum visuum perveniunt ad illum eundum punctum concavitatis communis ipsius nervi, et superponentur sibi apud illum punctum, et efficientur una forma; et positio uniuscuiusque punctorum superficiei visi que sunt in circuitu puncti quod est in axe communi apud duos axes duorum visuum est positio consimilis. Ergo forma cuiuslibet puncti eorum infigetur in duobus visibus in duobus locis consimilis positionis in respectu duorum punctorum que sunt in duobus axibus superficierum duorum visuum. Due igitur forme visi in quo coniuncti sunt tres axes infiguntur in duobus mediis duarum superficierum duorum visuum, et due forme puncti in quo sunt coniuncti tres axes infigentur in duobus punctis que sunt in duobus axibus superficierum duorum visuum, et quilibet punctus duarum formarum infigetur in duobus locis consimilis positionis de duobus visibus. Deinde due forme vise pervenient ad concavitatem communis nervi, et pervenient due forme que sunt in puncto quod est in duobus axibus ad punctum quod est in communi axe, et efficientur una forma. Et quelibet due forme que sunt in duobus punctis consimilis positionis a duobus visibus pervenient ad idem punctum punctorum circumdantium punctum qui est in axe communi, et sic due forme totius visi superponentur sibi et efficientur una forma, et sic visum comprehendetur unum.

2.15 ◉ Furthermore, when the two forms at the two points where the two [visual] axes intersect the surfaces of the two eyes are impressed on the point of the common axis that lies in the middle of the common nerve, the forms that are [impressed] on points surrounding both of the points where the two [visual] axes intersect the surfaces of the two eyes are impressed on points in the hollow of the common nerve that surround the point on the common axis. And any two points on the surfaces of the two eyes that are correspondingly situated with respect to the points in the middle of the surfaces of the two eyes where the two [visual] axes lie are also correspondingly situated in terms of direction and distance with respect to the same point in the hollow of the common nerve. And points that are correspondingly situated with respect to these points will lie on the same side of the point on the common axis where the lines intersect in the hollow of the common nerve as the two points on the surfaces of the two eyes, and their distance from that point will depend on their distance from the two [visual] axes. So the two forms impressed on the two points that are correspondingly situated with respect to the surfaces of the two eyes reach to that same point in the hollow of the common nerve, and they will be superimposed at that point so as to produce a single form; and every one of the points on the surface of the visible object that are in the vicinity of the point on the common axis is correspondingly situated with respect to the axes of the two eyes.⁑ Thus, the form of any of those points will be impressed on both eyes at two locations that are correspondingly situated with respect to the two points where the two [visual] axes intersect the surfaces of the two eyes. Accordingly, the two forms of the visible object upon which the three axes intersect are impressed on the middle of the surfaces of the two eyes, and the two forms of the point where the three axes intersect will be impressed on the two points where the two [visual] axes intersect the surfaces of the two eyes, and any point on the two forms will be impressed on two correspondingly situated locations on both eyes. Afterward, the two forms that are seen will reach the hollow of the common nerve, and the two forms will reach from their [respective] points on the two [visual] axes to a point on the common axis and will produce a single form. Each of the two forms on the two points that are correspondingly situated on the two eyes will then reach the same point among the surrounding points on the common axis, and so the two forms of the whole visible object will be superimposed and will produce a single form, and sight will thus perceive it as single.

2.16 ◉ Secundum ergo hunc modum due forme que infigentur duobus visibus ab uno viso cuius positio in respectu duorum visuum est consimilis efficiuntur una forma, et sic sentiens comprehendit unum visum, licet due forme infigantur ab eo in duobus visibus.

2.16 ◉ In this way, then, the two forms of a single object that is uniformly situated with respect to both eyes will be impressed on the two eyes and produce a single form, and so the sensitive faculty perceives the visible object as single, even though two forms of it are impressed on the two eyes.

2.17 ◉ Et cum due forme que sunt in duobus punctis que sunt in duobus mediis superficierum duorum visuum que sunt in duobus axibus pervenerint ad punctum quod est in axe communi, tunc quelibet due forme infixe in duabus superficiebus duorum visuum infigentur in duobus punctis que sunt in duobus axibus, et pervenient semper ad illud idem punctum concavitatis nervi communis, quod est in communi axe. Nam duo puncta per que transeunt duo axes duorum visuum non mutantur, quoniam positio duorum axium apud duos visus semper est eadem positio non transmutabilis. Ergo punctus concavitatis communis nervi ad quem pervenient due forme que infiguntur in duobus punctis que sunt in duobus axibus superficierum duorum visuum semper est idem punctus, et est punctus qui est in communi axe in quo concurrunt due linee exeuntes a duobus centris foraminum duorum ossium extensorum in duobus mediis concavitatum duorum nervorum. Istud igitur punctum quod est in concavitate communis nervi quod est in communi axe vocetur centrum.

2.17 ◉ Moreover, when the two forms on the two points in the middle of the surfaces of both eyes where the two [visual] axes lie reach the point on the common axis, both of the forms impressed on the surfaces of the two eyes will be impressed on two points on the two [visual] axes, and they will always reach the same point in the hollow of the common nerve, that point lying on the common axis. For the two points at which the two [visual] axes pass through the[ir respective] eyes do not change, because the situation of the two axes is always the same and invariant with respect to the two eyes. Thus, the point in the hollow of the common nerve reached by the forms impressed on the two points on the surfaces of the two eyes where the two [visual] axes lie is invariably the same point, that point lying on the common axis where the two lines passing from the centers of the two openings in the two eye sockets through the middle of the hollows of the two nerves intersect. Accordingly, this point, which lies on the common axis in the hollow of the common nerve, will be referred to as the »center.«

2.18 ◉ Hoc igitur declarato, declaratum est quod forma cuiuslibet comprehensi quod comprehenditur ambobus visibus in cuius superficiei puncto concurrunt axes duorum visuum infigitur in duobus locis superficierum duorum visuum que sunt duo media superficierum duorum visuum. Deinde iste due forme perveniunt a duobus visibus ad concavitatem communis nervi ad eundem locum, et superponuntur sibi, et efficiuntur una forma. Et due forme puncti in quo concurrunt duo axes ex viso infigentur in duobus punctis que sunt in duobus axibus superficierum duorum visuum, et ibunt ab istis duobus punctis ad punctum centri concavitatis communis nervi, et indifferenter sive punctus in quo concurrunt duo axes fuerit in axe communi sive extra. Sed tamen cum visum fuerit in axe communi et duo axes concurrunt in puncto ipsius quod est in axe communi, tunc due forme istius puncti erunt magis consimiles. Remotiones enim istius puncti a duobus punctis in quibus figuntur due forme istius puncti superficierum duorum visuum (et sunt illa que sunt super axes) erunt equales, quoniam duo axes in hac dispositione erunt equales in longitudine. Et similiter quilibet punctus propinquus isti puncto cuius remotiones a duobus punctis in quibus infiguntur sue forme sunt equales quantum ad sensum, forme eius erunt magis consimiles quam due forme visi quod est extra communem axem, quapropter forma visi quod est in communi axe, cum fuerit fixa in concavitate communis nervi, erit magis verificata. Sed cum visum fuerit extra communem axem et remotio eius non fuerit maxima, tunc sue due forme que infiguntur in duobus visibus non maxime differunt, quapropter forme eius que infiguntur in concavitate nervi communis non erunt due.

2.18 ◉ This then having been shown, it has been demonstrated that, when the axes of the two eyes intersect on the surface of anything perceived by both eyes, the form of that object is impressed on two places at the very middle of the surfaces of two eyes. Afterward, these two forms reach from the two eyes to the same place in the hollow of the common nerve, where they are superimposed to produce a single form. Moreover, the two forms of the point where the two [visual] axes intersect on the visible object will be impressed on two points on the surfaces of both eyes where the two [visual] axes lie, and they will proceed from these two points to the point in the center of the hollow of the common nerve, and it is irrelevant whether the point at which the two [visual] axes intersect lies on the common axis or beyond it. Nonetheless, if the visible object lies on the common axis and the two [visual] axes intersect on the point where the common axis meets that object, then the two forms of that point will correspond as perfectly as possible.⁑ For the distance of that point from the two points on the surfaces of the eyes where the two forms of that point are impressed (and those two points lie on the [visual] axes) will be equal, since the two [visual] axes will be equal in length under these circumstances. Likewise, as far as sense is concerned, every point near that point lies an equal distance from the two points [on the surface of the eyes] where their forms are impressed, and their forms will be in closer correspondence than the two forms of a visible object that lies [farther] beyond the common axis, so, when it is impressed in the hollow of the common nerve, the form of a visible object that lies on the common axis will be as definite as possible. But if what is seen lies outside the common axis, but not too far away, then the two forms of it that are impressed in the two eyes do not differ by much, so the forms of it that are impressed in the hollow of the common nerve will not be doubled.

2.19 ◉ Cum autem visum fuerit extra communem axem et maxime fuerit remotum ab ipso, et cum hoc axes duorum visuum concurrunt in aliquo puncto ipsius, tunc forma eius infigetur in concavitate communis nervi una forma, et forma puncti eius in quo duo axes concurrunt infigetur in puncto centri. Sed tamen forma eius non erit verificata sed dubitabilis. Forma igitur puncti visi in quo duo axes concurrunt infigetur in omnibus dispositionibus in puncto centri concavitatis communis nervi, sive punctus concursus fuerit in communi axe, sive extra illum. Quod autem remanet de forma visi infigetur in circuitu puncti centri. Si autem visum fuerit minimi corporis et propinquorum dyametrorum et fuerit in communi axe vel prope, tunc forma eius infigetur in concavitate communis nervi una forma; et cum hoc est verificata, et positio cuiuslibet puncti eius apud duos visus est positio consimilis, ut prius declaravimus. Si vero visum fuerit magni corporis et remotorum dyametrorum, et cum hoc fuerit in communi axe, tunc forma illius partis que est apud locum coniunctionis duorum axium que circumdat punctum coniunctionis infigetur in communi nervo una forma, et verificata. Et forma residuarum partium infigetur continua cum forma istius partis, quapropter forma totius visi figetur una in omnibus dispositionibus; sed forma extremorum et illorum que remota sunt a puncto concursus erit non certificata, quoniam non omnes puncti remoti a puncto concursus figentur sue forme in duobus punctis consimilis positionis in respectu amborum visuum in fine consimilitudinis. Sed forma cuiuslibet puncti remoti a puncto concursus figetur in duobus punctis amborum visuum quorum positio apud duos visus est positio consimilis in parte, et forte consimilis in remotione a duobus axibus et forte non consimilis in remotione a duobus axibus. Forme autem eorum quorum remotio non est consimilis figentur in concavitate communis nervi in duobus punctis obliquis a centro in una parte, sed erunt due; et si visum fuerit unius coloris, tunc illud fere nichil operabitur in ipsum propter consimilitudinem coloris et ydemptitatem forme. Si autem visum habuerit diversos colores, aut fuerit in eo lineatio, aut pictura, aut subtiles intentiones, tunc illud operatur in ipsum, qua propter forma extremorum erit dubitabilis, non certificata.

2.19 ◉ If what is seen lies beyond the common axis at a considerable distance from it, but the axes of both eyes intersect at some point on it, then its form will be impressed singly in the hollow of the common nerve, and the form of its point where the two [visual] axes intersect will be impressed in the central point. Nevertheless, its form will be indefinite rather than definite. Thus, under all conditions, the form of the point on the visible object where the two [visual] axes intersect will be impressed in the point at the center of the hollow of the common nerve, whether the intersection-point lies on the common axis, or whether it lies beyond it. The rest of the form of the visible object, for its part, will be impressed around the central point. Moreover, if what is seen is quite small and of approximately equal cross-sections, and if it lies on or near the common axis, then its form will be impressed in the hollow of the common nerve as a single form; it will also be definite, and each of its points is correspondingly situated with respect to the two eyes, as we explained before. If, however, what is seen is large and has long cross-sections, but if it also lies on the common axis, then the form of that part of it at the spot that includes the point where the two [visual] axes intersect and the surrounding points will be impressed in the common nerve as a single, definite form. The form of the remaining parts [of the object] will be impressed to form a continuum with the form of this part, so the form of the entire visible object will be impressed singly under all circumstances; but the form of its extremities and of those parts that lie far away from the point of intersection will not be definite, for not every point lying far from the point of intersection will have its form impressed on two points whose situations correspond very well with respect to both eyes. Rather, the form of every point that lies far from the point of intersection will be impressed on two points of the two eyes that correspond in direction with respect to those eyes, but they may or may not lie at corresponding distances from the two [visual] axes. The forms of points that do not lie at corresponding distances will be impressed in the hollow of the common nerve at two points lying on the same side of the center, but they will be double; and if the visible object is of one color, then the effect of doubling will hardly be noticed because of the correspondence in color and the sameness of the form. If, however, what is seen is multicolored, or if there is some design, or depiction, or [if there are] subtle features in it, then the effect of doubling will be noticeable, so the form of its extremities will be indefinite rather than definite.⁑

2.20 ◉ Et cum visum fuerit magni corporis et remotorum dyametrorum, et axes amborum visuum fuerint fixi in aliquo puncto eius et immobiles, tunc forma eius apparet una, et locus concursus eius et illud quod ei vicinatur erunt certificata et indubitabilia. Extrema autem et illa que eis vicinantur erunt non certificata propter duas causas: quarum una est quia extrema comprehenduntur per radios remotos ab axe, quapropter non bene erunt manifesta; secunda autem est quia non forma cuiuslibet puncti eius constituitur in concavitate communis nervi in uno puncto, sed quedam sunt quorum forma constituitur in duobus punctis non in uno. Cum igitur duo axes fuerint moti super omnes partes huius visi, tunc verificabitur forma eius. Si autem visum fuerit extra axem communem et remotum ab ipso, tunc forma eius non erit certificata, positio enim cuiuslibet puncti illius apud ambos visus non est positio consimilis propter inequalitatem remotionum puncti huius visi a duobus punctis superficierum duorum visuum in quibus instituuntur due forme eius et a duobus axibus. Cum igitur ambo visus obliquabuntur ad huiusmodi visum adeo quod axis communis veniat ad istud visum aut prope, tunc certificabitur forma eius.

2.20 ◉ Now if what is seen is large and has long cross-sections, and if the axes of both eyes are focused on one of its points and remain fixed, then its form appears single, and the point of intersection, as well as whatever surrounds that point, will be determinate and definite. Its extremities, though, and the points near its extremities will not appear definite for two reasons: first, because the extremities are perceived by rays lying far from the [common] axis, so [what is seen along those rays] will not be clear, and second, because not every one of those points has its form impressed at a single point in the hollow of the common nerve; instead, some of them have their form impressed at two points rather than one. Therefore, [only] when the two [visual] axes are moved over all the parts of such a visible object will its form be defined. But if what is seen lies beyond and at a considerable distance from the common axis, then its form will not be determinate, for none of its points is correspondingly situated with respect to the two eyes because of the unequal distance that any point on such a visible object lies from the two points on the surfaces of the two eyes where the two forms of that point are impressed as well as from the two [visual] axes. Accordingly, [only] when both eyes are inclined toward such a visible object so that the common axis ends up on or near that visible object will its form be determinate.

2.21 ◉ Et similiter cum ambo visus comprehenderint multa visa in simul et axes amborum visuum simul concurrerint in aliquod unum visorum illorum et fixi fuerint in illo, residua autem visa fuerint extra duos axes, et visum in quo concurrentes sunt duo axes fuerit minimi corporis, tunc forma visi in quo concurrentes sunt duo axes in concavitate nervi communis erit una forma et certificata. Et si visum fuerit super axem communem, tunc forma eius erit magis certificata quam forma visi que est extra axem communem. Et si in ipso sunt concurrentes duo axes, visa autem que comprehenduntur a visu in illo statu que sunt propinqua viso in quo duo axes sunt concurrentes—sed cum hoc fuerint minimi corporis—forma eius instituitur in concavitate communis nervi una in qua non erit dubitatio maxima, nam forma eius erit propinqua centro. Quod autem illorum visorum que comprehenduntur a visu in illo statu fuerit remotum a viso in quo sunt concurrentes duo axes forma eius instituetur in concavitate istius nervi dubitabilis. Et tunc aut erunt due forme et erunt se adinvicem penetrantes, quia sunt in una parte, quapropter inequalitas que est inter suas positiones in remotione non erit maxima, unde due forme erunt se penetrantes, aut forma quarumdam partium erit duplex, et forma quarumdam erit una. Et sic forma huiusmodi visibilium erit dubitabilis in omnibus dispositionibus propter diversitatem positionis radiorum exeuntium ad illud et quia radii exeuntes ad illud erunt remoti a duobus axibus. Forma autem obliqui visi a duobus axibus remoti a loco concursus duorum axium erit non certificata, dum fuerit remota a concursu duorum axium. Cum autem duo axes fuerint remoti et concurrentes in ipso, tunc verificabitur forma eius.

2.21 ◉ Likewise, when both eyes perceive several visible objects at once, and when the axes of both eyes intersect on one of those visible objects and remain focused on it so that the rest of the visible objects lie outside the two axes, and when the visible object upon which the two [visual] axes intersect is quite small, the form of the visible object upon which the two [visual] axes intersect, [when it is impressed] in the hollow of the common nerve, will be single and determinate. And if the visible object lies upon the common axis, then its form will be more determinate than the form of a visible object that lies outside the common axis. Finally, if the two axes also intersect on that same visible object, then, in this case, if any of the objects lying near the object upon which the two [visual] axes intersect is perceived by sight—assuming that [such neighboring] objects are quite small—its form is impressed in the hollow of the common nerve as a single form that will not be at all indefinite, for its form will lie near the center. On the other hand, in that same situation, when any of the visible objects that lie far from the visible object on which the two [visual] axes intersect is perceived, the form of it that is impressed in the hollow of the common nerve will be indefinite. And so there will be two forms that overlap, because they lie on the same side and the difference between their relative situations in terms of distance will not be inordinate, so the two forms will overlap, or else the form of some of the object’s parts will be doubled while the form of others will be single.⁑ And so the form of such visible objects will be indefinite under all circumstances because of the difference in relative situation among the rays extending to it and because the rays extending to it will lie far from the two [visual] axes. Moreover, the form of a visible object that lies to the side of the two [visual] axes and far from the intersection-point of the two [visual] axes will not be determinate as long as it lies far from the intersection-point of the two [visual] axes. When, however, the two [visual] axes are shifted to intersect upon that object, its form will be defined.

2.22 ◉ Cum axes duorum visuum concurrerint in aliquo viso, et cum hoc duo visus comprehenderint aliud visum propinquius duobus visibus in quo viso sunt concurrentes duo axes aut remotius, et fuerit cum hoc inter duos axes, tunc positio eius apud duos visus erit diversa in parte. Nam cum fuerit inter duos axes erit dextrum unius axis et sinistrum alterius, et radii exeuntes ad ipsum ab altero viso erunt dextri ab axe, et qui exeunt ad ipsum a reliquo viso erunt sinistri; et sic positio eius apud duos visus erit positio diversa in parte. Et forma huiusmodi visorum instituitur in duobus visibus in duobus locis diverse positionis, et due forme eius que instituuntur in duobus visibus perveniunt ad duo loca diversa concavitatum communis nervi, et erunt a duobus lateribus centri, quapropter erunt due forme, et non superponentur sibi.

2.22 ◉ If the axes of the two eyes intersect on some visible object, and, in addition, the two eyes perceive another visible object nearer or farther away from the two eyes than the visible object on which the two [visual] axes intersect, and if that object falls between the two axes, then it will [appear to] lie on opposite sides with respect to the two eyes. For since it lies between the two [visual] axes, it will lie to the right of one axis and to the left of the other, and the rays extending to it from the one eye will lie to the right of the [visual] axis, whereas the rays extending to it from the other eye will lie to the left [of the visual axis]; on that account it will [appear to] lie on opposite sides with respect to the two eyes.⁑ So the form of such visible objects is impressed on the two eyes at two spots that are not correspondingly situated, and the two forms of it that are impressed on the two eyes reach two different locations in the hollow of the common nerve, and the [forms] will lie on both sides of the center, so there will be two forms, and they will not be superimposed upon each other.

2.23 ◉ Et similiter cum fuerit visum in altero axe et extra reliquum forma eius instituetur in concavitate communis nervi in duobus locis, una scilicet in centro et alia obliqua a centro, et non superponentur sibi.

2.23 ◉ Likewise, if the visible object lies on one [visual] axis but outside the other, its form will be impressed in two locations in the hollow of the common nerve, i.e., one in the center and the other to the side of the center, and those forms will not be superimposed.⁑

2.24 ◉ Secundum igitur hos modos instituetur forma visibilium in duobus visibus et in concavitate communis nervi.

2.24 ◉ These, then, are the ways in which the form[s] of visible objects will be impressed on both eyes as well as in the hollow of the common nerve.

2.25 ◉ Omnia autem ea que diximus sic possunt experiri experimento cum quo veniet certificatio.

2.25 ◉ Moreover, everything we have discussed can be tested by experiment so we will attain certainty about it.

2.26 ◉ Accipiatur tabula lenis ligni cuius longitudo sit unius cubiti et cuius latitudo sit quattuor digitorum, et sit bene plana, et equalis, et lenis. Et sint fines sue longitudinis equidistantes et sue latitudines equidistantes, et sint in ipsa duo dyametri se secantes a quorum loco sectionis extrahatur linea recta equidistans duobus finibus longitudinis. Et extrahatur a loco sectionis etiam linea recta perpendicularis super lineam primam positam in medio, et intingantur iste linee tincturis lucidis diversorum colorum ut bene appareant, sed tamen duo dyametri sint unius coloris. Et concavetur in medio latitudinis tabule apud extremum linee recte posite in medio, et inter duos dyametros, concavitate rotunda, et cum hoc quasi piramidali tantum quantum poterit intrare cornu nasi quando tabula superponetur illi quousque tangent duo anguli tabule fere duo media superficierum duorum visuum, tamen non tangent.

2.26 ◉ Take a smooth wooden plaque that is one cubit long and four digits wide, and let it be perfectly flat, even, and smooth.⁑ Let the edges along its length, as well as those along its width, be parallel, and let there be two diagonals intersecting one another at a point through which a straight line is drawn parallel to the edges along the length. Then, through that [same] intersection-point let a straight line be drawn perpendicular to the first line, passing through [the plaque’s] middle, and let [each of] these [two perpendicular] lines be painted a different color, both colors being bright so that they are readily visible, but let the two diagonals be painted the same color. Then, in the middle of the bottom edge of the plaque, between the [endpoints of the] two diagonals, let a rounded notch be cut, but one that narrows inward so that, when the plaque is brought up to it, the bridge of the nose can fit into it in such a way that the two corners of the plaque almost touch, but do not actually touch, the two midpoints of the surfaces of the two eyes.

2.27 ◉ Sit igitur tabula in figura ABCD et dyametri AD [et] BC, et punctus sectionis sit Q; et linea extensa in medio longitudinis sit HQZ, et linea secans hanc lineam secundum angulos rectos sit KQT. Et concavitas que est in medio latitudinis tabule sit illa que continetur a linea MHN.

2.27 ◉ Accordingly, let ABCD in figure [6.72⁑.⁑] represent the plaque, let AD and BC be the diagonals, and let the intersection-point be Q; let line HQZ be the line passing longitudinally through the middle of the plaque, and let line KQT be the line that intersects this line at right angles. Finally, let the notch in the middle of the bottom edge of the plaque be circumscribed by [curved] line MHN.

2.28 ◉ Hac igitur tabula facta hoc modo, accipiatur cera alba ex qua fiant tria individua parva columpnata, et intingantur diversis coloribus; et erigatur unum individuorum in medio tabule in puncto Q, et applicetur tabule adeo quod non possit auferri a suo loco, et sit stans super tabulam statu equali. Duo autem individua reliqua erigantur super extrema linee late in duobus punctis K, T, et sic tria individua erunt in una verticatione. Et hoc quidem facto, elevet experimentator hanc tabulam, et superponat concavitatem que est in medio longitudinis cornu nasi et inter oculos adeo quod cornu nasi intret concavitatem et applicetur cum tabula, et fient duo anguli tabule apud duo media superficierum duorum visuum et propinqui ut tangant ipsa fere. Deinde experimentator debet inspicere individuum propositum in medio tabule et pupillam super ipsum tenere fortiter. Cum igitur experimentator inspexerit individuum positum in medio hoc modo, axes duorum visuum concurrent in hoc individuo et superponentur duobus dyametris aut erunt equidistantes illis. Et erit axis communis, quem prius determinavimus, superpositus linee extense in medio longitudinis tabule que est linea HZ.

2.28 ◉ With the plaque thus constructed, take some white wax and make three small, cylindrical pegs out of it, and paint them different colors; then stand one of the pegs on the center of the plaque at point Q, fix it to the plaque so that it cannot be displaced, and stand it straight up on the plaque. Now stand the other two pegs at endpoints K and T of the line [passing through the middle of the plaque] along the width so that the three pegs will lie on a single line. When this is accomplished, the experimenter should lift the plaque and place the notch in the middle of the bottom edge against the bridge of his nose between the eyes so that the bridge of the nose will lie snug against the plaque, while the corners of the plaque will be set at the two midpoints of the surfaces of the eyes and nearly touching them. Then the experimenter should look at the peg placed in the center of the plaque and focus his gaze intensely upon it. Accordingly, when the experimenter stares in this way at the peg placed at the center [of the plaque], the axes of the two eyes will intersect on that peg and will either coincide with, or be parallel to, the two diagonals. Also, the common axis, which we defined earlier,⁑ will coincide with line HZ drawn lengthwise through the middle of the plaque.

2.29 ◉ Deinde experimentator in hac dispositione debet intueri omnia que sunt in superficie tabule. Tunc autem inveniet unumquodque trium individuorum que sunt in punctis K, Q, T unum, et inveniet lineam KQT etiam unam. Linea autem HZ extensa in longitudine tabule invenietur due se secantes apud individuum positum in medio. Et similiter duo dyametri etiam, cum experimentator intuetur eos in hoc statu, invenientur quattuor, utrumque eorum scilicet duo.

2.29 ◉ Then, maintaining this situation, the experimenter should look at everything⁑ on the surface of the plaque. He will then find that each of the three pegs at points K, Q, and T [appears] single, and he will also find that line KQT [appears] single. Line HZ, however, which is drawn lengthwise through the middle of the table, will appear double, [its two images] intersecting at the peg placed in the center [of the plaque]. Likewise, in the same situation, when the experimenter looks at the two diagonals, they will appear quadruple, that is, each of them [will appear] double.⁑

2.30 ◉ Deinde experimentator debet ponere pupillam circa alterum individuorum que sunt in duobus punctis K, T ut duo axes concurrant in individuo posito in extremo. Deinde intueatur etiam in hac dispositione, et inveniet trium individuorum unumquodque unum et lineam positam in latitudine etiam unam, et inveniet lineam mediam extensam in longitudine tabule duas et utrumque dyametrorum duos.

2.30 ◉ Then the experimenter should direct his gaze toward either of the pegs at the two points K and T so that the two [visual] axes intersect on [either] one of the pegs placed at the endpoint. Then, in this situation, he should again look around, and he will find that each of the three pegs [appears] single, as well as the line passing [through the middle of the plaque] along the width, but he will find that the line passing lengthwise through the middle [of the plaque appears] double, as does each of the two diagonals.

2.31 ◉ Cum igitur experimentator comprehenderit has lineas et individua posita super tabulam, et auferet duo individua que sunt in duobus punctis K, T, et ponat ea super lineam HZ extensam in longitudine, unum scilicet in puncto L, quod sequitur visum, et reliquum in puncto S, quod est ultra individuum positum in medio. Deinde revertat tabulam ad suam primam positionem et dirigat pupillam ad individuum positum in medio. Tunc autem inveniet duo individua quattuor et obliqua a medio, duo scilicet in dextro et duo in sinistro, et inveniet ea super duas lineas que in rei veritate sunt una linea in medio, sed apparent due; et inveniet quelibet duorum quattuor super alteram duarum linearum.

2.31 ◉ Thus, when the experimenter has perceived these lines and the pegs that are placed on the table, he should remove the two pegs at the two points K and T and place them upon line HZ that extends lengthwise [through the middle of the plaque], one of them at point L, which is near the eyes, and the other at point S, which lies beyond the peg placed in the center [of the plaque]. Then he should reposition the plaque as before [against his nose] and direct his gaze at the peg placed in the center [of the plaque] . He will then find that the two pegs [appear as] four and [lie] to the sides of the central peg, i.e., two to the right and two to the left, and he will find that [they appear] to lie on two lines which are, in actuality, the one line [HZ] in the middle [of the plaque] which nonetheless appears double; he will also find that each of the pairs [of pegs appears to lie] upon one of those two lines.⁑

2.32 ◉ Et similiter si abstulerit duo individua ab hac linea et posuerit ea super alterum duorum dyametrorum, unum in parte visus et reliquum ultra individuum positum in medio, inveniet illa quattuor. Nam uterque dyametrorum apparebit duo, quapropter apparebunt super utramque linearum que sunt unius dyametri in rei veritate duo individua unum in parte visus et aliud ultra individuum positum in medio. Et similiter si posuerit duo individua super ambos dyametros, utrumque super alterum dyametrum, et posuerit ea in parte visus, inveniet illa quattuor, duo propinqua et duo remota.

2.32 ◉ Likewise, if he removes the two pegs from that line and places them upon either of the two diagonals, one on the side of the eye and the other beyond the peg that is placed at the center [of the plaque], he will find that they [appear] quadruple. For each of the diagonals will appear double, so upon each of the two [diagonal] lines that are actually [produced from] one [original] diagonal two pegs will appear, one on the side of the eyes and the other beyond the peg placed in the center [of the plaque].⁑ Likewise, if the two pegs are placed on the two diagonals, one upon each, and if they are [both] placed on the side of the eyes, the experimenter will find that they [appear] quadruple, two near [each other] and two far away [from each other].⁑

2.33 ◉ Deinde experimentator debet auferre duo individua a tabula et ponere alterum eorum super marginem tabule ultra punctum K et prope ipsum valde, ut super punctum R, et revertatur tabula ad suam primam positionem, et dirigat pupillam ad individuum positum in medio. Tunc quidem inveniet individuum positum in puncto R unum. Deinde auferat individuum a puncto R, et ponat ipsum in margine tabule etiam ultra punctum K super punctum remotum a puncto K, ut super punctum F, et dirigat pupillam ad individuum positum in medio, quoniam tunc inveniet individuum positum apud punctum F duo.

2.33 ◉ Then the experimenter should remove the two pegs from the plaque and place one of them at the edge of the plaque beyond point K but quite near it, e.g., at point R, and he should reposition the plaque as before [against his nose] and direct his gaze at the peg that is placed in the center [of the plaque]. In that case, he will definitely find that the peg placed at R [appears] single. Then he should remove the peg from point R and place it at the edge of the plaque beyond point K at a point far from point K, e.g., at point F, and he should direct his gaze at the peg placed in the center [of the plaque], for then he will find that the peg placed at point F [appears] double.

2.34 ◉ Experimentator autem inveniet omnia que diximus cum direxerit pupillam ad individuum positum in medio, aut ad individuum positum in linea recta in latitudine, aut ad punctum illius linee, quodcumque punctum sit, et dum duo axes sunt concurrentes in individuo posito in medio aut in aliquo puncto linee posite in latitudine. Si ergo experimentator direxerit pupillam in illo statu ad individuum positum extra lineam positam in latitudine aut ad punctum positum extra illam lineam, et concurrerint duo axes in aliquo puncto extra lineam positam in latitudine, tunc individuum positum in medio videbitur duo. Et si reliqua individua fuerint in duobus punctis K, T, tunc uterque eorum etiam videbitur duo. Deinde cum experimentator direxerit pupillam ad medium individuum aut ad aliquem locum linee posite in latitudine, statim dispositio revertetur, ut in prima figura.

2.34 ◉ Now the experimenter will encounter everything we have described when he directs his gaze at the peg placed in the center [of the plaque], or at a peg placed on the straight line [passing through the middle of the plaque] along the width, or at a point on that line, whatever point it may be, as long as the two [visual] axes intersect at the peg placed in the center [of the plaque] or at some point on the line [passing through the middle of the plaque] along the width. Under these circumstances, then, if the experimenter directs his gaze at the peg that is placed beyond the line [passing through the middle of the plaque] along the width or at a point located beyond that line, and if the two [visual] axes intersect at some point beyond the line passing through the middle, then the peg that is placed in the center [of the plaque] will appear doubled. Meanwhile, if the remaining pegs lie at the two points K and T, then each of them will also appear double. Then, if the experimenter directs his gaze to the central peg or to some place on the line [passing through the middle of the plaque] along the width, everything will revert right back to the original situation, as represented in the first figure.

2.35 ◉ Igitur a puncto B extrahantur linee BK, BR, BF. Linea igitur KB est maior linea BT, et linea KQ est equalis QT. Sic angulus TBQ est maior angulo QBK.

2.35 ◉ Accordingly, let lines BK, BR, and BF [in figure ⁑.⁑] be drawn from point B. Line KB is therefore longer than line BT, while line KQ is equal to [line] QT. So angle TBQ is greater than angle QBK.

2.36 ◉ Et angulus TBQ est equalis angulo KAQ. Ergo angulus KAQ est maior angulo KBQ.

2.36 ◉ But angle TBQ is equal to angle KAQ. Thus, angle KAQ is greater than angle KBQ.

2.37 ◉ Ergo remotio linee AK ab axe AQ est maior quam remotio linee BK ab axe BQ. Sed differentia inter has duas remotiones est modica, differentia enim inter duos angulos KAQ, KBQ est parva.

2.37 ◉ Therefore, line AK lies farther from axis AQ than line BK does from axis BQ. But the difference in the distance between these two is minimal because the difference between the two angles KAQ and KBQ is slight.

2.38 ◉ Et individuum quod est apud punctum K semper videtur ambobus visibus unum quando duo axes fuerint concurrentes in individuo quod est apud punctum Q. Et due linee AK, BK sunt equidistantes duobus radiis exeuntibus ad individuum quod est apud punctum K, dum duo axes concurrerint in individuum quod est apud punctum Q.

2.38 ◉ Now the peg at point K always appears single to the two eyes when the two [visual] axes intersect at the peg that lies at point Q. Moreover, the two lines AK and BK are parallel to the two rays extending to the peg at point K as long as the two axes intersect at the peg that lies at point Q.⁑

2.39 ◉ Et similiter dispositio individui quod est apud punctum R scitur, quoniam radii exeuntes ad ipsum erunt in verticatione duarum linearum AR, BR, et videbitur unum.

2.39 ◉ So, too, the situation of the peg at point R is known, for the rays extending to it will line up with the two lines AR and BR, so it will appear single.

2.40 ◉ Et duo anguli RAQ, RBQ non maxime differunt, et angulus KBR non habet sensibilem quantitatem quando punctus R fuerit valde propinquus puncto K.

2.40 ◉ Moreover, the two angles RAQ and RBQ do not differ much in size, whereas angle KBR has no perceptible size when point R lies very near point K.

2.41 ◉ Declarabitur igitur ex hac dispositione quod visum cuius positio apud duos axes est una positio in parte et remotio radiorum exeuntium ad ipsum a duobus visibus non est maxime differentie, illud visum videbitur duobus visibus unum.

2.41 ◉ From this example it will be obvious that, when a visible object lies on the same side of the two axes, and the rays extending to that object from the two eyes do not differ very much in their distance [from the visual axes], that visible object will appear single to the two eyes.

2.42 ◉ Anguli autem FAQ, FBQ sunt diversi diversitate maxima, et individuum quod est apud punctum F videbitur duo quando duo axes concurrerint in individuo quod est apud punctum Q.

2.42 ◉ On the other hand, angles FAQ and FBQ differ considerably in size, so the peg at point F will appear double when the two [visual] axes intersect at the peg that is at point Q.

2.43 ◉ Declarabitur igitur ex hac dispositione quod visum ad quod positio radiorum exeuntium a duobus visibus est diversa in remotione a duobus axibus maxima diversitate videtur duo, etsi positio eius in respectu duorum axium est eadem positio in parte.

2.43 ◉ From this example it will therefore be evident that, if the rays extending from the two eyes to a visible object lie at significantly different distances from the two [visual] axes, the object appears double, even if it lies on the same side of those axes.

2.44 ◉ Positio autem linee HQZ in respectu axium duorum visuum est positio diversa in parte, radii etenim exeuntes ad partem HQ a dextro visu sunt sinistri ab axe AQ, radii autem exeuntes ad hanc partem a sinistro visu sunt dextri ab axe BQ. Radii vero exeuntes ad partem QZ a dextro visu sunt dextri ab axe AQ, et radii exeuntes ad ipsam a sinistro visu sunt sinistri ab axe BQ, et radii qui exeunt ad ipsam sunt diverse positionis in parte. Et omnis punctus istius linee remotio duorum radiorum exeuntium ad ipsum a duobus visibus a duobus axibus est equalis; et ista linea et omnia posita super ipsam preter individuum positum in medio semper videntur duo cum duo axes concurrerint in individuo posito in medio.

2.44 ◉ Line HQZ, however, does not lie on the same side of the two [visual] axes, for the rays extending toward [segment] HQ from the right eye lie to the left of [visual] axis AQ, whereas the rays extending toward it from the left eye lie to the right of [visual] axis BQ. On the other hand, the rays extending toward [segment] QZ from the right eye lie to the right of axis AQ, whereas the rays extending to it from the left eye lie to the left of axis BQ, so the rays extending to it lie on opposite sides [from those extending to HQ]. But the distance between the two rays extending to each point on this line from the two eyes and the two [visual] axes is equal; yet this line, and everything that lies on it, except for the peg that is placed in the center, invariably appears double if the two [visual] axes intersect at the peg placed in the center.⁑

2.45 ◉ Declaratum est igitur ex hac dispositione quod visum cuius positio in respectu duorum axium est diversa in parte semper videtur duo, etsi remotiones radiorum exeuntium ad ipsum a duobus visibus a duobus axibus sunt equales. Remotiones enim quorumlibet duorum radiorum exeuntium a duobus visibus ad aliquod punctum eius erunt in duabus partibus diversis, quapropter due forme cuiuslibet puncti eius instituentur in duobus punctis concavitatis communis nervi a duobus lateribus centri.

2.45 ◉ On this basis it has therefore been shown that a visible object that lies on different sides of the two [visual] axes always appears double, even if the rays extending to it from the two eyes lie at equal distances from the two [visual] axes. For any of the two rays extending from the two eyes to any point on the object will lie on opposite sides [of the eyes], so the two forms of each of its points will be impressed on two points on both sides of the centerpoint in the hollow of the common nerve.

2.46 ◉ Et similiter etiam est dispositio utriusque dyametrorum, scilicet quoniam radii exeuntes ad utrumlibet eorum a visu sequente ipsum erunt a medio visus, et propinqui axi, et sub axe, et supra axem; et radii exeuntes ad ipsum a reliquo visu erunt declinantes a reliquo axe. Qui vero a dextro visu ad sinistrum dyametrum erunt sinistri ab axe; qui autem exeunt a sinistro visu ad dextrum erunt dextri ab axe. Forme quidem dyametrorum istorum et omnia etiam posita super ipsos videntur duo preter individuum positum in medio quando duo axes concurrerint in medio individuo.

2.46 ◉ The same thing also holds for the two diagonals, i.e., the rays extending to either of them from the eye will follow in order from the center of the eye, being near the [visual] axis, below the [visual] axis, or above the [visual] axis; and the rays extending to the diagonal from the other eye will be inclined to the other axis. The rays extending from the right eye to the left-hand diagonal will lie to the left of the [visual] axis, whereas the rays extending from the left eye to the right-hand diagonal will lie to the right of the [visual] axis.⁑ The forms of these diagonals, and everything else that lies upon them, appear double except for the peg in the center [of the plaque] when the two [visual] axes intersect on that central peg.

2.47 ◉ Declarabitur igitur ex hoc quod visum quod in respectu alterius visus est oppositum medio eius, in respectu autem reliqui est obliquum a medio, videtur duo. Nam forma puncti que instituitur in medio alterius visus venit ad centrum. Forma autem puncti obliqui a medio reliqui visus veniet ad punctum aliud a centro et obliquum a centro secundum obliquationem puncti superficiei visus.

2.47 ◉ From this it will be clear that a visible object that lies directly opposite the middle of one eye but lies to the side of the middle of the other appears double. For the form of the point that is impressed in the middle of the one eye reaches [straight through to] the center [of the common nerve]. But the form of a point to the side of the middle of the other eye will reach some point other than the center [of the common nerve], and its displacement from the center will depend upon its displacement on the surface of the eye.

2.48 ◉ Ex hac igitur experimentatione et expositione declaratur bene quod visum in quo currunt duo axes semper videtur unum; et quod unumquodque visorum etiam in quibus concurrunt radii qui sunt consimilis positionis in parte inter quos non est maxima diversitas in remotione a duobus axibus videtur etiam unum; et quod visum in quo concurrunt radii consimilis positionis in parte et diverse positionis in remotione a duobus axibus maxima diversitate videtur duo; et quod visum quod comprehenditur per radios diverse positionis in parte videtur duo, etsi remotiones radiorum exeuntium ad ipsum a duobus axibus sunt equales; et quod omnia ista erunt sic dum duo axes concurrerint in uno viso.

2.48 ◉ Thus, on the basis of this experiment and its explanation it is quite evident that if the two [visual] axes intersect on an object, it always appears single; and [it is evident] that, if the rays that converge on an object lie on the same side [of their respective axes], and if their distance from the two [visual] axes does not differ by much, the object appears single; and [it is evident] that, if the rays that converge on an object lie on the same side but at substantially different distances from the two [visual] axes, the object appears double; and [it is evident] that, if the rays that apprehend an object lie on different sides [of the visual axes], the object appears double, even if the rays extending to it are equidistant from the two [visual] axes; and [it is obvious] that all of this will obtain as long as the two [visual] axes intersect on a single visible object.

2.49 ◉ Et omnia visa assueta sunt opposita ambobus visibus, et ambo visus inspiciunt ad quodlibet eorum. Ergo duo axes duorum visuum semper concurrunt in eis, et positio radiorum residuorum qui concurrunt communi puncto eorum est positio consimilis in parte, et non differunt in remotione a duobus axibus maxima differentia. Et ideo quodlibet visibilium assuetorum visorum videtur ambobus visibus unum, et nullum visibilium videtur duo nisi raro. Nullum enim visibilium videtur duo nisi cum positio eius in respectu amborum visuum fuerit diversa maxima diversitate, aut in parte, aut in remotione, aut in utraque; et positio unius visi apud duos visus non diversatur quidem maxima diversitate nisi raro.

2.49 ◉ All ordinary visible objects face both eyes, and both eyes look at any such object. Thus, the two axes of the two eyes always intersect on them, and the remaining rays that intersect at a common point on them lie on the same side [of their respective visual axes], and their distances from the two [visual] axes do not differ by much. As a result, any of the ordinary visible objects appears single to the two eyes, and none of them appears double except on rare occasions. For none of the [ordinary] visible objects appears double unless its situation with respect to both eyes is inordinately skewed in terms of direction or distance, or in terms of both; but it is only rarely that the situation of a given visible object with respect to the two eyes is inordinately skewed.

2.50 ◉ Causa igitur propter quam unumquodque visorum assuetorum videtur unum ambobus visibus declarata est ratione et experientia.

2.50 ◉ Thus, the reason that any of the ordinary visible objects appears single to both eyes has been shown through deduction and experiment.

2.51 ◉ Et etiam, cum experimentator abstulerit individuum quod est in medio tabule, et inspexerit punctum sectionis quod est in medio tabule, et intuetur tunc lineas scriptas in tabula, inveniet duos dyametros quattuor. Et inveniet cum hoc duos illorum quattuor propinquos sibi et duos a se remotos, et cum hoc omnes se secantes super punctum medium qui est punctus sectionis duorum dyametrorum qui est super axem communem. Et inveniet utrumque illorum remotorum magis remotum a medio quam sit in rei veritate. Deinde cum experimentator cooperierit alterum visum, videbit duos dyametros, et videbit spatium inter eos maius quam in rei veritate secundum suam piramidationem, quod autem est magis amplum de ipso est latitudo tabule. Et apparebit quod dyameter remotus a medio est dyameter qui sequitur visum coopertum.

2.51 ◉ Now, if the experimenter removes the peg at the center of the plaque and focuses on the point of intersection at the plaque’s center, and if he then looks at the lines that are drawn on the plaque, he will find that the two diagonals [appear to be] four. He will also find that two of the four diagonals [appear to lie] near each other, and two [appear to lie] far from one another, but still, all of them [appear to] intersect at the centerpoint, which is the point of intersection for the two diagonals and lies on the common axis. He will find, as well, that each of the [apparent] diagonals that lie far apart [from one another] lie farther from the middle than the actual diagonals do. Then, if the experimenter covers one eye, he will see two diagonals, and he will see that the separation between them [seems] larger than it really is according to their actual divergence, and this [divergence] is widest at the top edge of the plaque. Moreover, the diagonal that appears to lie far from the centerpoint will be the one in line with the eye that is covered.

2.52 ◉ Ex quo declaratur quod duo dyametri qui videntur propinqui cum visio fuerit in utroque visu sunt illi quorum uterque videtur visu sequenti et quod duo dyametri remoti sunt illi quorum uterque videtur visu obliquo. Propinquitas autem duorum quattuor est quia, cum duo axes concurrerint in individuo posito in medio, tunc uterque dyametrorum comprehendetur a visu sequenti per radios valde propinquos axi, quapropter forme eorum propter hoc erunt in concavitate communis nervi valde propinqui centro. Et erit punctus sectionis eorum in ipso centro, unde videntur propinqui sibi et medio. Remotio autem duorum quattuor est quia uterque dyametrorum comprehendetur etiam alio visu obliquo ab ipso, quapropter comprehenditur per radios remotos ab axe. Et alterum comprehenditur per radios dextros ab axe, et reliquum per radios sinistros ab axe alio, quapropter forme eorum instituentur in concavitate communis nervi remote. Infiguntur enim in duabus partibus contrariis in respectu centri, et cum hoc remotis a centro, unde duo dyametri habent duas formas propinquas sibi et duas formas remotas a se. Quare vero comprehenditur remotio utriusque remotorum a medio maior quam sua remotio vera est quia remotio que est inter duos dyametros comprehenditur ab utroque visu maior quam sit in rei veritate. Et hoc apparet quando experimentator cooperit alterum visum et inspexerit per reliquum. Quare vero, quando experimentator cooperit alterum visum et inspexerit per reliquum tantum, inveniet spatium inter duos dyametros magis amplum quam in rei veritate est, quia spatium quod est inter duos dyametros comprehenditur ab utroque visu valde propinquum visui, et omne quod est valde propinquum visui videtur maius quam sit in rei veritate. Et causa huius declarabitur post cum loquemur de deceptionibus visus.

2.52 ◉ From this is is evident that the two diagonals that appear [to lie] near [one another] when vision takes place through either eye are the ones that are seen in line with [their respective] eye, whereas the two diagonals that appear [to lie] far [from one another] are the ones that are seen by the eye that lies to their sides. Moreover, the reason two of the four [appear to lie] near [each other] is that, when the two axes intersect on the peg that is placed in the center [of the plaque], each of the diagonals will be perceived by the eye in line with it according to rays that are quite near the [visual] axis, so their forms will lie quite near the centerpoint in the hollow of the common nerve.⁑ But the intersection-point of those diagonals will be at the centerpoint itself, so they appear [to lie] close to one another as well as to the centerpoint. On the other hand, the reason two of the four [appear to lie] far [from one another] is that each of the diagonals will also be perceived by the alternate eye that lies to its side, so it is perceived by rays that lie far from the [visual] axis. Moreover, one of them is perceived by rays that lie to the right of the axis, whereas the other [is perceived] by rays to the left of the other axis, so their forms will be impressed at disparate locations in the hollow of the common nerve. For they are impressed on opposite sides of the centerpoint and far from it, as well, so the two diagonals have two forms [that appear to lie] near each other and two [that appear to lie] far from one another. Now the reason that each [of the diagonals that appear to lie] farther [from one another] appear to lie farther from the centerpoint than they actually do is that the distance between the two diagonals is perceived by each eye to be greater than it actually is. And this is made clear when the experimenter covers either eye and looks with the other. As a result, when the experimenter covers one eye and looks with the other, he will find that the separation between the two diagonals [appears] greater than it actually is, because the separation between the two diagonals is perceived by each eye from up close, and whatever is very close to the eye appears larger than it actually is. But we shall explain the reason for this later when we discuss visual illusions.⁑

2.53 ◉ Ex consideratione igitur dispositionum dyametrorum que sunt in tabula et individuorum positorum super eos non in medio, apparet quod omne visum positum super axem communem et comprehensum a visu per axem radialem comprehendetur in suo loco, sive comprehendatur uno visu et per unum axem axium duorum visuum, sive comprehendatur per duos visus et per ambos axes. Et declaratur quod omne visum comprehensum per unum visum et per axem radialem, quando visum non est super axem communem, comprehendetur in loco propinquiori communi axi quam suo loco vero. Et hoc etiam sequitur in eis que comprehenduntur per residuos radios preter axem. Quoniam, cum visus comprehenderit rem visam secundum quod est, et instituetur forma in concavitate communis nervi in uno loco et continua sibi invicem secundum continuationem rei vise, et punctus visi qui est super axem radialem cum non fuerit super axem communem, videatur in loco propinquiori communi axi quam suo loco vero, tunc puncta residua etiam videntur in loco propinquiori communi axi quam suo loco vero, quia sunt continuata cum parte que est apud extremum axis.

2.53 ◉ By thus examining the dispositions of the diagonals on the plaque, as well as of the pegs that are placed upon them apart from the center [of the plaque], one sees that every visible object that is placed on the common axis and that is perceived by sight along the visual axis will be perceived where it actually lies, whether it is perceived with one eye along one of the axes of the two eyes, or whether it is perceived by both eyes along both [visual] axes. And it is evident that, if it does not lie on the common axis, any visible object that is perceived by one eye along the visual axis will be perceived to lie closer to the common axis than it actually does. This is also the case for visible objects that are perceived by the rest of the rays beyond the axis. For, if sight perceives the visible object as it actually exists, and if its form is impressed at one spot in the hollow of the common nerve in continuous order [of parts] according to the continuous order [of parts] in the visible object itself, then, since the point that lies on the visual axis, assuming it does not lie on the common axis, appears nearer to the common axis than it actually is, the remaining points [on the object] also appear nearer the common axis than they really are, because they are continuous with the part at the endpoint of the [visual] axis.

2.54 ◉ Et si axes duorum visuum concurrent in aliquo viso extra axem communem, sequitur etiam ista dispositio, scilicet quoniam videtur in loco propinquiori communi axi quam suo loco vero. Sed ista positio raro accidit, cum enim illi axes duorum visuum concurrerint in aliquo viso, tunc in pluribus dispositionibus axis communis transibit per illud visum. Et nunquam axes duorum visuum concurrent in aliquo viso extra axem communem nisi per laborem aut per impedimentum cogens visum ad hoc, et hec dispositio non apparet in visis assuetis. Nam cum accidit hoc in aliquo viso, continget in omnibus visis continuis cum illo visu, unde positio visorum apud se invicem non transmutabitur propter hoc. Et cum positio illius visi in respectu visorum vicinantium non fuerit transmutata, tunc non apparebit transmutatio sui loci cum acciderit in visis assuetis. Quando ergo consideratur hec via predicta, declarabitur ex illa experientia quod hoc sequitur in omnibus visis in quibus concurrunt axes duorum visuum que sunt extra axem communem.

2.54 ◉ If the axes of the two eyes intersect on some visible object lying outside the common axis, the same thing follows, i.e., the object appears to lie nearer the common axis than it actually does. But this situation rarely occurs, for, when the axes of the two eyes intersect on some visible object, it is often the case that the common axis will pass through that visible object. Moreover, the axes of the two eyes will never intersect on a visible object that lies outside the common axis without effort or without some outside interference forcing the eyes into such a situation, but this situation does not show up in the case of ordinary visible objects. For when this occurs in the case of any visible object, it will happen for all the visible objects continuous with that one, so the situation of the visible objects among each other will not be changed on this account.⁑ But if the situation of that visible object does not change with respect to neighboring visible objects, then it will not appear to change when the change occurs among ordinary visible objects. Thus, when this is investigated according to the method described earlier, it will be clear from the experiment that this follows for all visible objects that lie outside the common axis when the axes of both eyes intersect on them.

2.55 ◉ Et etiam oportet experimentatorem accipere tres scrotulas pargameni parvas equales, et scribet in una verbum aliquod scriptura manifesta. Et in residuis scribet illam eandem partem, et in illa quantitate, et in illa figura, et ponat individuum unum in medio tabule, ut prius, et ponat alterum individuum super punctum K. Deinde applicet unam scrotulam cum individuo quod est in medio tabule, et aliam in puncto K, et servet se ut positio eius sit sicut positio prime scrotu le. Et ponat tabulam, ut prius fecit, et dirigat pupillam ad scrotulam que est in medio individuo, et intueatur illam. Tunc quidem comprehendet partem scriptam super illam certa comprehensione. Et comprehendet cum hoc in illa dispositione aliam scrotulam et partem scriptam in ea, sed non bene declaratam sicut est pars consimilis illi que est scripta in media scrotula, licet sint consimiles in figura, forma, et quantitate.

2.55 ◉ Now the experimenter should take three small strips of parchment of equal size, and he should write some clearly lettered word on one of them. On the rest he should write that same word [making it] the same size and shape, and he should place one of the [wax] pegs at the center of the plaque, as before, and he should place another at point K. Then he should fasten one of the strips to the peg at the center of the plaque and another to the peg at point K, and he should take care to keep it oriented the same way as the first strip. He should then position the plaque [against the bridge of his nose], as he did before, and he should direct his gaze to the strip attached to the central peg and focus on it. In that case, of course, he will have a clear perception of the word written on it. In this same situation, moreover, he will also see the other strip and the word written on it, but not as clearly as he does the identical word written on the middle strip, even though the words are identical in shape, form, and size.

2.56 ◉ Deinde in hac dispositione oportet experimentatorem accipere tertiam scrotulam manu sequenti punctum K, et ponat illam in verticatione duarum scrotularum que sunt in tabula et in rectitudine extensionis linee que est in latitudine tabule que est in superficie tabule quantum ad sensum, sed tamen sit remota a tabula. Et huiusmodi verticatio vocetur verticatio facialis. Et observet se experimentator ut positio tertie scrotule et positio partis que est in illa, quando ponit scrotulam, sit similis positioni duarum scrotularum que sunt in tabula. Et tunc figat ambos visus in scrotula posita in medio, et dirigat pupillam ad ipsam, et tunc quidem comprehendet tertiam scrotulam, si non fuerit multum remota a tabula, sed comprehendet formam partis que est in ea dubitabilem et non intelligibilem. Et non inveniet illam sicut invenit formam partis similis illi que est in medio tabule, nec sicut invenit formam partis que est apud punctum K, dum ambo visus direxerint pupillam ad scrotulam que est in medio.

2.56 ◉ Then, keeping the same arrangement, the experimenter should take the third strip with the hand that lies on the side of point K, and he should place that strip in line with the two strips that are [already] on the plaque along the extension of the line passing through the [middle of the] plaque along its width and lying on the plaque’s surface as far as sense is concerned, but let the strip be [placed] beyond the plaque. Now this sort of alignment will be called a facing alignment. And when he puts it in place, the experimenter should make certain that the third strip and the word written on it are oriented the same way as the two strips on the plaque. He should then focus both eyes on the strip placed in the center and direct his gaze toward it, and in that case he will certainly perceive the third strip if it does not lie too far from the plaque, but he will perceive the form of the word on it in an indistinct and undecipherable way. So he will not find it to be like the form of the word that is identical to it at the center of the plaque, nor does he find it to be like the form of the word at point K as long as both eyes are focused on the strip at the center.

2.57 ◉ Deinde auferat experimentator individuum quod est apud punctum K et scrotulam que est in illo, et appropinquet tunc scrotulam quam tenet in manu quousque applicet eam ad latus scrotule applicate cum individuo posito in medio, et preservet se quod scrotula sit perpendicularis super lineam positam in latitudine. Et diriget pupillam, sicut prius, ad scrotulam positam in medio. Tunc quidem in medio comprehendet ambas partes que sunt in duabus scrotulis comprehensione manifesta et certificata, et non erit inter formas duarum partium in declaratione et certificatione differentia sensibilis.

2.57 ◉ At this point the experimenter should remove the peg at point K, along with the strip attached to it, and he should bring the strip he is holding in his hand nearer [the middle of the plaque] until he can stand it next to the strip that is affixed to the peg placed in the center [of the plaque], and he should take care to stand the strip straight up along the line passing through [the middle of the plaque] along the width. Then, as before, he should direct his gaze toward the strip placed in the center. In that case, he will indeed perceive both words on the two parchment strips clearly and distinctly, and there will be no perceptible difference in clarity and distinctness between the forms of the two words.

2.58 ◉ Deinde experimentator moveat scrotulam quam tenet in manu motu subtili super lineam positam in latitudine tabule, et preservet se ut situs eius sit sicut erat prius. Et intendat certificare scrotulam que est in medio, et intueatur bene duas scrotulas in hoc statu. Tunc quidem videbit scrotulam motam quod quanto magis removetur a medio, tanto diminuitur declaratio partis que est in ea. Cum igitur venerit apud punctum K, tunc inveniet formam partis intelligibilem, sed non tanto quanto cum erat apud suam applicationem cum secunda que est in medio.

2.58 ◉ The experimenter should then slowly move the strip he is holding in his hand along the line passing through [the middle of] the plaque along its width, and he should make certain that its orientation remains as it was before. He should maintain his focus on the middle strip and examine both strips closely as they are so disposed. In that case, he will see that, the farther the moving strip is displaced from the center, the less distinct the word written on it becomes. Thus, when it reaches point K, the experimenter will find that the form of the word is [still] decipherable, but not as clearly as it was when it was placed next to the other strip placed in the center.

2.59 ◉ Deinde experimentator moveat scrotulam etiam, et extrahat illam a tabula, et removeat illam paulatim et paulatim in verticatione linee posite in latitudine. Et intueatur considerans optime, et dirigat pupillam ad scrotulam positam in medio. Quoniam tunc inveniet scrotulam motam quod quanto magis removetur a medio, tanto minus apparebit pars scripta in ea, adeo quod non erit intelligibilis omnino. Deinde cum moverit illam post hoc, videbit illam quod quanto magis removetur a medio, tanto magis latebit forma illius partis scripte in ea.

2.59 ◉ The experimenter should now continue to move the strip, drawing it away from the plaque, and he should move it little-by-little along the line passing [through the plaque’s middle] along its width. And he should examine it closely while directing his gaze at the strip placed in the center. In that case he will find that the farther the moving strip is displaced from the center, the less [clearly] the word written on it will appear until it will become wholly undecipherable. And when he moves it beyond this point, he will see that the farther it is moved from the center the less visible the form of the word written on it becomes.

2.60 ◉ Et etiam cooperiat experimentator visum qui sequitur punctum T, et figat tabulam in eadem dispositione, et dirigat pupillam unius visus qui sequitur punctum K ad scrotulam positam in medio. Et applicet aliam scrotulam ad latus scrotule posite in medio, sicut fecit prius. Tunc quidem inveniet partem que est in alia scrotula manifestam etiam, inter quam et scrotulam positam in medio non est differentia sensibilis. Deinde moveat secundam scrotulam, ut primo fecit, et intendat scrotulam positam in medio, et dirigat pupillam ad ipsam. Tunc quidem inveniet partem que est in secunda scrotula apud motum latere, et cum pervenerit ad punctum K, tunc erit inter suam certificationem in hoc statu et suam certificationem apud applicationem suam cum ea que est in medio differentia sensibilis. Deinde moveat hanc scrotulam, et extrahat illam a tabula, ut primo fecit, et intueatur scrotulam positam in medio. Tunc quidem inveniet quod scrotula mota quanto magis removetur a medio, tanto magis diminuitur declaratio que est in ea, adeo quod forma eius non erit intelligibilis; et quanto magis post removetur a medio, tanto magis latebit.

2.60 ◉ The experimenter should now cover the eye that corresponds with point T, and he should maintain the plaque in the same arrangement, and he should direct the gaze of the eye corresponding with point K at the strip placed in the center. He should then place the other strip beside the strip placed in the center, just as he did before. In that case he will find that the word on that other strip is still clear and that there is no perceptible difference [in clarity] between it and [the word written on] the strip placed in the center. Then he should move the second strip, as he did initially, and focus on the strip placed in the center, directing his gaze at it. In that case he will find that the word on the second strip loses visibility as it is moved, and when it arrives at point K, there will be a perceptible difference between its clarity at this position and its clarity when it was placed next to the strip at the center. He should then move the strip, drawing it away from the plaque, as he did before, and he should focus on the strip placed in the center. Accordingly, he will find that the farther the moving strip is displaced from the center, the less distinct what is on it becomes until its form will no longer be decipherable, and the more it continues to be displaced from the center, the less discernible it becomes.

2.61 ◉ Apparet igitur ex hac consideratione quod manifestissimum visibilium facialium visui que comprehenduntur ambobus visibus est illud quod est apud concursum duorum axium, et quod est propinquius concursui duorum axium est manifestius remotiori, et quod forma remoti visi ad concursum duorum axium est non certificata, etsi comprehendatur utroque visu. Amplius apparet ex hac consideratione quod manifestissimum visibilium facialium que comprehenduntur uno visu est illud quod videtur per axem radialem, et illud quod est propinquius illi est manifestius quam illud quod est remotius, et quod remotum visum a radiali axe habet formam dubitabilem non certificatam. Amplius apparet quod visus non comprehendit rem visam que est remotorum dyametrorum vera comprehensione nisi moveat radialem axem super omnes eius dyametros et super omnes eius partes, sive comprehensio sit ambobus visibus sive uno. Visus enim, cum fuerit fixus in oppositione visi quod est maximorum dyametrorum, non comprehendet totum vera comprehensione, sed solummodo illud quod est supra axem et prope certificata comprehensione. Residue vero partes eius, et illud quod remotum est ab axe scilicet, comprehendet, sed non certe, licet visum sit faciale—et indifferenter sive comprehensio sit utroque visu sive uno tantum.

2.61 ◉ From this investigation it is thus evident that a facing visible object is seen most clearly with both eyes when it lies at the intersection of the two [visual] axes, and [it is evident] that what lies nearer to the intersection of the two [visual] axes appears more clearly than what lies farther away from it and that the form of a visible object that lies far from the intersection of the two [visual] axes is indeterminate, even if it is perceived with both eyes. Moreover, if an object in facing alignment is perceived with one eye, it also becomes evident through this investigation that the object is perceived most clearly with one eye along the visual axis, and [it is evident, as well] that what lies near it appears more clearly than what lies farther from it and that the form of any visible object lying far from the visual axis is indistinct and indeterminate. Furthermore, it is apparent that sight does not correctly perceive a visible object that has large cross-sections unless it moves the visual axis over all its cross-sections and all its parts, whether it is perceived with both eyes or with one. For when it is focused on a facing visible object that has exceptionally large cross-sections, sight will not perceive the entire object correctly but [will] only [perceive] what lies on or near the [visual] axis in a determinate way. It will perceive the remaining parts of that object, specifically those parts that lie far from the [visual] axis, but not distinctly, even when the visible object has a facing alignment—and it does not matter whether the perception occurs with both eyes or with one alone.

2.62 ◉ Postea oportet experimentatorem accipere pargamenum quattuor digitorum in omni dimensione in quo scribat lineas scriptura subtili, tamen manifesta et intelligibili. Deinde auferat individuum positum super tabulam, et superponat tabulam prope visum, ut prius fecit, et erigat pargamenum super lineam positam in latitudine quod est in medio tabule. Et dirigat pupillam utroque visu ad medium pargameni, et intueatur ipsum. Quoniam tunc inveniet scripturam que est in pargameno apertam et intelligibilem, sed tamen scriptura que est in medio pargameni est manifestior quam que est in extremis quando visus direxerit pupillam ad medium pargameni et non fuerit motus super omnes eius dyametros.

2.62 ◉ Next, the experimenter should take a square piece of parchment that is four digits on a side with lines of tiny writing on it, but writing that is still clear and decipherable. Then he should remove the peg that is placed on the plaque and position the plaque up to the eyes, as he did before, and stand the parchment [sheet] up on the line passing through the center of the plaque along its width. He should then direct the gaze of both eyes at the middle of the parchment and focus on it. Accordingly, he will find that the writing on the parchment is clear and decipherable but that the writing on the middle of the parchment is even clearer than the writing toward the edges when the eye directs its gaze toward the center of the parchment and does not move over all its cross-sections.

2.63 ◉ Deinde obliquet pargamenum adeo quod secet lineam positam in latitudine in puncto posito in medio tabule, qui est punctus sectionis. Obliquatio autem pargameni super lineam positam in latitudine sit parva. Et inspiciat ambobus visibus medium pargameni. Quoniam tunc inveniet scripturam legibilem, sed non tantum quantum cum pargamenum erat faciale.

2.63 ◉ He should then incline the parchment so that it intersects the line passing [through the plaque’s middle] along the width at the centerpoint of the plaque, which is the point of intersection. But the obliquity of the parchment should be slight with respect to the line passing along the width. The experimenter should then look at the middle of the parchment with both eyes. Accordingly, he will find the writing legible, but not as legible as when the parchment faced him directly.

2.64 ◉ Deinde experimentator debet obliquare pargamenum obliquatione maiori prima ita quod medium eius sit super punctum sectionis, et dirigat etiam pupillam utroque visu ad medium eius. Tunc quidem videbit scripturam latentiorem prima. Deinde etiam obliquet pargamenum paulatim paulatim ita quod medium eius semper sit in puncto sectionis, et intueatur eam successive. Et tunc inveniet scripturam latere apud obliquationes pargameni, et quanto magis pargamenum fuerit obliquum, tanto magis latebit scriptura, adeo quod pargamenum appropinquet linee extense in medio longitudinis tabule. Et tunc scriptura que est in pargameno videbitur multum dubitabilis, et fere non intellibilis et non certificata.

2.64 ◉ The experimenter should now incline the parchment more sharply than before so that its midpoint stays over the point of intersection, and he should again direct the gaze of both eyes at its middle. In that case, he will see the writing less clearly than before. He should then continue to incline the parchment little-by-little so that its midpoint remains over the point of intersection, and he should examine it at each point as it is turned. He will then find that the writing loses visibility as the parchment is [increasingly] slanted, and the more sharply the parchment is slanted, the less visible the writing will be until the parchment nearly coincides with the line drawn lengthwise through the center of the plaque. At that point the writing on the parchment will appear quite indistinct, [being] wholly indecipherable and indeterminate.

2.65 ◉ Deinde oportet experimentatorem revertere pargamenum ad primam positionem, et erigere ipsum super lineam positam in latitudine, et cooperire alterum visum, et inspicere pargamenum reliquo visu. Et tunc inveniet scripturam manifestam et legibilem. Deinde obliquet pargamenum, ut prius fecit, et inspiciat ipsum uno visu. Et tunc inveniet scripturam latentiorem quam cum erat apud oppositionem facialem. Deinde obliquet pargamenum plus paulatim paulatim, et intueatur ipsum multotiens. Et tunc inveniet quod quanto magis obliquatur, tanto magis latet pars scripta, adeo quod pargamenum appropinquet dyametro qui sequitur visum apertum.

2.65 ◉ The experimenter should then replace the parchment to its original position and stand it up on the line passing [through the plaque’s center] along its width, and he should cover one eye and look at the parchment with the other. He will then find the writing to be clear and legible. Then he should incline the parchment, as he did before, and look at it with one eye. In that case he will find the writing to be less visible than it was when it faced him directly. He should then continue to incline the parchment little-by-little while [re]examining it frequently. He will thus find that, the more sharply it is inclined, the less visible the text written [on it] becomes until the parchment nearly coincides with the diagonal that corresponds with the open eye.

2.66 ◉ Declarabitur ergo ex hac consideratione quod manifestissimum visibilium que sunt super axem radialem est illud quod est faciale visui, et illud cuius positio est magis facialis est manifestius illo cuius positio est minus facialis, et quod illud quod est obliquum ab axe radiali obliquatione maxima est dubitabile et non intelligibile, sive visio sit utroque visu sive uno.

2.66 ◉ From this investigation it will thus be obvious that a visible object lying on the visual axis and directly facing the eye is most clearly seen and that one facing the eye more directly is seen more clearly than one that faces it less directly, and [it is obvious] that an object that is sharply slanted with respect to the visual axis appears indistinct and undecipherable, whether vision occurs through both eyes or through one eye.

2.67 ◉ Deinde oportet experimentatorem revertere individuum quod erat super tabulam, et ponere ipsum in medio tabule, et applicare ipsum ad punctum sectionis, ut in prima consideratione. Deinde erigat pargamenum super alteram partem linee posite in latitudine super verticationem facialem, et dirigat pupillam utroque visu ad individuum positum in medio. In hac quidem dispositione comprehendet pargamenum et scripturam que est in ipso, sed illud quod vicinatur individuo posito in medio erit manifestum, et quod remotum est ab illo est dubitabile et latens. Et quanto magis removetur ab individuo, tanto magis latet.

2.67 ◉ At this point the experimenter should replace the peg that was on the plaque, and he should place it at the middle of the plaque and fasten it at the point of intersection, as it was during the first investigation. Then he should stand the parchment on one side of the line passing [through the plaque’s center] along its width so that it faces the eye directly, and he should direct the gaze of both eyes at the peg placed in the center. In this situation he will perceive the parchment, as well as the writing on it, but what lies nearer the peg placed in the center will be clear, whereas what lies far from it is indistinct and lacking in visibility. Moreover, the farther the writing is displaced from the peg, the less visible it gets.

2.68 ◉ Et etiam oportet experimentatorem obliquare pargamenum in hoc statu ita quod secet lineam positam in latitudine super aliquod punctum alterius eius partis, et sit parva obliquatio. Et dirigat pupillam ad individuum positum in medio. Tunc quidem videbit scripturam que est in pargameno latentiorem quam cum erat facialis. Deinde obliquet plus pargamenum, et dirigat pupillam ad individuum positum in medio. Tunc quidem videbit scripturam dubitabilem, non manifestam nec legibilem.

2.68 ◉ The experimenter should also incline the parchment in this situation so that it intersects the line passing [through the plaque’s center] along its width at some point on the side [of the center] where it stands, but the inclination should be slight. He should then direct his gaze to the peg placed in the center. In that case, he will see that the writing on the parchment is less visible than it was when the parchment faced the eye directly. Then he should incline the parchment more sharply while directing his gaze at the peg placed in the center. Accordingly, he will see that the writing is indistinct, and [therefore] unclear and illegible.

2.69 ◉ Deinde oportet experimentatorem cooperire alterum visum et inspicere uno visu, et revertat pargamenum in sua prima positione, et erigat ipsum super partem linee posite in latitudine que sequitur visum inspicientem, et dirigat pupillam unius visus ad individuum positum in medio. Tunc quidem comprehendet etiam scripturam que est in pargameno, et videbit illam que est prope individuum manifestiorem remota, et videbit illam que est remotissima ab individuo dubitabilem et non legibilem.

2.69 ◉ The experimenter should then cover one eye and look with the other eye, and he should replace the parchment in its original position and stand it up on the side of the line passing [through the plaque’s center] along its width that corresponds to the open eye, and he should direct the gaze of that eye toward the peg placed in the center. Accordingly, he will perceive the writing on the parchment, but he will see what lies near the peg [at the center] more clearly than what lies far from it, and he will see that what lies farthest from that peg appears indistinct and illegible.

2.70 ◉ Deinde obliquet pargamenum ita quod secet lineam positam in latitudine super punctum partis super quam erat erectum, et inspiciat individuum positum in medio illo eodem visu. Tunc quidem videbit scripturam que est in pargameno dubitabilem et illegibilem magis quam cum pargamenum erat faciale. Deinde obliquet pargamenum magis paulatim paulatim, et videbit quod quanto magis obliquatur pargamenum, tanto magis latet scriptura.

2.70 ◉ Next, he should incline the parchment so that it intersects the line passing [through the plaque’s center] along its width at the point on the side where it has been stood, and he should look at the peg placed at the center with that same eye. He will then see that the writing on the parchment is more indistinct and less legible than it was when the parchment faced the eye directly. He should continue inclining the parchment little-by-little, and he will see that the more sharply inclined the parchment is, the less visible the writing becomes.

2.71 ◉ Apparet igitur ex hac consideratione quod visum quod est faciale est manifestius viso obliquo, etsi visum non fuerit super axem radialem et fuerit extra axem. Visum enim, quando multum est obliquum, latet multum, etsi sit super axem radialem, sive visio sit utroque visu sive uno tantum.

2.71 ◉ From this investigation it is thus evident that a visible object that faces the eye directly is [seen] more clearly than one that is oblique, even if the visible object does not lie on the visual axis but lies outside the axis. For when a visible object is very sharply slanted, it loses visibility to a considerable extent, even if it lies on the visual axis, whether vision takes place through both eyes or through one alone.

2.72 ◉ Et etiam oportet experimentatorem auferre individuum a tabula, et erigere pargamenum super extremum tabule, et superponere finem eius fini latitudinis tabule quod est CD, et dirigat pupillam utroque visu ad medium pargameni. Quoniam tunc inveniet scripturam manifestam et legibilem.

2.72 ◉ The experimenter should now remove the peg from the plaque and stand the parchment at the top edge of the plaque, placing its [left] side flush with side CD of the plaque, and he should direct the gaze of both eyes on the middle of the parchment. He will then find that the writing is clear and legible.

2.73 ◉ Deinde obliquet pargamenum ita quod secet latitudinem tabule super punctum Z quod est in medio latitudinis tabule, et dirigat pupillam utroque visu ad medium pargamenum. Tunc quidem videbit scripturam latentiorem quam prius. Deinde addat in obliquatione pargameni paulatim paulatim, et videbit scripturam latere paulatim paulatim, adeo quod, si obliquatio pargameni fuerit maxima, videbit scripturam valde latentem in eadem dispositione in qua erat quando considerabatur in medio tabule; et similiter si consideraverit ipsum in hoc loco uno visu.

2.73 ◉ Then he should incline the parchment so that it intersects the upper edge of the plaque at point Z, which bisects the plaque’s upper edge, and he should direct the gaze of both eyes at the middle of the parchment. In this situation he will see that the writing is less visible than before. He should then increase the slant of the parchment little-by-little, and he will see the writing become less and less visible until the parchment becomes so sharply slanted that the writing will lose visibility to an inordinate extent, just as was the case when he was examining the parchment in the center of the plaque; and the same holds in this case if he carries out the examination with one eye.

2.74 ◉ Deinde oportet experimentatorem ponere individuum super punctum Z et erigere pargamenum super alteram partem latitudinis apud extremum tabule, sicut fecit in medio tabule, et diriget pupillam ad individuum positum in medio, et intueatur pargamenum, et consideret scripturam. Tunc quidem videbit dispositionem sicut videbat eam quando erat in medio tabule, sive consideretur utroque visu sive uno.

2.74 ◉ At this point the experimenter should place the peg at point Z and stand the parchment to one side at the top of the plaque, just as he did in the middle of the plaque, and he will direct his gaze at the peg placed in the center [of the top edge] while looking at the parchment and examining the writing [on it]. He will see that the situation is the same as the one he observed when the experiment was carried out in the middle of the plaque, whether the examination is made with both eyes or with one.

2.75 ◉ Deinde oportet experimentatorem etiam experiri scrotulas parvas quas prediximus apud extremum tabule, et videbit dispositionem in eis sicut cum erant in medio, scilicet quoniam pars que est in media scrotula est manifestior parte que est in scrotula remota a medio. Et quanto scrotula magis est remota a medio, tanto magis latebit pars. Sed tamen videbit quod remotio a medio apud quam latet pars posita in extremo, quando consideratio fuerit apud extremum tabule, proportionalis est ad remotionem a medio apud quam latet pars posita in extremo, quando consideratio fuerit in medio tabule, est enim secundum remotionem radiorum exeuntium ad extremum ab axe. Proportio igitur remotionis apud quam latet forma posita in extremo a forma posita in medio ad remotionem forme posite in medio a visu est eadem proportio in consideratione apud medium tabule et in consideratione apud extremum eius.

2.75 ◉ The experimenter should then try the three small strips we described earlier, [placing them] at the top edge of the plaque, and he will see the situation in this case to be like the one when the strips were tried in the middle of the plaque, i.e., the word on the middle strip is clearer than the word on a strip that lies away from the middle. And the farther the strip is displaced from the center, the less visible the word [on it] will become. However, he will notice that the distance from the middle according to which the word loses visibility when the experiment is carried out at the top edge of the plaque is proportional to the distance from the middle according to which the word loses visibility when the experiment is carried out at the center of the plaque, for it depends on the length of the ray extending to the top edge along the [visual] axis. Thus, at the point when the form loses visibility, the ratio of the eye-to-object distance to the distance of the object from the middle [of the plaque] is the same whether the examination is carried out at the center of the plaque or at its top edge.⁑

2.76 ◉ Et similiter etiam si experimentator abstulerit tabulam et posuerit inde pargamenum in quo est scriptura in maiori distantia quam longitudo tabule sit, et ubi possit legere illam, et fuerit faciale visui, et intueatur ipsam, deinde obliquaverit ipsum in loco suo, inveniet scripturam latere. Et si magis obliquaverit, magis latebit, ita quod, si multum obliquaverit ipsum, adeo quod positio eius sit propinqua positioni radiorum exeuntium ad medium eius, tunc videbit scripturam que est in pargameno latentem valde, adeo quod non possit legi. Et hoc videbit sive consideretur utroque visu sive uno tantum.

2.76 ◉ So, too, if the experimenter sets the plaque aside and positions the parchment with the writing on it farther away than the length of the plaque, but where he can read it, and if he keeps it directly facing the eye while examining it, then inclines it while it remains in place, he will find that the writing loses visibility. And as he continues to incline the parchment, the writing will lose more visibility so that, when he inclines it so sharply that it nearly coincides in orientation with the rays extending to the parchment’s center, he will then see that the writing on the parchment loses a great deal of its visibility until it can no longer be read. And he will observe this whether he looks with both eyes or with one eye only.

2.77 ◉ Et similiter, cum fixerit aliquam scrotularum parvarum in loco opposito visui remotiori quam sit longitudo tabule, et posuerit ipsam facialem visui, et direxerit pupillam ad ipsam utroque visu, et posuerit aliam scrotulam obliquam super illam aut dextrum aut sinistrum, et erexerit eam ita quod sit facialis, inveniet eam latentiorem.

2.77 ◉ Likewise, when he focuses on one of the small strips facing the eye at a greater distance than the length of the plaque and holds it so that it faces him directly while he directs his gaze at it with both eyes, then, when he places another strip to its right or left side and stands it so that it faces him directly, he will find that it is less visible [than the middle strip].

2.78 ◉ Deinde si aliquis moverit secundam scrotulam et removerit eam paulatim paulatim a scrotula ad quam dirigit pupillam, inveniet partem que est in scrotula que est in extremo quod quanto magis remotior est a secunda scrotula, tanto magis latet forma partis, adeo quod fiet illegibilis omnino. Et similiter, si consideraverit has duas scrotulas uno visu, inveniet talem dispositionem.

2.78 ◉ Then, if someone moves the second strip farther and farther from the strip upon which he directs his gaze, he will find that the farther the remote strip gets from the second strip [in the middle], the less visible the form of the word [on the remote strip] gets until it will become absolutely illegible. So, too, if he carries out the examination with the two strips using one eye, he will get the same results.

2.79 ◉ Declaratur igitur ex istis considerationibus omnibus quod manifestissimum visibilium in omnibus remotionibus est illud quod est super axem radialem, et quod illud quod est propinquius axi est manifestius remotiore ab ipso, et quod visum remotum ab axe maxima remotione est dubitabilis forme et non certificabilis, et indifferenter sive visio sit uno visu sive utroque, amplius et quod visum faciale est in omnibus remotionibus manifestius viso obliquo, et quod quanto magis positio visus appropinquatur positioni faciali, tanto erit manifestius, et quod visum obliquum super lineas radiales obliquatione maxima habet formam multum dubitabilem et non certificatam, sive visio sit uno visu sive utroque, et sive visum sit super axem sive extra axem.

2.79 ◉ From all of these investigations, then, it is evident that, whatever its distance [from the eye], an object that lies on the visual axis is [seen] most clearly, while what lies nearer that axis is [seen] more clearly than what lies farther from it, and [it is evident] that when a visible object lies extremely far from the [visual] axis its form is indistinct and indeterminate, no matter whether vision takes place with one eye or with two. It is also evident that a visible object facing the eye directly, whatever its distance from the eye, is [seen] more clearly than one that is inclined and that the closer the visible object gets to a directly facing alignment the more clearly it will be [seen], and [it is evident] that when a visible object is slanted very sharply with respect to the radial lines, its form is quite indistinct and indeterminate, whether vision takes place through one eye or through two, and whether the object lies on the [visual] axis or outside it.

2.80 ◉ Quare vero visum multum obliquum est dubitabilis forme, licet remotio eius sit mediocris, et licet magnitudo sit comprehensa secundum quod est, et quare visum faciale est manifestius obliquo, hoc est quia forma visi multum obliqui instituitur in superficie visus congregata propter suam obliquationem. Quoniam, cum visus fuerit multum obliquus, tunc angulus quem subtendit visum super centrum visus erit parvus, et pars visus in qua instituitur forma illius visi erit minor multum parte in qua instituitur forma eius si fuerit faciale visui. Et partes eius parve subtenduntur apud visum angulis insensibilibus propter maximam obliquationem, pars enim parva, cum multum fuerit obliqua, tunc due linee exeuntes a centro visus ad extrema illius partis parve fient quasi una linea; quapropter sentiens non comprehendet angulum contentum inter eas neque partem quam distinguunt ex superficie visus.

2.80 ◉ Now the reason why a sharply slanted visible object has an indistinct form, even if the object lies at a moderate distance and its size is perceived as it actually is, and the reason why a visible object that faces the eye directly is [seen] more clearly than an oblique one is that the form of a sharply slanted visible object is impressed on the surface of the eye according to the compression that is due to its obliquity. For, if the visible object is sharply slanted, then the angle subtended by the object at the center of sight will be small, and the area on the eye upon which the form of that visible object is impressed will be much smaller than the area upon which the object’s form is impressed when it faces the eye directly. So the small parts [of that form] subtend imperceptible angles at the center of sight on account of the sharp slant [of the object], for when [such] a small part is sharply slanted, the two [radial] lines extending from the center of sight to the edges of that small part will form what amounts to a single line; the sensitive faculty will therefore not perceive the angle formed by them or the area on the surface of the eye that they demarcate.

2.81 ◉ Et visum multum obliquum erit dubitabile, quia forma eius que infigitur in visu erit congregata maxima congregatione, et partes eius parve erunt insensibiles, et ideo forma eius erit dubitabilis. Et ideo, si in huiusmodi viso fuerint subtiles intentiones, non comprehendentur a visu propter latentiam suarum partium parvarum et propter congregationem forme. Visum autem faciale est econtrario, nam forma eius que instituitur in visu erit ordinata secundum quod est in superficie visi, et partes eius parve que possunt comprehendi a visu erunt manifeste. Et cum partes parve visi fuerint manifeste et ordinate in superficie visus secundum suam ordinationem in superficie visi, tunc forma erit manifesta et non dubitabilis.

2.81 ◉ Moreover, a visible object that is sharply slanted will be indistinct because the form of it that is impressed in the eye will be inordinately compressed, and its small parts will [then] be imperceptible, so its form will be indistinct. If, therefore, there are subtle characteristics in such a visible object, they will not be perceived by sight because of the invisibility of its small parts as well as the compression of its form. On the other hand, a visible object that faces the eye directly presents the opposite case, for the form of it that is impressed on the eye will be arranged just as it is on the surface of the visible object, and the small parts [on it] that can be perceived by sight will be evident. And since the small parts of the visible object are evident and are arranged on the surface of the eye as they are arranged on the visible object’s surface, the form will be clear, not indistinct.

2.82 ◉ Et universaliter intentiones subtiles, et partes subtiles, et ordinatio partium visi non comprehenduntur a visu vera comprehensione nisi cum forma imprimatur in superficie membri sentientis et instituatur quelibet pars eius in parte sensibili superficiei membri sentientis. Et cum visum fuerit multum obliquum, tunc forma eius non imprimetur in visu, nec forme aliquarum partium parvarum infigentur in parte sensibili visus. Hoc enim non fit nisi quando visum est faciale, aut quando obliquatio eius fuerit parva, et fuerit remotio eius cum hoc ex remotionibus mediocribus in respectu intentionum que sunt in illo viso.

2.82 ◉ Generally, subtle characteristics, subtle parts, and the arrangement of the parts of a visible object are not perceived correctly by sight unless the form is impressed on the surface of the sensitive organ and each of its parts is impressed⁑ on a perceptible part of the sensitive organ’s surface. But when the visible object is extremely slanted, its form will not be [adequately] impressed on the eye, nor will the form of any of its small parts be impressed on a perceptible part of the eye. For this happens only when the visible object faces the eye directly, or when its inclination is slight and, in addition, it lies at a moderate distance in respect to the characteristics possessed by that visible object.

2.83 ◉ Comprehensio vero magnitudinis visi obliqui multum secundum quod est, cum fuerit in remotione mediocri, licet obliquatio eius sit maxima, non est ex ipsa forma visi que instituitur in visu tantum, sed ex ratione extra formam, scilicet ex hoc quod comprehendens comprehendit diversitatem duarum remotionum duorum extremorum eius cum hoc quod comprehendit mensuram forme. Et cum visus comprehenderit diversitatem remotionum duorum extremorum visi multum obliqui, et comprehenderit differentiam maximam inter eas, statim virtus distinctiva ymaginabitur positionem illius visi, et comprehendet mensuram eius secundum diversitatem remotionum duorum extremorum eius, et secundum mensuram partis in qua instituitur forma, et secundum mensuram anguli cui subtenditur illa pars apud centrum visus, non solummodo ex ipsa forma. Et cum virtus distinctiva comprehenderit diversitatem remotionum duorum extremorum visi multum obliqui, et comprehenderit obliquationem eius, statim percipiet congregationem forme. Comprehendit igitur mensuram eius cum senserit quantitatem obliquationis eius, non secundum mensuram forme, sed secundum positionem eius. Et partes parve et subtiles intentiones que sunt in viso non possunt comprehendi ratione si visus non senserit illas partes aut illas intentiones.

2.83 ◉ Now the correct perception of the size of a sharply slanted visible object when it lies at a moderate distance, even when its slant is inordinate, is not based solely upon the actual form of the visible object impressed on the eye, but upon a deduction that goes beyond the [simple perception of the] form, i.e., from the perceiver’s grasp of the difference in distance [from the center of sight] between the two edges of the object along with the perception of the form’s size. When sight perceives the difference in distance [from the center of sight] of the two edges of a sharply slanted visible object and perceives the full amount of this difference, the faculty of discrimination will immediately imagine the orientation of that visible object and will perceive its size according to the difference in distance [from the center of sight] of its two edges, as well as according to the size of the area upon which the form [of the object] is impressed and the size of the angle subtended by that area at the center of sight, [so the overall perception is] not based upon the form alone. And when the faculty of discrimination perceives the difference in distance [from the center of sight] of the two edges of a sharply slanted visible object and [thus] perceives its obliquity, it will immediately perceive the compression of [its] form. Accordingly, it perceives its size when it senses the amount of its obliquity, not according to the size of the form but according to its orientation. But the subtle parts and features possessed by the visible object cannot be perceived through deduction if sight does not sense those parts or those features.

2.84 ◉ Latentia igitur forme visi accidit ex congregatione forme eius in visu et ex latentia partium eius parvarum. Et apparentia forme visi, cum fuerit in remotione mediocri, est propter impressionem forme in visu secundum quod est et propter hoc quod sentit visus partes eius parvas.

2.84 ◉ Hence the form of the visible object loses visibility because of the compression of the form on the eye as well as from the invisibility of its small parts. The form of a visible object that lies at a moderate distance becomes visible because the form impressed in the eye [represents the object] as it actually is and because sight senses its small parts.

2.85 ◉ Quare igitur forma visi maxime obliqui est dubitabilis, forma autem visi facialis est manifesta declaratum est.

2.85 ◉ Why the form of an sharply slanted visible object is indistinct, whereas the form of a visible object that faces the eye directly is clear has thus been explained.

2.86 ◉ Hiis autem declaratis, incipiendum est de sermone de deceptione visus et declarare causes et species earum.

2.86 ◉ And now that these points have been explained, it is time to begin the discussion of visual illusions and to describe their causes and their kinds.

◉[Capitulum 3]

◉[Chapter 3]

Tertium capitulum de causis quibus visui accidit deceptio

3.1 ◉ Declaratum est in ipso primo tractatu quod visus nichil comprehendit ex visibilibus que sunt cum eo in uno aere que recte comprehendit nisi visus congregaverit has intentiones, et sunt: remotio; [et] oppositio; et lux; et hoc quod corpus eius sit aliquantum; et quod sit densum aut habeat aliquam densitatem; et quod aer medians inter ipsum et visum sit diafonum continue diafonitatis in quo nullum corpus densum interponatur. Hiis igitur existentibus et visu inspiciente salvo ex occasionibus et impedimentis, visus comprehendet illud visum. Si autem visus caruerit aliquo istorum, non comprehendet visum quod caret illo.

3.1 ◉ In the very first book of this treatise it was demonstrated that sight perceives none of the visible objects that lie in the same air with it and are perceived directly unless all the following conditions are met, namely: [there must be some] distance [between eye and object]; [the object must be] facing [the eye]; [there must be] light; the object must be of some [perceptible] magnitude; the object must be opaque or have some opacity in it; and the air between the object and the eye must be continuously transparent, with no opaque body interposed [between eye and object]. When these conditions are met and the eye that does the looking is free of injuries or obstructions, sight will perceive that visible object. If, however, any of these conditions is not met, sight will not perceive a visible object that lacks that particular qualification.⁑

3.2 ◉ Declaratum est etiam in secundo tractatu quod visus nullum visibile comprehendit nisi in tempore; ergo et tempus etiam est unum eorum que exiguntur ad hoc quod visus compleatur.

3.2 ◉ It was also shown in the second book that sight perceives every visible object in some amount of time;⁑ time, therefore, is also one of the things necessary for vision to be accomplished.

3.3 ◉ Et sanitas visus etiam.

3.3 ◉ The eye must also be healthy.

3.4 ◉ Et declaratum est in capitulo predicto quod, cum visum fuerit extra axem radialem et remotum ab eo, non comprehendetur a visu certificata comprehensione, licet sit faciale. Et declaratum est etiam quod, si visum fuerit obliquum super lineas radiales maxima obliquatione, non compre hendetur a visu vera comprehensione, licet sit super axem radialem et oppositum medio visus. Visus igitur non comprehendit visum secundum quod est, licet sit oppositum ei, nisi cum fuerit visum in propria positione, scilicet cum fuerit faciale visui aut fere, et cum fuerit cum hoc super axem radialem aut prope.

3.4 ◉ In the preceding chapter it was also shown that, when the visible object lies far outside the visual axis, it will not be perceived in a determinate way by sight, even if it faces the eye directly.⁑ And it was also shown that, if the visible object is sharply slanted with respect to the radial lines, it will not be correctly perceived by sight, even if it lies on the visual axis directly opposite the middle of the eye.⁑ Thus, sight does not perceive the visible object as it actually exists, even when it faces the eye, unless the visible object is properly oriented, i.e., unless it is directly facing the eye, or nearly so, and unless it lies on or near the visual axis.

3.5 ◉ Intentiones autem quibus completur comprehensio visi secundum quod est sunt octo: remotio prima; oppositio; lux; aliqua quantitas corporis; densitas; diafonitas aeris; tempus; sanitas visus. Hiis igitur omnibus aggregatis visum comprehendetur vera comprehensione, et si visum caruerit aliquibus istorum et cum hoc fuerit comprehensum a visu, tunc non comprehendetur vera comprehensione.

3.5 ◉ The conditions, moreover, according to which a visible object is perceived as it actually exists number eight: first, distance; [then] a facing orientation; light; some bulk; opacity; transparency in the air; time; and a healthy eye. When all of these conditions are met a visible object will be correctly perceived; if the object lacks any of them yet is still perceived by sight, then it will not be correctly perceived.

3.6 ◉ Dicamus igitur quod unumquodque istorum in respectu uniuscuiusque visibilium habet latitudinem in qua visus comprehendit visum secundum quod est, et dum ista fuerint congregata in visu et unumquodque eorum fuerit in latitudine mediocri secundum quam completur comprehensio visi secundum quod est, tunc visus comprehendet illud visum secundum quod est. Et si unum istorum aut plura uno pertransierint illam latitudinem multum, visus non comprehendet illud visum secundum quod est. Visum enim valde remotum a visu non comprehenditur a visu vera comprehensione, et similiter valde visum propinquum visui non comprehendetur a visu vera comprehensione, et inter duas has extremitates sunt plures remotiones ex quibus visus comprehendit visum vera comprehensione sine dubio. Sed tamen remotiones ex quibus visus comprehendit rem visam vera comprehensione sunt ad aliquem terminum, et nulla earum erat maxima nec in remotione nec in propinquitate; et in unoquoque visibilium sunt secundum illud visibile. Visibile enim magni corporis comprehenditur a visu vera comprehensione in remotione in qua latet visum parvi corporis, et similiter visum fortis lucis comprehenditur a visu ex remotione ex qua latet visum debilis lucis.

3.6 ◉ Accordingly, we should observe that, for every visible object, each of these conditions has a range within which sight perceives the object as it actually exists, and as long as all these conditions are met during the visual process, and as long as each of them falls within the normal range according to which the visible object is perceived as it actually exists, sight will perceive that visible object as it actually exists. But if one or more of these conditions falls very far outside that range, sight will not perceive the object as it actually exists. For when a visible object lies too far from the eye, it is not correctly perceived by sight, and, by the same token, when a visible object lies too close to the eye it will not be correctly perceived by sight, but between these limits there are numerous distances at which sight correctly perceives the visible object without any uncertainty. Nevertheless, the distances at which sight perceives a visible object correctly are limited, none of them having been too great or too small in extent; and for each visible object there is a corresponding range of distances. Indeed, a visible object with a large bulk is correctly perceived by sight at a distance in which a visible object of small bulk disappears from sight, and likewise, an intensely luminous visible object is perceived by sight at a distance in which a feebly lit visible object disappears from sight.

3.7 ◉ Et etiam visum quod non est oppositum medio visus sed obliquum a medio maxima obliquatione cuius nulli parti occurrit axis radialis nec propinquat non comprehenditur a visu vera comprehensione. Et visum quod comprehenditur duobus visibus in quo non occurrunt axes duorum visuum, et radii consimilis positionis cuius situs apud duos visus non est positio consimilis, non comprehendetur a visu vera comprehensione. Et visum oppositum medio visus super cuius aliquod punctum erit axis radialis aut prope, cum non fuerit maximorum dyametrorum, comprehendetur a visu vera comprehensione, etsi axis non moveatur per omnes eius dyametros. Et visum comprehensum duobus visibus in quo concurrunt duo axes radiales et in quo concurrunt radii consimilis positionis cuius positio apud duos visus est consimilis, comprehendetur a visu vera comprehensione. Et visum faciale visui aut modicum obliquum comprehendetur a visu vera comprehensione, sed parva obliquatio in qua visus comprehendit rem visam certe est secundum intentiones que sunt in viso. Et similiter remotio ab axe radiali parva in qua comprehenditur visum certe est secundum intentiones que sunt in viso, visum enim in quo non sunt subtiles intentiones comprehenditur a visu certe, licet sit extra axem radialem tamen remotum parva remotione. Et similiter comprehenditur certe cum fuerit obliquum super lineas radiales parva obliquatione. Visum autem in quo sunt subtiles intentiones non comprehendetur certe cum fuerit extra axem radialem et fuerit sua remotio ab axe sicut remotio ex qua comprehenditur certe forma visi in quo non sunt subtiles intentiones. Et similiter non comprehendetur forma eius certe si fuerit obliquum super lineas radiales tali obliquatione in illa in qua comprehenditur certe forma visi in quo non sunt subtiles intentiones.

3.7 ◉ Furthermore, a visible object that does not face the middle of the eye directly but lies so far to the side that none of its parts touches the visual axis or lies near it is not correctly perceived by sight. Moreover, if a visible object is perceived with both eyes but the axes of both eyes do not intersect on it, or if the rays that are correspondingly situated with respect to the two eyes are not correspondingly situated [on the object], then it will not be correctly perceived by sight. But if a visible object faces the middle of the eye, and the visual axis touches some point on it, or nearly does, then, if that object does not have excessively large cross-sections, it will be correctly perceived by sight, even if the [visual] axis does not scan all of the cross-sections. Also, when an object is perceived by both eyes, and the two visual axes intersect on it, or rays that are correspondingly situated with respect to the two eyes touch it at corresponding locations, it will be correctly perceived by sight. Moreover, a visible object that faces the eye directly or that is [only] slightly oblique [to it] will be correctly perceived by sight, but how slight the obliquity must be for sight to perceive the visible object in a determinate way depends upon the characteristics possessed by the visible object. Likewise, how small the displacement from the visual axis must be for the visible object to be perceived in a determinate way depends upon the characteristics possessed by the visible object, for a visible object that has no subtle characteristics is perceived in a determinate way by sight, even when it lies a small distance from the visual axis. So, too, it is perceived in a determinate way when it is [only] slightly oblique with respect to the radial lines. On the other hand, a visible object with subtle characteristics will not be perceived in a determinate way when it lies outside the visual axis and its distance from the visual axis is the same as the distance at which the form of an [equivalent] visible object with no subtle characteristics is perceived in a determinate way. Likewise, its form will not be perceived in a determinate way when the object has the same obliquity with respect to the radial lines as an [equivalent] object without subtle characteristics does when it is perceived in a determinate way.

3.8 ◉ Et etiam visum in quo est modica lux et non bene illuminata non comprehendetur a visu vera comprehensione, et maxime cum fuerint in eo subtiles intentiones. Et similiter visum fortiter luminosum et lucidum aut visum tersum super quod oritur fortis lux non comprehendetur a visu vera comprehensione. Et inter lucem debilem et lucem scintillantem sunt plures luces ex quibus visus comprehendit rem visam vera comprehensione. Et etiam lux in qua visus comprehendit formam visi vera comprehensione erit secundum intentiones que sunt in viso et secundum magnitudinem visi. Visum enim in quo non sunt subtiles intentiones etiam comprehenditur a visu in parva luce in qua potest latere forma visi habentis subtiles intentiones. Et similiter visum magni corporis comprehenditur a visu in parva luce in qua potest latere visum minimum.

3.8 ◉ Moreover, a visible object that is slightly luminous or poorly illuminated will not be perceived by sight correctly, especially if there are subtle features in it. So, too, a visible object that is intensely luminous or shining or a polished body upon which intense light shines will not be correctly perceived by sight. But between faint and brilliant light there are numerous [gradations of] light according to which sight correctly perceives a visible object. But the light according to which sight correctly perceives the form of a visible object will depend on the attributes possessed by the object as well as on its size. For a visible object that possesses no subtle characteristics is perceived by sight in light that is [so] weak that the form of a visible object possessing subtle characteristics may disappear from sight in it.⁑ By the same token, a visible object of large bulk is perceived by sight in light that is [so] weak that a tiny visible object may disappear from sight in it.

3.9 ◉ Et visum etiam, cum fuerit valde parvum et fuerint in eo subtiles intentiones et partes distincte, non comprehendetur a visu vera comprehensione, ut animalia quorum membra sunt distincta, et figura membrorum eorum et membra, adeo sunt parva quod visus non potest comprehendere. Talia enim animalia, si comprehendantur a visu, non certe comprehenduntur. Cum autem corpus animalis est magnum, tunc membra erunt sibi proportionalia, et tunc visus comprehendet unumquodque illorum membrorum distinctorum. Et sic comprehendet formam eius secundum quod est. Et similiter omnia visibilia in quibus sunt intentiones valde subtiles non certe comprehendentur a visu. Et si ille intentiones fuerint proportionales visibilibus magni corporis, tunc visus comprehendet illa visibilia vera comprehensione si ille intentiones fuerint proportionales visibilibus.

3.9 ◉ Furthermore, if the visible object is extremely small and there are subtle features or small individual parts in it, it will not be correctly perceived by sight, e.g., animals whose members are distinct, and the shape of their members, as well as the members themselves, are so small that sight cannot perceive [them]. In fact, if such animals are perceived by sight, they are not perceived in a determinate way. When, however, the animal has a large body, its members will be proportionate[ly large], and sight will then perceive each of those individual members. Thus, sight will perceive its form as it actually exists. Similarly, no visible object that possesses extremely small features will be properly perceived by sight. But if those features are proportionate[ly large] in large visible objects, then sight will perceive those visible objects correctly if those features are proportionate to [the size of] the visible objects.

3.10 ◉ Et etiam cum visum fuerit diafonum et fuerit in eo aliqua densitas parva valde, non comprehendetur a visu vera comprehensione. Et cum non fuerit diafonum, aut fuerit in eo parva diafonitas et densitas eius fuerit manifesta, comprehendetur a visu vera comprehensione. Et quanto magis diafonum fuerit tenuioris coloris, tanto magis indigebit maiori densitate, et quanto magis fuerit fortioris coloris, tanto magis poterit comprehendi a visu cum parva densitate cum qua visum tenuis coloris non poterit comprehendi vera comprehensione. Et erunt invisibilia que sunt in aere medio inter visum et rem visam cum ille aer fuerit spissus et turbidus, ut sunt nubule, et fumi, et similia. Et quando illa visibilia sunt subtilia aut fuerint in eis intentiones subtiles, non comprehendentur a visu vera comprehensione. Et similiter, quando aere in medio interponetur corpus diafonum visui et rei vise in quo corpore fuerit aliqua spissitudo, illud visum non comprehendetur a visu vera comprehensione. Si autem aer fuerit clarus diafonus et subtilis et consimilis diafontitatis, et non interponatur in ipso corpus densum, tunc visus comprehendet visibilia que sunt in illo aere vera comprehensione. Et similiter, si in aere fuerit aliqua spissitudo parva et fuerint in eo visibilia non minima carentia intentionibus subtilissimis, tunc visus comprehendet illa visibilia vera comprehensione, et non impedietur ab illo aere, licet sit spissus aliquantulum. Spissitudo autem aeris in quo visum comprehenditur vera comprehensione est secundum intentiones que sunt in viso, visum enim in quo non sunt intentiones subtiles comprehendetur certe a visu in aere in quo quidem est aliqua spissitudo in quo aere non comprehendetur certe visum aliud in quo sunt subtiles intentiones.

3.10 ◉ Furthermore, if the visible object is transparent but there is just a bit of opacity in it, it will not be correctly perceived by sight. However, if it is not transparent, or if it only has a bit of transparency in it, and its opacity is obvious, it will be correctly perceived by sight. And the fainter the coloring of the transparent object is, the more opacity it will require [to be properly seen], whereas the more intense the color, the more [readily] it can be perceived by sight when its opacity is so slight that a faintly colored visible object [with the same opacity] could not be correctly perceived. Moreover, when the air between the eye and a visible object is hazy or foggy, as [happens when] clouds, smoke, and the like are [present], things in such air will be invisible. Moreover, if those visible objects are subtle or there are subtle features in them, they will not be correctly perceived by sight. Likewise, when a transparent body with some opacity is placed in the air between the eye and a visible object, that visible object will not be correctly perceived by sight. If, however, the air is transparent and clear and of sheer and uniform transparency, and if there is no opaque body placed in it [between eye and objects], then sight will perceive the visible objects in that air correctly. Likewise, if the air is slightly hazy and there are visible objects in it that are not too small and that lack subtle features, sight will correctly perceive those visible objects, and it will not be hindered by the air, even if it is somewhat hazy. However, the amount of haziness in the air according to which a visible object is correctly perceived depends on the features possessed by the visible object, for a visible object that possesses no subtle features will be correctly perceived by sight in air that is hazy enough that another visible object possessing subtle features will not be perceived through it in a determinate way.

3.11 ◉ Et etiam visum, cum fuerit motum motu valde veloci et cum pertransierit spatium in quo comprehendetur a visu in minimo tempore, non comprehendetur a visu vera comprehensione. Verbi gratia, quando aliquis respicit a foramine a quo est motus ultra quod aliquod visum movetur motu velocissimo valde, et comprehenderit visus illud visum ab illo foramine, tunc visus non comprehendet quiditatem eius, nec certificabit formam eius bene. Si autem fuerit motum in oppositione visus per spatium non maxime magnitudinis in tempore sensibili, tunc comprehendetur a visu certe.

3.11 ◉ In addition, when a visible object is moved quite swiftly, and it traverses a space in which it will be perceived by sight in a minimal amount of time, it will not be correctly perceived by sight. For instance, when someone looks through a window outside of which some visible object moves [by] extremely swiftly, if sight perceives that visible object through that window, it will not perceive what kind of thing it is, nor will it determine its form properly. On the other hand, if the object moves in a plane facing the eye along a space that is not too great during a perceptible amount of time, it will be perceived by sight in a determinate way.

3.12 ◉ Et etiam motus velocissimus circularis, ut motus troci, non comprehendetur a visu, licet trocus comprehendatur, et comprehendet trocum aut corpus motum per motum troci quasi quiescens. Et similiter motus tardissimus non comprehendetur a visu in parvo tempore, et comprehendetur in tempore sensibili quasi quiescens et immobile.

3.12 ◉ Also, extremely swift rotary motion, such as the motion of a top, will not be perceived by sight, even though the top is perceived, so it will perceive the top, or a body moving with the top’s motion, as if it were immobile. In the same vein, a motion that is extremely slow will not be perceived by sight in a short amount of time, so in a perceptible amount of time it will be perceived as if it were at rest and immobile.⁑

3.13 ◉ Sanitas habet latitudinem. In quadam enim infirmitate minutie corporis visi absconduntur, in minori percipiuntur.

3.13 ◉ The health [of the eye] has a range. For in the case of certain infirmities the minute features of a body that is seen are invisible, whereas in the case of a less [infirm eye] they are perceived.

3.14 ◉ Et generaliter quilibet situs in quo non verificatur forma rei vise sicut est in veritate est situs egressus a temperantia ad rem illam proportionata. Egreditur autem situs rei vise a temperamento in longitudine, vel propter maximum longitudinis excrementum vel maximam eiusdem diminutionem. In situ fit egressio a temperantia per maximam ab axe elongationem, per situs corporis respectu duorum visuum diversitatem, per maximam eius declinationem. In luce egressum a temperamento efficit fortitudo eius maxima vel debilitas nimia; in magnitudine diminutio quantitatis rei vise; in soliditate raritatis intentio; in aere nimia eius spissitudo; in tempore nimia eius duratio; in visus sanitate debilitas visus magna vel eius immutatio secundum egritudinem.

3.14 ◉ Generally speaking, any spatial disposition according to which the form of a visible object is not defined [according to the object] as it actually exists is a spatial disposition that falls outside the [range of] moderation that is proportionate to that object. In terms of distance,⁑ the spatial disposition of a visible object falls outside [the range of] moderation either according to a maximum increase or a maximum decrease in extent. In terms of distance away from the [visual] axis, spatial disposition falls outside [the range of] moderation by exceeding a maximum, whereas in terms of orientation with respect to both eyes, an object falls outside the range of moderation by slanting too much. In the case of light, too great an intensity or excessive faintness causes it to fall outside [the range of] moderation; in the case of magnitude, an [excessive] diminution in the size of a visible object [causes it to fall outside the range of moderation]; in the case of opacity, [too great an] increase in transparency [causes it to fall outside the range of moderation]; in the case of [the transparency of] air, an excess of opacity in it [causes it to fall outside the range of moderation]; in the case of time, an excessive [brevity] in its duration [causes it to fall outside the range of moderation]; and in the case of ocular health, a substantial weakening of the eye or a change produced in it by disease [causes it to fall outside the range of moderation].

3.15 ◉ Habet autem temperamentum latitudinem que sic patebit. Viso aliquo corpore sicut est, et paululum a visu elongato vel adducto, dum videtur distans a veritate insensibili proportione adhuc est de temperamento, et ita donec proportionalis sit et sensibilis apparentie immutatio. Mensuratur etiam temperamenti latitudo in quolibet istorum secundum proportionem eius ad alia septem, et secundum colorem et partium corporis parvitatem. Igitur, latitudo temperamenti longitudinis attenditur et secundum colorem, et secundum minutias que in corpore fuerint, et secundum lucem et sex alia que dicta sunt.

3.15 ◉ Now what it means to fall within the range of moderation will be explained as follows. If some object is seen as it actually exists and is moved somewhat farther away from or somewhat nearer to the eye, as long as the difference between appearance and reality is imperceptible, the range is moderate, and it continues to be until the difference is appreciable and there is a perceptible change in appearance. Furthermore, the range of moderation for each condition varies proportionately to the other seven, and according to color as well as to the smallness of the parts of the body. Thus, the range of moderation for distance depends not only on color, but also on the tiny features that are in the body, as well as on the light and the six other conditions that have been mentioned.

3.16 ◉ Secundum coloris varietatem, quoniam corpus fortis et acuti coloris a maiori longitudine percipitur quam obtusi et debilis, unde latitudo temperamenti longitudinis maior est proportionata ad colorem fortem quam ad debilem.

3.16 ◉ [The range of moderation for distance] depends on the type of color, for a body that has an intense and bright color is perceived at a greater distance than [one whose color is] dull and faint, so the range of moderation for distance is proportionately greater for an intense color than for a faint one.

3.17 ◉ Similiter si fuerint in corpore viso note notabiles, a maiori longitudine comprehenduntur quam si multum parve, unde maior est longitudinis temperantia respectu partium corporis notabilium quam respectu minutarum.

3.17 ◉ Similarly, when the distinguishing features of the body of a visible object are noticeable, they are perceived at a greater distance than [they would be] if they were tiny, so [the range of] moderation for distance is greater with respect to the noticeable parts of the body than with respect to the tiny [parts].

3.18 ◉ Pari modo maius erit temperamentum longitudinis ad rectam corporis oppositionem proportionatum quam ad eius declinationem. Similiter erit maius secundum propinquitatem corporis ab axe quam secundum elongationem.

3.18 ◉ In the same vein, [the range of] moderation for distance will be proportionately greater for a body that faces the eye directly than for one inclined to it. So, too, it will be greater when the body is closer to the [visual] axis than when the body is farther [from it].

3.19 ◉ Eodem modo, maior est temperamenti longitudinis latitudo in forti luce quam in debili.

3.19 ◉ Likewise, the range of moderation for distance is greater in intense light than in faint light.

3.20 ◉ Et maior si corpus visum fuerit magnum quam si parvum.

3.20 ◉ And [the range of moderation for distance is] greater if the body that is seen is large than if [it is] small.

3.21 ◉ Similiter corpus multum solidum a maiori longitudine percipitur quam minus solidum, unde soliditati corporis proportionatur longitudinis temperamentum.

3.21 ◉ So, too, a body that is absolutely opaque is perceived at a greater distance than one that is less opaque, so the opacity of the body is proportionate to [the range of] moderation for distance.

3.22 ◉ Ad qualitatem aeris proportionatur temperamentum longitudinis, quoniam spissitudo aeris ab aliqua longitudine corporum visui abscondit que ab eadem vel a maiori longitudine claritas exponit.

3.22 ◉ [The range of] moderation for distance is proportionate to the quality of the air [through which an object is seen], for hazy air can mask bodies from sight at a given distance, whereas at the same or at a greater distance it reveals them when it is clear.

3.23 ◉ Temporis quantitati proportionatur temperamentum longitudinis, quoniam in tempore aliquo motus corporis percipitur ab aliqua longitudine et a maiori percipietur in maiori tempore.

3.23 ◉ [The range of] moderation for distance is proportionate to time, for in a certain amount of time the motion of a body is perceived at a given distance, whereas it will [only] be perceived at a greater distance in a greater amount of time.

3.24 ◉ Pari modo in aliquo modo santitatis visus a maiori longitudine videbitur corpus quam in minori.

3.24 ◉ Likewise, when the eye enjoys a certain modicum of health, a body will be seen at a greater distance than [when the eye is] less [healthy].

3.26 ◉ Similiter mensuratur temperamentum situs secundum proportionem factam ad longitudinem, ad colorem, ad minutias corporis, ad lucem, et ad alia que enumeravimus.

3.26 ◉ By the same token, [the range of] moderation for spatial disposition is measured proportionately to distance, as well as to color, to the small features of the body [that is being looked at], to light, and to the other conditions we enumerated.

3.33 ◉ Et tu considera et singulis adapta, et videre poteris defacili. Et eodem modo proportionabis temperamentum cuiuslibet istorum ad omnia alia, et videbis quod dictum est per singula.

3.33 ◉ But you [must] examine and adjust each one [to its counterparts], and you will be able to see quite easily [how the range varies for each]. In the same way you will relate the [range of] moderation for each of them to all the rest, and you will see that what has been said applies to every one of them.

3.34 ◉ Quando ergo singula eorum que enumerata sunt fuerint in latitudine temperamenti sui, apparebit rei vise veritas forme sicut est in re. Quando autem non apparet forma sicut est in veritate, egressum est aliquid predictorum a temperamento aut plura eorum. Igitur causa quare errat visus in comprehensione formarum non est nisi egressus alicuius predictorum a temperamento aut plurimum, et hec dicenda in hac erant parte.

3.34 ◉ Thus, when each of the conditions that have been listed falls within its proper range of moderation, the true form of the visible object will appear as it actually exists. However, when the form does not appear as the [object] actually exists, one or more of the aforementioned conditions has fallen outside [the range] of moderation. Thus, the only reason sight errs in perceiving forms is because one or more of the aforementioned conditions has fallen outside [the range of] moderation, and these are the points that were to be established in this section.

◉[Capitulum 4]

◉[Chapter 4]

4.1 ◉ Planum est ex libro secundo quod rerum fit comprehensio per sensum, scientiam, sillogismum. Cum autem accidit error in eis quorum fit comprehensio per solum sensum, scimus quod est error sensus tantum. Cum in eis que per scientiam comprehendit quis erraverit, in scientia tantum error erit. Si vero in his que per sillogismum comprehenduntur erret quis, erit error in sillogismo tantum. Sensus adquirit lucem et colorem tantum, sicut dictum est.

4.1 ◉ It is evident from the second book that the perception of things is accomplished through [brute] sensation, recognition, or deduction. Now when an error occurs in the case of things that are perceived through brute sensation, we know that this involves an error of sensation alone. When someone errs in the case of things he perceives through recognition, the error will involve recognition alone. Finally, if someone errs in the things that are perceived through deduction, the error will involve deduction alone. Sensation apprehends light and color only, as has been pointed out.

4.2 ◉ Scientia vero pretendit ea que prius sunt visa et in sensu habita, ut lux solis cognoscitur quod plurimum visa est, et inter lucem solis et lucem lune discernitur. Et licet fiat comprehensio lucis per sensum tantum, tamen per scientiam accidit distinctio lucium. Similiter accidit per scientiam notitia figurarum, ut trianguli, quadrati, circuli, et aliarum similium. Similiter notitia asperitatis, lenitatis, umbre, decoris, et similium, per sillogismum fit comprehensio eorum, que supra explanavimus, licet ea non plurimum noverit sensus.

4.2 ◉ Recognition, however, includes everything that has been seen before and that is retained by the sense;⁑ for instance, the light of the sun is recognized because it is seen so frequently, and the light of the sun and the light of the moon are differentiated [through such recognition]. And even though the perception of light [itself] occurs through brute sensation, the differentiation of [types of] light still occurs through recognition. Likewise, a grasp of shapes, such as the shape of a triangle, of a square, of a circle, or of the like, occurs through recognition. The same holds for our grasp of roughness, smoothness, shadow, beauty, and the like; these are perceived through deduction, as we explained above, even if the sense [of sight] has not apprehended them frequently.

4.4 ◉ Omnis autem comprehensio rerum continetur sub aliquo horum trium modorum, et cum error evenit in comprehensione formarum, non accidit nisi in aliquo istorum.

4.4 ◉ Every perception of objects falls under one of these three heads, and when an error arises in the perception of forms, it occurs in one of these ways alone.

4.5 ◉ Accidit error sensui si corpus in quo sit multa colorum particularium diversitas occurrat visui sub luce multum debili, ut vestis aliqua diversis coloribus et in minutis picturata apparebit unius coloris. Et erit error in sensu per lucem a temperamento suo egressam, ceteris a temperantia non egressis.

4.5 ◉ An error of [brute] sensation occurs when a body that has many different colors is presented to sight in extremely faint light; for instance, certain clothing of various colors with fine designs will appear to be of a single color. And this error will occur in sensation because the light [falls] outside its [range of] moderation, whereas the remaining conditions will not have fallen outside their [range of] moderation.

4.6 ◉ In scientia error accidit cum in magna longitudine videtur aliquando homo notus existimatur esse alius similiter cognitus, unde ab aliqua longitudine videns fratrem putat se videre patrem vel aliquod in hunc modum. Et est error in scientia propter egressum solius longitudinis a temperamento.

4.6 ◉ An error of recognition occurs at times when a person known [to the viewer] is seen at a great distance and is judged to be someone else who is similarly known, so someone seeing his brother at a certain distance thinks he is seeing his father or something of the sort. And this error in recognition is due solely to the fact that the distance has fallen outside [the range of] moderation.

4.7 ◉ In sillogismo accidit error, ut quando motis nubibus existimatur esse lune motus. Et accidit error iste ex intemperata longitudine, quoniam nisi longitudinis est temperantia non evenit, ita ut baculum hic fundo aque infixum, et aquam super eminentem in motu videmus, sed non lignum, et motum aque transeuntis percepimus.

4.7 ◉ An error of deduction occurs, for example, if the moon is judged to be in motion when it is the clouds that are moving. And this error occurs because of inordinate distance, for where the distance is moderate this does not happen, so that, for instance, when a stick is lodged under water, and we see the water moving above it, rather than [seeing] the stick [moving] we perceive the motion of the water as it flows by.⁑

4.8 ◉ Accidit autem error predictus in motu lune cum nubes fuerint multe et continue, et causa eius est quoniam, sicut patuit superius, non comprehenditur motus nisi per accessum alicuius ad aliud vel recessum consideratum. Cum ergo paucitas fuerit nubium, possumus discernere motus earum propter uniuscuiusque ad stellam aliquam accessum apparentem aut recessum. Cum ergo celum nubibus fuerit coopertum, propter continuitatem earum non discernimus motum; verumtamen lunam modo in parte una videmus, modo in alia, unde ipsam motu celerrimo moveri concludimus. Eodem modo erit error per situm a temperamento egressum.

4.8 ◉ The aforementioned error occurs in the case of the moon’s motion when there are many clouds in continuous succession, and the reason for this error, as was shown above, is that motion is perceived only when something is seen to approach something else or to recede from something else.⁑ Thus, when there are few clouds, we can discern their motion according to the way each of them approaches or passes beyond some star that is seen. When the sky is covered with clouds, then, we do not perceive their motion because of their close succession; rather, we glimpse the moon [through them, appearing to be] somewhere at one time and elsewhere at another, so we conclude that it is moving very swiftly. In a similar manner, an error will arise when the spatial disposition [of a given object] falls outside [the range of] moderation.

4.9 ◉ Et per unumquodque octo supra dictorum est comprehensio per sensum, per scientiam, et per sillogismum.

4.9 ◉ And it is according to the eight previously mentioned conditions that perception occurs through [brute] sensation, or through recognition, or through deduction.⁑

◉[Capitulum 5]

◉[Chapter 5]

Pars quinta, in modis erroris visus propter sensum ex qualibet causarum errorem sensui inducentium

5.1 ◉ Ex predictis palam quod non est comprehensio per sensum nisi lucis et coloris tantum. Non ergo accidit error sensui nisi in luce et colore, nec accidit error per lucem aut colorem nisi propter intemperatam debilitatem eius aut fortitudinem, vel propter colorum minutorum diversitatem et debilium. Et hec colorum diversitas in luce debili venit ad oculum tamquam aliquid obscurum et tenebrosum, et etiam in luce forti, quando substantia colorum fuerit valde parva.

5.1 ◉ From what has been said before it is clear that only light and color are perceived through [brute] sensation. Thus, an error of [brute] sensation occurs only in the case of light and color, and an error involving light or color occurs only because of their inordinate weakness or intensity, or according to a difference among tenuous or weak colors. But in faint light this variation in color will reach the eye as a sort of darkness or shadow, and [this happens] even in intense light when the colors are exceedingly tenuous.

5.4 ◉ Longitudo inducit errorem sensus. Cum temperata fuerit elongatio corporis a visu, et fuerint in corpore partes minute in coloribus diverse ad quas proportionata partium elongatio sit intemperata, apparebit corpus illud unius coloris tantum, quoniam extra temperantiam est longitudo respectu particularium, licet omnia alia conveniant in temperantia. Et est error iste sensualis cum sensus comprehensivus sit coloris.

5.4 ◉ Distance causes an error in [brute] sensation. When the distance⁑ of a body from the eye is moderate, but there are small parts of various colors in the body, and the size of those parts is not proportionate to the distance [of the body from the eye], that body will appear to be of one color only, for the distance falls outside [the range of] moderation in relation to the particular features, even though all of the other conditions fall within [the range of] moderation. So this error is due to sensation since [it is] the sense [of sight that] apprehends color.

5.7 ◉ Situs sensum errare facit. Cum maxima fuerit corporis visi declinatio, occultabuntur visui minute eius particule. Et si fuerit in partibus minutis colorum diversitas, apparebit in totali corpore colorum unitas. Et accidit error propter situm tantum, quia opposito corpore visui in situ recto aliis sicut sunt immotis, percipientur et partes corporis et coloris cum solus situs egressus sit a temperamento. Idem error accidit ex situs intemperantia cum elongatio partium minutarum ab axe fuerit magna.

5.7 ◉ Spatial disposition causes [brute] sensation to err. When the inclination of a body that is seen is excessive, its small parts will be invisible to sight. Moreover, if the small parts are of different colors, the colors will appear to be blended throughout the whole object. And this error is due solely to spatial disposition, for when a body faces the eye directly with the other [preconditions] unchanged, just as they are, the parts of the body and of the color will be perceived [so the error arises] only if the spatial disposition falls outside [the range of] moderation. The same error occurs on account of an inordinate[ly skewed] spatial disposition when the distance of the small parts away from the [visual] axis is considerable.

5.8 ◉ Lux multum debilis errorem facit. Abscondit enim visui particulas corporis, et pretendit unitatem tenebrosi coloris. Et si lux ad temperantiam reduceretur, diversitas colorum aut diminutio partium non occultaretur quando lux sola extra temperantiam est sita.

5.8 ◉ Extremely faint light causes an error. For the tiny parts of a body are invisible to sight [in such light], and it produces a blending of shadowy colors. But if the light is brought back within [the range of] moderation, the difference in colors or the smallness of the parts will not be obscured [so this error arises]⁑ when the light alone falls outside [the range of] moderation.

5.9 ◉ Magnitudo errorem invehit. Cum partes corporis minutissime dissimiles fuerint totali in colore, latebunt visum partes ille propter sui parvitatem, et similiter eorum colores. Et apparebit color unicus in corpore, magnitudine sola extra temperantiam sita, quod non appareret si parvitas partium temperamentum non exiret.

5.9 ◉ Magnitude brings about error. When the smallest parts of a body differ in color from the whole, those parts will disappear from sight on account of their smallness, and the same for their colors. So the color will appear blended in the body when the magnitude alone falls outside [the range of] moderation, but this blending would not appear if the smallness of the parts did not pass beyond moderation.

5.10 ◉ Soliditas causa est erroris sensualis si remissa fuerit soliditas, ut in cristallo, unde cum superponitur ei corpus coloratum, videtur cristallum colore illo affectum propter soliditatis parvitatem a temperamento egressam, quod non accideret si cristallum magis solidum esset.

5.10 ◉ Opacity is a cause of an error in sensation if the opacity is scant, as [it is] in the case of glass, so when a colored body is placed behind it, the glass seems to take on that [body’s] color because its opacity is so attenuated as to fall outside [the range of] moderation, but this would not happen if the glass were more opaque.

5.11 ◉ Ex raritate aeris procedit error sensualis. Cum intercidit visum et corpus oppositum flamma, licet fortis coloris sit corpus visum, videbitur tenebrosum, et sola aeris raritas egressa est temperamentum.

5.11 ◉ An error of sensation arises from the transparency of the air. When a flame is interposed between the eye and a facing body, even when the color of the body that is seen is intense, that body will appear shadowy, but [it is] only the transparency of the air [that] has fallen outside [the range of] moderation.

5.12 ◉ Tempus est causa erroris. Quoniam, si subito super corpus diversorum colorum fiat visus directio, apparebit color singularis donec prolongetur inspectionis duratio, luce dico sub qua comprehenditur corpus non forti.

5.12 ◉ Time is the cause of error. For, if sight is abruptly directed toward a body of different colors, the body will appear to be of a single color until the glance is prolonged, provided, I [should] add, that the light in which the body is perceived is not intense.

5.13 ◉ In luce enim debili non statim immutatur visus secundum quemlibet colorum particularium, quod accideret in luce forti.

5.13 ◉ Indeed, in faint light sight is not immediately affected by any individual color, as it would be in intense light.

5.14 ◉ Visus aliquando errorem pretendit. Luce enim forti in visu cadente, leditur visus, et statim ad colorem alicuius corporis conversus ipsum tenebrosum recipit donec paululum steterit et lesio recesserit. Pari modo, cum aderit oculis infirmitas, occultabitur visui colorum veritas, under error fit ex sola visus qualitate a temperamento recedente.

5.14 ◉ Sight [itself] sometimes presents an error. For if an intense light strikes the eye, it disrupts sight; so, as soon as the eye is directed toward the color of any body, it receives that color in a shadowy way until it rests a bit and the disruption fades. By the same token, when the eye suffers an infirmity, the true colors [of objects] will be obscured from sight, so an error arises solely from the fact that the condition of the eye falls short of moderation.

5.15 ◉ Patet ergo quod accidunt errores visui secundum quodlibet predictorum considerati, et accidunt in sensu tantum cum ex solo sensu fiat comprehensio colorum.

5.15 ◉ It is therefore evident that errors arise in sight according to each of the aforementioned cases under consideration, and they occur in sensation only, because the perception of colors takes place through [brute] sensation.

◉[Capitulum 6]

◉[Chapter 6]

Pars sexta in modis erroris visus per scientiam accidentis per quamlibet causarum errorum visus

6.1 ◉ Dictum est in libro secundo quod non nisi per scientiam fit diffinitionis rei adquisitio. Provenit enim diffinitio ex similitudine vel dissimilitudine alicuius rei cum alia in communi forma.

6.1 ◉ It was claimed in the second book that it is only through recognition that [sight] apprehends what an object is.⁑ For [the perception of] what a thing is arises from the similarity or dissimilarity of one object to another in [terms of] a common form.

6.2 ◉ Et proprium est scientie communicare rem visui presentem cum re prius visa in forma recepta, et ex hac communicatione adquiritur diffinitio rei cuiuscumque. Diversificatur autem scientia in scientia individui et universalis, aut utriusque, et omnis error scientie erit error in aliquo istorum aut in utroque.

6.2 ◉ And it is in the nature of recognition to assimilate an object that is currently in view to an object that has been seen before according to an acquired form, and from this assimilation sight apprehends what any thing is. Moreover, recognition is differentiated according to recognition of the individual, or [recognition] of the universal, or [recognition] of both, so every error in recognition will occur in either or both of these categories.

6.3 ◉ Cum ergo res aliqua aut alia aut alterius speciei apparet quam sit in rei veritate, erit error in diffinitionis assignatione, nec accidit error iste nisi aliquod istorum predictorum fuerit extra temperamentum.

6.3 ◉ Therefore, when some object appears other than it actually is or of another kind than it actually is, there will be an error in ascribing [the proper] definition [to it],⁑ and this [type of] error does not occur unless one of the aforementioned conditions falls outside [the range of] moderation.

6.45 ◉ Error enim scientie in longitudine erit. Si a longitudine magna videatur homo notus, apparebit forsitan esse alius videnti notus, unde aliquando videns Petrum visum dicit esse Martinum, cum constet utrumque ei esse notum.

6.6 ◉ In forma communi erit error. Si quis ab aliqua longitudine videat equum et putet se videre asinum, in utraque formarum—scilicet singularis et communis—est error, ut si quis a longitudine magna videt equum sibi notum et existimat se videre asinum sibi cognitum. Pari modo accidit error in arboribus triplex: in individuis, in communibus formis, in utrisque. Unde aliquando una amigdalus existimatur alia; aliquando a longitudine magna pirus magna apparet amigdalus; aliquando pirus Petri apparet amigdalus Martini. Eadem triplicitas erroris ex longitudine accidit plurimum in vestibus, lapidibus, et aliis.

6.6 ◉ There will be error in terms of the common form. If someone sees a horse from some distance and assumes that he sees an ass, there is an error in both forms—i.e., individual and common—as [happens] for instance, when someone sees a horse that is known to him at a considerable distance and assumes he sees an ass that he knows. Similarly, a threefold error occurs in the case of trees: according to individuals, according to common forms, and according to both. Hence, one almond tree is sometimes judged to be another one; or from a great distance a large pear tree sometimes appears to be an almond tree; or at times Peter’s pear tree appears to be Martin’s almond tree. The same threefold error according to distance often happens in the case of clothing, stones, and other things.

6.7 ◉ Aliquando videtur res incognita et contingit error in scientia, sicut si aliquis ignem viderit longe remotum in aere, existimat se stellam videre. Planum autem quemlibet errorem predictum cadere in scientiam cum in eo fiat assignatio diffinitionis rei vise que non est in ea veritate. Palam etiam quod accidit error prefatus ex longitudine extra temperantiam exeunte. Ea enim ad temperamentum reducta, aliis erroris et causis, sicut sunt, manentibus, non accidit error in scientia predictus.

6.7 ◉ Sometimes an unfamiliar thing is seen and an error in recognition arises, as [happens] when someone sees a fire far off in the air and judges that he sees a star. It is, moreover, clear that each of the previously discussed errors occurs in recognition when a definition that does not actually pertain to it is ascribed to the visible object. It is also clear that the aforesaid error occurs because the distance falls outside [the range of] moderation. For if that distance is restored to moderation while other errors and causes, such as they are, persist, the aforementioned error in recognition does not occur.

6.8 ◉ Situs errorem infert scientie. Cum corpus aliquod multum fuerit elongatum ab axe, non erit certa forme comprehensio. Unde aliquando in hoc situ Petrus existimabitur Martinus; aliquando equus putabitur esse asinus, sicut in arboribus et vestibus; aliquando equus notus putabitur Brunellus. Et in hac incertitudine forsan eligetur veritas, forsan falsitas. Cum enim incertum sit in hoc situ iudicium, casualis erit electio.

6.8 ◉ Spatial disposition produces an error in recognition. When some body lies extremely far from the [visual] axis, there will not be a determinate perception of its form. Accordingly, in such a situation Peter may be judged to be Martin; or a horse may be judged to be an ass, as happens with trees and clothing; or a horse that is known will sometimes be assumed to be [the ass] Brunellus.⁑ In the case of this indistinct sort of perception, a correct [ascription] may be chosen, or a false one may be. Indeed, if the judgment is indeterminate in this situation, the choice will be fortuitous.

6.9 ◉ Accidit autem error ex intemperamento situs, quoniam, ipso ad temperantiam reducto, non errabit iudicium ex scientia sumptum.

6.9 ◉ This error arises from an immoderate spatial disposition, for if it is restored to moderation, the judgment based on recognition will not be erroneous.

6.10 ◉ Pari modo in magna corporis declinatione non verificantur particule minute, unde accidit in hoc situ error figure, coloris, magnitudinis; forsan enim quadratum videtur circulare, et ita in quantitate et colore.

6.10 ◉ By the same token, when a body is slanted to an extreme extent, its tiny parts are not [perceived] distinctly, so in this situation there arises an error [in the judgment] of shape, or color, or size; [in such a situation] in fact, a square may appear circular, and similar errors may arise in the case of size and color.

6.11 ◉ Egressio lucis a temperamento errorem inducit scientie. Debilitas enim lucis nimia errorem infert forme, unde accidit error in crepusculis in animalibus, vestibus, arboribus—scilicet triplex: vel in individuo, vel in specie, vel in utroque—quod non accideret in temperata luce.

6.11 ◉ An error in recognition arises from light’s falling outside [the range] of moderation. For excessively faint light causes an error [in perception] of the form, so during twilight an error occurs in [the perception of] animals, clothing, or trees—and this error is threefold: according to individual [nature], according to kind, or according to both—and it would not occur in moderate light.

6.12 ◉ Amplius, si fuerit egressus lucis a temperamento, proportionato viso opposito visui, accidit error predictus, licet non sit intemperata in se lux, sicut evenit in quadam ave arabice aluerach dicta. Non enim videri potest nisi de nocte. Tamquam ignis de die vero, cum non plene discernatur, forsan papilio cui est similis putabitur. Et sic accidit error in diffinitione rei ex intemperata luce.

6.12 ◉ Furthermore, when light falls outside the range of moderation that is proportionate to a visible object that faces the eye, the aforementioned error occurs, even when the light is not immoderate in and of itself, as happens in the case of a certain flying creature called »aluerach« in Arabic.⁑ For it can be seen only at night. But just as a fire is not clearly discerned when [it is viewed] in daylight, [that creature] may be taken [in daylight] for a moth, which it resembles. And so an error occurs in the definition of the object on account of immoderate light.

6.14 ◉ Quantitas extra temperantiam suam errare facit scientiam, unde aliquando formica pre sui parvitate existimatur musca tritico innata, et aliquando eadem causa sinapis granum reputatur nasturtium.

6.14 ◉ Size that falls outside its [range of] moderation causes recognition to err, so sometimes, because of its smallness, an ant is judged to be a fly perched on wheat, and sometimes, for the same reason, a mustard seed is taken for a [seed of] water cress.

6.1617 ◉ Soliditas a temperamento egressa errorem efficit. Cum cristallo continuatur corpus rubeum, alia cristalli facie visui opposita, existimabit videns colorem cristalli esse rubedinem, unde error est scientie, quia in coloris diffinitione.

6.18 ◉ Raritas aeris nimis diminuta erroris est causa, unde in eius spissitudine fit error in rei diffinitione. Similiter, si oculo et corpori viso interponatur corpus cuius raritas extra temperantiam est respectu raritatis aeris temperate, sicut est vitrum, existimabitur color corporis oppositi mixtus ex colore proprio et colore vitri. Et est iste error in coloris diffinitione. Pari modo, si anteponatur oculo pannus multum rarus et post illum videatur corpus, apparebit color corporis mixtus.

6.18 ◉ An inordinate decrease in the transparency of the air is a cause of error, so an error in [judging] what a thing is occurs when the air is hazy. Likewise, if an object is placed between the eye and some object that is seen, and if the transparency of that body is immoderate with respect to the moderate transparency of the air, as is glass, the color of the facing body will be judged as a mixture of its own color and the color of the glass. And so there is an error in the definition of [what is] colored. By the same token, if a sheer cloth is placed in front of the eye and a body is seen behind that cloth, the color of the body will appear mixed [with that of the cloth].

6.20 ◉ Sed oritur questio quomodo post panni oppositionem appareat coloris corporis oppositi mixtura cum partiales corporis colores non accedant ad oculum nisi per panni foramen, et ex panno non accedat ad oculum color nisi ex filis eius per que non transit color corporis.

6.20 ◉ But there arises the question of how the color of a body facing the eye from behind the cloth appears mixed [with that of the cloth] since the colored spots on the body only reach the eye through the interstices in the cloth, whereas the color of the cloth reaches the eye only from the threads, through which the color of the body does not pass.

6.21 ◉ Et huius rei veritas est quod, licet partiales corporis colores singillatim veniant, et in sua loca cadant, nec commisceantur filorum coloribus, sed filorum colores sint ab eis separati intra visum et extra, nec sit ibi aliqua confusio, tamen, quia valde propinqua sunt puncta in que incidunt color corporis superficialis et color fili, cum non sit distantia sensibilis inter ea, videntur quasi punctus, unde colores illi apparent unus ex eis mixtus.

6.21 ◉ The truth of the matter is that, even though the spots of color on the body reach [the eye] discretely and fall on their [separate] places [on the eye] so as not [actually] to mingle with the colors of the threads, and even though the colors of these threads are separate from those [other] colors both in and outside the eye so that there is no [actual] commingling of them, nonetheless, since the spots upon which the color of the body’s surface and the color of the thread strike [the surface of the eye] are extremely close to one another, there being no perceptible separation between them, the [neighboring spots] appear to coalesce, so their colors appear as a perfect blend.

6.22 ◉ Si autem magna sint panni foramina, discernetur et panni et coloris corporis veritas sine mixtura, et quanto compressior fuerit foraminum strictura verior apparebit mixtura, unde viso corpore post pannum lane videbitur mixtura colori plurimum consonans colorum filorum. Foramina enim panni lanei sunt in se stricta, et quoniam pilis panni teguntur, efficiuntur et strictiora.

6.22 ◉ If, however, the interstices in the cloth are large, the actual color of the cloth and of the body will be discerned without mingling, but the narrower these interstices become, the more evident the mingling will be. Accordingly, when a body is viewed through wool cloth, the blend of colors will frequently appear to conform to the color of the threads, for the interstices of wool cloth are narrow in and of themselves, and since the threads are covered with hair, the interstices are made even narrower.

6.2324 ◉ Aliud erroris ex raritate exemplum cum aliquis ioculator facit ymagines ligneas moveri, umbre earum inspicienti per pannum, sicut solet fieri lineum subtilem, apparebunt aves aut animalia formis ymaginum consona, nec accidit error iste in diffinitionis assignatione nisi ex raritatis aeris diminutione.

6.25 ◉ Temporis distantia preter temperamentum erroris scientie est causa. Si quis per foramen inspiciat corpus transiens veloci motu, non plene adquiret formam corporis, unde accidet error in individuo, in specie, vel in utroque, ut in equis, hominibus, arboribus. Similiter accidit etiam sine foramine; si quis subito aliquid videat quod statim a visu recedat errabit in comprehensione illius forme, unde forsan erit error in specie, individuo, vel utroque. Et erit error iste in solo tempore.

6.25 ◉ An interval of time that falls outside [the range] of moderation is a cause of error in recognition. If someone looks through a window at a body that passes by swiftly, he will not apprehend the form of that body clearly, so an error in [perceiving] its individual [nature], its kind, or both will occur, as [happens] in the case of horses, human beings, and trees. The same thing also happens when there is no window; if someone glimpses something that immediately disappears from sight, he will err in the perception of its form, so there may be an error in [the perception of its] kind, or [of its] individual [nature], or [of] both.⁑ But this error will be due solely to time.

6.27 ◉ Visus solus errorem facit. Si lux solis fortis descendat super colorem viridem fortem vel intensam rubedinem, adhibito visu, ledetur. Et cum aliquid deinceps inspexerit, aliud quidem ei quam sit in veritate apparebit, aut alterius coloris, propter presentiam lesionis. Et modo simili accidunt errores plurimi.

6.27 ◉ Sight by itself causes error. If intense sunlight shines on a bright-green or deep-red color, and sight is turned toward it, it will be disrupted. Then, if the eye looks at something else, the object will appear to be something other than it actually is, or of another color than it actually is, because of the continuing disruption. And several errors occur in a similar way.

6.2930 ◉ Pari modo in oculorum egritudine aliquando equus apparet asinus, et accidit error triplex predictus et in pluribus. Et planum est errorem esse in scientia ex sola immoderantia visus.

6.31 ◉ Palam ergo sunt errores qui in visu scientie accidunt secundum singulas erroris visus causas.

6.31 ◉ Hence, it is clear that there are errors of sight that occur in recognition according to the particular causes of visual error.

◉[Capitulum 7]

◉[Chapter 7]

Pars septima in modis erroris visus qui accidunt in sillogismo secundum singulas erroris visus causas

7.1 ◉ Plurima eorum quorum in visu sit comprehensio adquiruntur ex sillogismo, sicut patuit ex precedenti libro, et precessit explanatio eorum quorum per sillogismum sit comprehensio et quod ex eis occurrat sensui compositio in formis singulis. Cum ergo accidit error in aliquo illorum, erit error in comprehensione facta per sillogismum. Bipartita est autem partitio erroris in sillogismo; aut enim erit in propositionibus aut in earum congregatione. In propositionibus tripliciter: aut enim falsa loco vere sumitur, aut particularis loco universalis, aut in comparatione propositionum erratur. Verbi gratia, si fuerint in re visa partes que appareant et partes que lateant, que tamen comprehensibiles sunt visui, si in illam figatur visus intentio, cum videntem partes ille pretereant, ex eis tantum que in re visa adquirit concludit. Cum etiam conclusiones aliquas quas rei illi accidentes considerat, existimat eas ei accidere ex partibus eius apparentibus, quoniam non nisi eas computat. Cum vero intuitus diligentiam in re illa figit partes prius latentes, percipit et errorem cognoscit. Enumerabo igitur errores eorum que comprehenduntur per sillogismum quorum numerus est 22, ut sic pateant errores in sillogismo. Et hec enumeratio erit secundum unamquamque octo causarum prius dictarum.

7.1 ◉ Many of the things perceived by sight are apprehended through deduction, as was shown in the preceding book, and what [sorts] of things are perceived through deduction have been explained, and [it has been explained] that, on the basis of these things, a composite of particular forms reaches the sense [of sight]. Thus, when an error occurs in any of those things, there will be an error in perception that is based on deduction. Now deductive error is of two kinds, for it will occur either in the premises [of the deduction] or in the way those premises are arranged together. In the case of premises there are three [types of error]: a false premise is taken for a true one; a particular [premise] is taken for a universal one; or there is an error in the correlation of premises. For instance, if there are parts on a visible object that are apparent and parts that are not apparent but still perceptible to sight, when the form of that object is impressed on the eye and those parts [that are not apparent] are not seen, then the final perception [of the object] is based exclusively on those parts of the visible object that are [actually] apprehended. Moreover, when it examines the final perceptions arising from that object, [the visual faculty] bases its conclusions on the parts that are apparent, for it can only take them into account. However, when a close inspection of that thing reveals the parts that were not apparent before, the visual faculty perceives and recognizes its error. Accordingly, in order to make them clear, I shall list the errors [that pertain to] those things that are perceived through deduction, those things being twenty-two in number. And this listing will be [presented] according to each of the eight previously discussed causes.

Distinctio 1 ◉ Et primo secundum longitudinem

7.2 ◉ Dico igitur quod longitudo egressa a temperamento errare facit videntem in longitudine, sicut accidit cum quis arbores valde remotas inspexerit, licet plurimum distent inter se; videbuntur quasi coniuncte aut saltim existimabuntur sibi propinque.

7.2 ◉ Accordingly, I say that when the distance falls outside [the range of] moderation it can cause the viewer to err about distance, as happens when someone looks at trees that are very distant. Even if they are quite far apart from one another, he will see them contiguous to one another or will at any rate judge them to be near one another.⁑

7.3 ◉ Ob eandem causam evenit quod stelle alique reputantur quasi coniuncte, licet plurimum distent in veritate. Ob hoc stelle erratice existimabuntur ab omnibus in eadem superficie cum fixis, licet plurimum elongate sint ab eis. Est igitur error in longitudine propter egressum longitudinis a temperantia, et est error iste in sillogismo cum longitudinis tantum per sillogismum fiat comprehensio.

7.3 ◉ For the same reason, it happens that certain stars are assumed to cluster together even though they are very far apart. Accordingly, the planets will be judged by everyone to lie on the same surface as the fixed stars, even though they lie quite far from them. There is thus an error in [the perception of] distance because the distance falls outside [the range of] moderation, and this is an error in deduction since the perception of distance occurs only through deduction.

7.4 ◉ Longitudo extra temperantiam situs errorem inducit, quoniam a tali longitudine corpus declinatum apparebit rectum, et ob hoc corpus quadratum in hac longitudine declinatum videbitur oblongum. Eodem modo oblonga apparebit circularis forma si in hac longitudine fuerit declinata, nec accidet error iste nisi ex declinationis occultatione que latet in tanta longitudine, si enim appareret declinatio, non esset assignate quare occultaretur veritas corporalis forme. Est igitur error in solo situ ex longitudinis immoderatione.

7.4 ◉ A distance that falls outside [the range of] moderation causes an error in [the perception of] spatial disposition, for from such [an inordinate] distance an inclined body will appear to face the eye directly, and so a square body that is slanted will appear oblong at that distance. By the same token, a circular form will appear oval at that distance if it is inclined, and this error will arise only because the inclination is hidden from sight at such a distance, for if the inclination were apparent, there would be nothing to obscure the actual form of the body. Hence, there is an error in [the perception of] spatial disposition only because of the inordinate distance.

7.5 ◉ Et quare ignoretur situs est hec ratio: Excessus unius radiorum in latus quadrati cadentium super longitudinem alterius non est proportionalis respectu totalis remotionis cor poris a visu, proportione dico sensibili; unde propter insensibilitatem excessus non existimabitur maior aliquo aliquis radius.

7.5 ◉ The reason that the spatial disposition will not be [properly] apprehended is as follows: The difference in length between [any] one of the rays falling on the side of the square and [any] other [ray] is disproportionate[ly small with respect] to the whole distance of the body from the eye, in terms, that is, of a perceptible ratio; so, on account of the imperceptibility of the difference, no one ray will be judged longer than any other.

7.6 ◉ Reputatur ergo oblonga quadrati forma, quoniam unum latus eius non declinatum respectu visus cadit in partem oculi, et in minorem incidit forma lateris declinati, quoniam sub minori angulo. Et erit minoritatis perceptio secundum quod fuerit quadrati declinatio, et quoniam non attenditur declinatio, existimabitur unum latus maius alio, quoniam sub maiori angulo, proinde forma apparebit oblonga. Pari ratione in circulari forma, unus dyameter maior apparet alio, unde reputatur oblonga. Et est error iste ex intemperata longitudine, quod non accideret si temperata esset.

7.6 ◉ Thus, the form of the square is deemed to be oblong because the side of the square that is not inclined with respect to the viewer falls on one area of the eye whereas the form of the side that is inclined falls on a smaller area, because it subtends a smaller angle. But the perception of its smallness will depend on the inclination of the square, and since the inclination is unnoticed, one side will be judged longer than the other because [it is seen] under a smaller angle, which is why the form will appear oblong. For the same reason, in the case of a circular form, one diameter appears longer than the other, so it is deemed to be oval. And this error is the result of inordinate distance and would not arise if the distance were moderate.

7.7 ◉ Si vero longitudo, licet intemperata, non fuerit multum magna, sed valida sit illius corporis declinatio, perpendet fortassis videns declinationem sed non declinationis veritatem; immo minorem existimabit quam sit. Et conferet declinationem lateris angulo sub quo comprehenditur, unde minor apparebit quantitas lateris quam sit, et sic reputabitur quadrati forma oblonga, sed minus quam prius.

7.7 ◉ However, if the distance, though immoderate, is not too great, and the inclination of the body is substantial, then the viewer may take the inclination into account, but not the actual inclination; instead, he will judge it to be less [sharp] than it is. And he will analyze the inclination of the side by the angle under which it is perceived, so the side will appear smaller than it is, and he will thus suppose that the form of the square is oblong, but less oblong than [it appeared] before [when the distance was inordinate].⁑

7.8 ◉ Superfluitas longitudinis errorem generat corporeitatis, corporeitas enim est ex deviatione superficiei, et comprehenditur notitia corporeitatis ex notitia huiusmodi deviationis. Cum ergo accidit error in corporeitate, erit in superficiei vel superficierum dispositione, velut si superficies corporis incurvata ex aliqua longitudine videatur plana, aut plana existimetur curva. Et hec apparentia erit in figura, est enim figura superficierum corporis dispositio. Respicit etiam situm dispositio superficierum, unde corporeitas includitur sub figura et situ, unde errorem corporeitatis gerit in se error figure et situs. Accidit autem error figure absque situs errore ex longitudinis immoderatione.

7.8 ◉ An excessive distance produces an error in [the perception] of corporeity, for [the perception of] corporeity is based on the curvature of the surface, so the notion of corporeity is grasped from the notion of this sort of curvature. Thus, when an error arises in regard to corporeity, it will be in regard to the disposition of the surface or surfaces [of an object], for instance, when the curved surface of a body appears flat at a certain distance, or when a flat [surface] is judged to be curved. And this appearance will involve shape, for shape is the arrangement of the surfaces of a body. The arrangement of surfaces also has to do with spatial disposition, so corporeity is a matter of both shape and spatial disposition. Hence, an error in [regard to] corporeity carries with it an error in [regard to] shape and spatial disposition. But, on the basis of inordinate distance, an error in [regard to] shape [can] happen without an [accompanying] error in [regard to] spatial disposition.

7.9 ◉ Verbi gratia, figura multorum laterum equalium directe visui opposita in longitudine intemperata circularis apparet non ob aliud quidem nisi quia anguli figure divisi sunt et imperceptibiles visui. Longitudo enim illa abscondit visui etiam proportionalia toti, etsi non totum.

7.9 ◉ For instance, a figure with many equal sides facing the eye directly at an inordinate distance appears circular for no other reason than that the corners of the figure are manifold and [thus] imperceptible to sight. For at that distance the [corner segments, while] nonetheless proportional to the whole figure, are invisible to sight, even though the whole figure is not.

7.10 ◉ Eodem erroris tenore ab hac longitudine, linea curva existimatur recta, non enim perceptibilis est maioritas accessus unius linee partis incurvate ad visum super partis eiusdem remotioris accessum, quare occultatur incurvatio partium, licet error non accidat in situ linee illius.

7.10 ◉ The very same type of error [occurs] when a curved line is assumed to be straight at this distance, for the [relative] closeness to the eye of one part of the curved line in comparison to the [relative] remoteness of the other is imperceptible, so the curvature of the parts is not apparent, even though no error may arise in [regard to] the spatial disposition of that line.

7.1112 ◉ Similiter visa spera ab hac longitudine, reputabitur superficies plana quoniam propinquitas tumoris eius imperceptibiliter propinquitatem extremitatum ab hac longitudine excedit, unde existimatur equalis partium propinquitas— unde superficiei planitudo, inde est quod sol et luna superficiales videntibus reputantur, que erronea excluderetur figure reputatio si temperata esset longitudo.

7.13 ◉ In magnitudine corporis erit error ex intemperata longitudine, quoniam videbitur multo minus quam sit in veritate.

7.13 ◉ There will be an error in [the perception of] the size of a body on account of inordinate distance, for it will appear much smaller than it actually is.

7.14 ◉ Huius rei ratio est quoniam, ut diximus, longitudo intemperata est que partes proportionales toti proportione etiam sensibili abscondit visui, et cum fuerit occultatio partium sensui perceptibilium, anguli in quos cadunt non sentiuntur, licet sint totali angulo proportionales.

7.14 ◉ The reason for this, as we said, is that a distance is inordinate if the parts that are sensibly proportionate to the whole are invisible to sight, and when the perceptible parts [of an object] cannot be sensed, the [visual] angles they subtend are not sensed, even if they are proportionate to the whole [visual] angle.

7.15 ◉ Unde, cum discurrit axis rem visam, absconduntur ei linee multe ex ea et partes multe, unde minor efficitur totalis apparentia.

7.15 ◉ Hence, when the [visual] axis scans the visible object, many of its lines and many of its parts are not apparent to it, so the whole is made to appear smaller [than it actually is].

7.16 ◉ Amplius magnitudo partis alicuius corporis non consideratur nisi secundum magnitudinem anguli in quem cadit, et magnitudo anguli attenditur secundum partem in visu sectam. Et partis secte quantitas non existimatur nisi secundum duo puncta illius partis terminalia, et puncta illa sunt sensibilia et parti secte proportionalia, quoniam a longitudine tanta existimatur res visa secundum fines toti viso proportionales. Aliter enim non essent fines illi sensibiles. Et fines partis secte directe opponuntur finibus partis vise ei proportionalibus. Puncta ergo illa partis secte terminalia abscondunt ex re visa partes sensibiles. Cum ergo incedit axis super singulas rei partes ex singulis partibus, absconduntur partes sensibiles, et ita minor apparet totalis rei vise quantitas. Cum autem videtur corpus a temperata longitudine, puncta terminalia partis secte valde sunt parva et quasi insensibilia ad ipsam collata. Fines enim rebus visis insensibiles eligit in temperata longitudine estimatio videntis, unde non absconduntur toti proportionales partes, quare corpus non apparet minus quam habeat veritas eius. Amplius, sicut dictum est in superioribus, magnitudo non adquiritur in corpore nisi ex longitudinis et anguli collatione. Et iam dictum est quod in immoderata longitudine apparet minor angulus, quia minor est in veritate, sed remotionis non fit discretio.

7.16 ◉ Furthermore, the size of any part of a body is gauged only according to the size of the angle it subtends, and the size of the angle depends on the [size of] the area demarcated on the eye [by the visual cone]. But the size of the area that is demarcated [by the visual cone] is judged exclusively on the basis of the two terminal spots [defining] that area, and those spots are sensible and proportionate [in size] to the area that is demarcated [by the visual cone], because from such a distance the visible object is judged according to limits that are proportionate to the whole of the visible object. Otherwise, in fact, those limits would not be sensible. Now the limits of the area demarcated [by the visual cone on the eye] lie in a direct line with the limits of the areas on the visible object that are proportionate to them. Hence, the terminal spots of the area that is demarcated [by the visual cone on the eye] block out sensible areas on the visible object [that are in line with them]. Therefore, as the axis touches on specific parts among the individual portions of the object, it fails to sense [some] parts that are [proportionately] sensible, and so the whole visible object appears smaller [than it actually is]. But when a body is seen at a moderate distance, the terminal spots of the area that is cut off [by the visual cone on the eye] are tiny and imperceptible relative to that area [as a whole]. Indeed, the judgment of the viewer culls out the imperceptible limits in the visible object [when it is seen] at a moderate distance, so no areas that are proportionate to the whole are invisible, which is why the body does not appear to be smaller than it actually is.⁑ Furthermore, as has been said above, size is apprehended in a body only by collating distance and [visual] angle.⁑ And it has already been said that, at an inordinate distance, the angle appears smaller because it actually is smaller, but there is no discernment of distance.

7.17 ◉ Iam enim superius patuit quod remotio moderata comprehenditur per corpora interposita, immoderata vero minime. Cum ergo remotio rei vise sit ignota, fiat fortassis collatio ipsius ad longitudinem notam. Et existimabit eam minorem, quare putabitur in angulo minoritas et in longitudine quam sit in veritate, unde error in corporis quantitate. Et quanto augmentabitur longitudo invalescet error, et adeo poterit augmentari longitudo quod existimabitur quantitas corporis quasi punctalis, et si ultra creverit longitudo, occultabitur visui corpus illud.

7.17 ◉ In fact, it was shown above that a moderate distance is perceived on the basis of intervening bodies, whereas at an inordinate distance [this basis for judgment] does not apply at all.⁑ Therefore, when the distance of the visible object is undetermined, it may be assimilated [by the faculty of discrimination] to a determinate distance. And the viewer will judge the object to be smaller [than it actually is] because he will suppose the [visual] angle and the distance to be smaller than they actually are, so [there will be] an error [in the perception of] the size of the body. And as the distance increases, the error is reinforced until the distance can become so great that a body will be judged to be the size of a point, and if the distance is further increased, that body will disappear from view.

7.19 ◉ Simili modo accidit corporis occultatio in temperata longitudine non ex ipsa remotione sed ex coloris corporis debilitate. Et patet occulationem fieri in debili colore, quoniam, si loco huius corporis in eadem elongatione statuatur corpus eiusdem quantitatis in quo sit fortitudo coloris, non latebit visum sicut corpus in quo fuerit coloris debilitas, quare aliquando occultat corpus visui non elongatio, non diminuta quantitas, sed sola coloris debilitas.

7.19 ◉ Likewise, a body can become invisible at a moderate distance, not because of the distance itself but because of the faintness of the body’s color. And it is clear that visibility is lost in the case of faint coloring, for if the body [that cannot be seen because of its faint color] is replaced at the same distance by an intensely colored body of the same size, this [latter body] will not be invisible to sight as [was] the faintly colored body, so sometimes it is not distance or smallness but, rather, weak color by itself that causes a body to become invisible.

7.20 ◉ Amplius evenit aliquando corporis occultatio ex coloris eius similitudine cum interpositorum ipsi et visui corporum colore, et hoc in temperata longitudine. Unde corpus album a longe positum, effusa nive super superficiem interiacentis terre, non discernetur, nive vero remota percipitur. Et palam quod erit occultatio ex hac colorum ydemptitate, quoniam, si loco corporis illius opponatur visui ab eadem remotione corpus equale alterius coloris, non occultabitur.

7.20 ◉ Furthermore, a body may happen to lose visibility because of the similarity between its color and the color of bodies that lie between it and the eye, and this [can happen] at a moderate distance. Accordingly, when snow blankets the intervening ground, a white body lying at a distance will not be discerned, but the distant snow is perceived. And it is obvious that the body will be lost to sight because of the sameness of color, for if the [white] body is replaced at the same distance by an equivalent body of a different color, this [latter body] will not be invisible.

7.21 ◉ Cum igitur aliqua res opposita visui non percipitur, poterit esse causa absconsionis superfluitas elongationis ad partem visus insensibilem formam dirigentis, vel quasi punctalem. Quod si in partem visus sensibilem forma inciderit, poterit iterum preterire visum aut propter coloris remissionem aut colorum rei vise et corporum interiacentium conformitatem.

7.21 ◉ Hence, when any object facing the eye fails to be perceived, the reason for its invisibility may be that the distance over which the form is radiated is inordinate [so that the form is projected] upon an imperceptible spot on the eye, or upon a spot that amounts to a point. If, however, the form is projected upon a perceptible spot on the eye, it may escape notice because of a weak color or because the colors of the visible object and the colors of intervening objects are similar.

7.22 ◉ Amplius accidit error in rei vise quantitate etiam in temperata longitudine. Quoniam corpore aliquo secundum moderationem elongato et viso, occultabuntur visui partes eius minute que quidem in minori elongatione apparerent, licet fortassis non plene, et paululum amplius elongate iterum minus plene. Et minuetur comprehensionis plenitudo invalescente remotionis augemento donec occurrat partium occultatio, licet non egrediatur temperantiam illa elongatio.

7.22 ◉ Furthermore, an error [in perceiving] the size of a visible object can occur at a moderate distance. For if some body is seen at a moderate distance, tiny parts of it will disappear from sight, but those parts would be seen at a shorter distance, although perhaps not clearly, and if the distance is increased somewhat, they will be seen even less clearly. And as the distance increases, the clarity of perception decreases until the parts disappear from sight, even though the distance may not fall outside [the range] of moderation.

7.23 ◉ Iterum immoderata remotione pars aliqua plene comprehenditur, et aliqua minimarum eius partium occultatur, quoniam elongatio rei egressa est a temperamento proportionato ad partes illas, licet non respectu totalis corporis aut comprehense partis. Et licet nota sit homini hec longitudo, tamen accidit error in comprehensione quantitatis partium, et hoc propter angulum sub quo pars comprehenditur cuius capacitas minor existimatur quam habeat veritas. Et causa apparentie minoritatis eius est ex punctis terminalibus secte in visu partis partium occultantibus, et anguli capacitatem constringentibus. Igitur, cum immoderata fuerit rei vise ab aliquo distantia, perveniet error in eius quantitate dupliciter: et ex anguli minoritate et ex longitudinis incertitudine. Immoderata vero longitudine erit error in quantitate minutarum partium ex errore anguli tantum. Et hee sunt cause quare corpus existimatur minus quam sit in temperata longitudine.

7.23 ◉ Likewise, at an inordinate distance a certain portion [of the object] is perceived clearly while certain of its tiny parts are invisible, for the distance of the object has fallen outside [the range of] moderation in relation to those parts, even though it has not done so with respect to the whole body or the portion of it that is perceived. Moreover, even though the distance may be known to the viewer, the error in perceiving the size of the parts still occurs because the size of the [visual] angle under which a [given] part is perceived is judged to be less extensive than it actually is. And the reason the angle appears smaller is that the terminal spots of the area that [the forms of] the parts demarcated on the [surface of the] eye are invisible, so the extent of the angle is shrunk [by that much].⁑ Therefore, when the [size of] the visible object is inordinate[ly small] with respect to the given [moderate] distance, an error in [the perception of] its size will arise on the basis of two things: the smallness of the [visual] angle and the indeterminate [measure of its] distance. At an inordinate distance, however, the error in [the perception of] the size of the tiny parts will be due to an error [in the perception of the size] of the angle only. These, then, are the reasons why a body is judged to be smaller than it is at a moderate distance.

7.24 ◉ Immoderatio longitudinis aliquando errorem inducit maioritatis, unde in longitudine non temperata (minima scilicet), quando corpus visum fuerit multum prope oculum, videbitur corpus maioris quantitatis quam in longitudine temperata vel quam sit re vera.

7.24 ◉ An inordinate distance sometimes causes an error [that leads to an exaggerated perception] of size, so that at an inordinate distance (i.e., one that is too small), when the body that is seen lies very near the eye, the body will appear larger than it does at a moderate distance and larger than it actually is.

7.25 ◉ Et hoc duplici de causa, quoniam, ut dictum est, intellectus longitudinem et angulum considerat et inde quantitatem corporis sillogizat, et in hac elongatione angulus piramidalis est valde magnus. Et elongatio corporis non existimatur nisi a visus superficie ad superficiem corporis, non enim potest cadere in visus estimationem longitudo ad interiora visus penetrans a corpore viso cum pars eius interior radiis non subiaceat nec mensurari a visu queat. Sillogizat ergo visus ex anguli capacitate et nota longitudine. Vera autem remotio corporis attenditur secundum lineam a centro oculi ad corpus procedentem, cum respectu centri fiat consideratio anguli. Et in temperata corporis distantia semidyameter oculi qua vera corporis elongatio excedit apparentem, insensibilis est respectu totalis distantie corporis, unde non facit errorem in longitudinis estimatione. Sed corpore circa oculum existente, erit magnitudo semidyametri proportionalis distantie corporis proportione sensibili. Erit igitur aliquando maior, aliquando equalis, aliquando minor, sed proportione modica, velut subdupla vel huiusmodi; unde in propinquitate rei vise excrementum anguli piramidalis et sensibilis minoritas longitudinis estimate respectu vere inducunt apparentiam maioritatis in corpore.

7.25 ◉ And this happens for two reasons, for, as has been said, the intellect gauges both the distance and the [visual] angle, and on that basis it deduces the size of the body, but at this [very close] distance the [visual] angle is quite large.⁑ Meanwhile, the distance of the body is gauged exclusively from the surface of the eye to the surface of the body, for the distance extending from the visible body to the interior of the eye cannot be taken into account in the judgment of sight, because the interior part of the eye is not affected by the rays, nor does sight try to measure it. Thus, sight carries out its deduction on the basis of the extent of the angle and the determination of distance. Now the actual distance of the body is measured by the line extending from the center of the eye to the body, since the [visual] angle is gauged from the center [of the eye]. And when the body lies at a moderate distance, the radius of the eye, which is the amount by which the actual distance of the body exceeds its apparent distance, is imperceptible in relation to the overall distance of the body, so it does not produce an error in the judgment of distance. But when the body is near the eye, the radius will have a sensible size in relation to the body’s distance. Accordingly, it may be greater than, equal to, or less than [the distance between the object and the eye’s surface], but it will be proportionate to some extent, e.g., half as large or some such; hence, when the visible object lies near the eye, the increase in the angle of the visual cone along with the perceptible discrepancy between estimated and actual distance leads to the perception that the object is larger [than it actually is].

7.26 ◉ Immoderata extensio remotionis errorem invehit distinctionis. Pariete igitur aliquo a longe intuito, si in parte eius fuerit color tenebrosus, fiet videnti fides colorem illum esse distinctionem partium, unde continuum ex hoc errore reputatur discretum. Similiter, si prope parietem illum crescat altitudo herbarum, videbitur distinctio partium inter quas fuerit pars occulta ab oppositione herbarum, unde non reputabitur paries aliquid continuum.

7.26 ◉ An inordinate distance produces an error [in the perception] of disjunction. Accordingly, if a wall is looked at from afar, and there is some dark color on a portion of it, the viewer will be convinced that this color represents a division between segments, so, on the basis of this error, something that is continuous is taken to be disjoined. Likewise, if tall plants are growing near that wall, the [visible] portions [of the wall] interspersed between the parts [of the wall] occluded by the facing plants will appear to be separated, so the wall will not be judged as continuous.

7.27 ◉ Pari modo, luce solis in parietem descendente non multum forti, si corpus umbram iaciat que umbra in parietem cadat, accidit error idem in partium sine intermedio separatione.

7.27 ◉ By the same token, when sunlight that is not particularly intense shines on a wall, if some object casts a shadow upon the wall, the same error occurs in [the judgment] that there is a disjunction of segments that [actually] have no intermediate [gaps].

7.28 ◉ Palam ergo quod error distinctionis est in sillogismo ex immoderantia remotionis.

7.28 ◉ It is therefore clear that the error [in perceiving] disjunction is an error of deduction caused by inordinate distance.

7.29 ◉ Longitudo a moderatione egressa erroris continuitatis est causa. Corpora enim a longe visa in colore similia sibi propinqua creduntur continua. Hinc accidit quod tabule parietis vel scanni apparent aliquando continue, licet adinvicem sint divise modica, dico, distinctione. Et accidit hoc in temperata remotione vise, sed immoderata quantum ad comprehensionem distinctionis tam parve.

7.29 ◉ A distance that falls outside [the range of] moderation is the cause of an error [in perceiving] continuity. For bodies of a similar color that abut one another and are seen from afar are taken to be continuous. Hence, the planks of a wall or bench may happen to appear continuous, even though they are slightly separated, i.e., by disjunction. And this happens when the visible object lies at a moderate distance that is nonetheless inordinate as far as the perception of such a tiny separation is concerned.

7.30 ◉ Et ita ex hoc remotionis errore discretum creditur continuum.

7.30 ◉ Thus, on the basis of this error [which stems] from [inordinate] distance, something that is disjoined is taken to be continuous.

7.31 ◉ Et quoniam secundum considerationem continuitatis et discretionis attenditur numeri comprehensio, accidit error in numero cum in rebus discretis apparebit unitas aut in re una pretendetur pluralitas.

7.31 ◉ Moreover, since the perception of number entails a consideration of continuity and discontinuity, an error in [the perception of] number occurs when discrete objects appear as a unity or a single object presents the appearance of being [divided up into] more than one object.

7.32 ◉ Egressus remotionis a moderamine errorem efficit motus. Si quis ad partem in qua lunam, aut solem, aut stellam aliquam viderit moveatur cum plurimum motus, lunam ante se videat elongatam non minus quam in principio motus. Concludit ipsam in partem eandem moveri, et ab eo recedere, et ob hoc elongationes durare. Et accidit hoc luna etiam ad partem eius properante. Et huius erroris ratio est quia notum est videnti quod in hiis inferioribus, statutis duobus corporibus quorum unum moveatur in partem aliquam, si permanserit ydemptitas situs uni respectu alterius, necesse est aliud moveri in partem oppositam et motu equali.

7.32 ◉ Inordinate distance creates an error [in the perception] of motion. For if someone looks toward the moon, or the sun, or some star while he moves briskly [toward it], he notices that the moon gets no closer to him than [it was] at the beginning of his motion. He concludes that it is moving in the same direction [as he] and {therefore] it is [continually] receding from him, and from this [he concludes] that it maintains a constant distance [from him]. And this happens as the moon also hastens in the same direction. The reason for such an error is that the viewer knows that down here, when two bodies are set up so that one moves in a given direction, if each maintains the same spatial disposition with respect to the other, it follows necessarily that the other one [appears] to move in the opposite direction at an equal velocity.⁑

7.33 ◉ Cum ergo in hiis non percipiatur situs motus moventis ad stellam motam, occulte ex propositionibus iam dudum animo notis, infertur sillogistice motio. Et occultatur situs eius moventi ad stellam immutatio, quoniam via quam peragit motu suo non est proportionalis ipsius stelle magnitudini, multo magis excessus postreme propinquitatis eius ad stellam super primam propinquitatem non est sensibilis respectu totalis remotionis. Idem error accidit in motu nubium, creditur enim velocissimus esse lune motus, licet non sit, et nos supra explanavimus.

7.33 ◉ Thus, since in the case of celestial bodies the change of the moving viewer’s spatial disposition with respect to the moving star is not perceived, the motion [of the star] is unconsciously deduced on the basis of premises that are already known by the soul. So the change in his spatial disposition with respect to the star is imperceptible to the moving viewer, because the path he follows in the course of moving is disproportionate in size to the star itself, [which makes it] all the more [evident that] the difference between his distance from the star at the beginning [of his motion] and his distance from the star at the end [of his motion] is imperceptible with respect to his overall distance [from the star]. The same error occurs in the case of the movement of clouds, for it is the moon that is believed to be moving swiftly, even though it is not, but we have explained this above.⁑

7.34 ◉ Evagatio remotionis a temperamento errorem infert quietis. Si quis a longe visus motu moveatur non veloci, quiescere putabitur, unde stellas erraticas credimus immotas, licet insit eis motus velocitas.

7.34 ◉ A distance that falls outside [the range of] moderation produces an error [in the perception] of rest. If someone who is seen from afar does not move swiftly, he will be judged to be at rest, which is why we take the planets to be immobile, even though they move quickly.

7.35 ◉ Et hec est quietis stellarum estimatio, quoniam vie quas incedunt etiam in tempore magno non sunt perceptibiles visui a tanta remotione, unde durante situs earum respectu videntis ydemptitate, existimantur quiescere.

7.35 ◉ And this judgment that the planets are immobile is due to the fact that the paths they follow, even during a substantial time-period, are not perceptible to sight at such a [great] distance, so, since they continue to maintain the same spatial disposition with respect to the observer, they are judged to be immobile.

7.36 ◉ Pari modo si corpus aliquod a longitudine magna moveatur super radios visus, et est accedendo ad visum vel recedendo ab eo, putabitur immotum nisi motus eius fuerit valde fortis. Et accidit error iste quoniam, ut supra patuit, motus non comprehenditur in corpore nisi quia modo videtur cum aliquo corpore, modo cum alio. Hic autem excluditur hec perceptio, quoniam via quam incedit movens super radios imperceptibilis est a tanta longitudine.

7.36 ◉ In the same way, if some body [seen] from afar moves along the line-of-sight, either approaching or receding from the eye, it will be judged to be at rest unless its motion is extremely swift. And, as was shown above, this error arises because the motion of a body is not perceived unless at one moment it is seen [in conjunction] with one body and at another moment [in conjunction] with another body.⁑ In this case, however, such a perception is precluded, because the path that the moving object follows along the line-of-sight is imperceptible at such an [inordinate] distance.

7.39 ◉ Superflua longitudo errorem ingerit asperitatis. Unde in capillis alicuius picte ymaginis a longitudine intemperata existimatur asperitas enim cum expressa fuerit pictura. Quia notum est asperitatem esse in veris capillis, concludit eam animus similiter illis inesse propter expressionem forme. Idem error accidit in vestibus depictis et animalium pilis expresse depictorum.

7.39 ◉ An excessive distance produces an error [in the perception of] roughness. Accordingly, the hair of someone who is depicted in a painting that is viewed at an inordinate distance is judged to have texture because that texture is represented by the painting. Since it is known that real hair has texture, the soul concludes by resemblance that there is texture in the painted hairs according to the way their form is represented. The same error occurs in the case of clothing with designs and with the hair of animals that are represented in paintings.⁑

7.42 ◉ In hiis autem omnibus non est asperitas sed immensa lenitas; et licet a corporibus lenitis fiat reflexio lucis non ab asperis, tamen in pictura aliquando videtur reflexio lucis, nec ob hoc excluditur opinio asperitatis. Quoniam opinanti est certum aliquando in eodem corpore asperitatis et reflexionis fieri concursum, sicut accidit in capillis hominis nigerimis et bene lotis, reflectitur enim lux in eis licet asperis.

7.42 ◉ In all these cases, however, instead of actual texture there is utter smoothness; and even though light is reflected from smooth bodies rather than from rough ones, still, [the fact that] light may be seen to reflect from [the surfaces of] paintings does not obviate the conclusion that [the depicted hair has] texture. For to whoever reaches that conclusion it is unquestionable that roughness and reflectivity can coexist in the same body, as happens in the case of human hair that is pitch-black and luxuriant, for it reflects light even though it has texture.

7.43 ◉ Unde ex hac similitudine accidit error in estimatione asperitatis picture per immoderatam remotionem ad corpus pictum proportionatam. Non enim poterit comprehendi lenitas in pictura nisi cum multum fuerit certa; unde distantia respectu aliarum rerum temperata extra temperantiam est ad adquistionem lenitatis comparata.

7.43 ◉ Hence, on the basis of this similarity there arises an error in the judgment of texture in the painting because of the inordinate distance in relation to the object that is painted. For the smoothness of a painting cannot be perceived unless it is quite distinct; hence, a moderate distance with respect to other things is inordinate with respect to the apprehension of smoothness.

7.44 ◉ Ex evagata remotione accidit error in lenitate. Si enim a magna longitudine opponatur visui corpus in quo est modica asperitas, putabitur lene, asperitas enim non adquiritur in corpore nisi ex diversitate situs partium inter se vel luce eminentium et umbra depressarum, sicut explanatum est superius. Et a tali longitudine non attenditur diversitas situs partium aut proiectio umbre eminentium super depressas, unde iudicatur in eo lenitas.

7.44 ◉ On the basis of inordinate distance an error occurs in [the perception of] smoothness. For if a body that is somewhat rough faces the eye from a considerable distance, it will be judged as smooth, for the roughness of a body is apprehended only through variations in the relative spatial disposition of the [object’s] parts or the light of prominent portions and the shadow of depressed portions, as was explained above.⁑ But from such a distance variations in the [relative] spatial disposition of the [object’s] parts or the casting of shadows upon depressed portions by prominent ones is not apprehended, so the object is judged as smooth.

7.46 ◉ Ex immoderatione elongationis oritur error raritatis. Cum circa oculum erigitur acus aut aliquid subtile multum, licet appareat visui maius quam sit, ei tamen nihil occultat de opposito pariete aut alio opposito corpore. Unde, cum fiat raritatis comprehensio in corpore ex eo quod post ipsum possumus aliquid videre, in acu erecta aut in aliquo consimili raritas existimabitur, cum post ipsam totus paries videatur. Quare autem acus prope visum sita maior appareat patet ex superioribus. Quare autem in tanta propinquitate nihil abscondat visui ex opposito pariete est quia remotio tam modica respectu occultationis acus est immoderata. Si enim paululum elongetur ab oculo acus illa, occultabitur pars parietis maior acu ipsa.

7.46 ◉ Because of inordinate distance, an error [in the perception] of transparency arises. When a needle or something very thin is stood right in front of the eye, although that needle may appear larger than it [actually] is to sight, it still does not occlude any portion of a wall or other object beyond it. Since the perception of transparency in a body is based on the fact that we can see something behind it, then, transparency will be imputed to a needle, or to anything like it, that is stood [right in front of the eye], because the entire wall can be seen behind it. The reason that the needle appears larger [than it actually is] when placed near the eye has been explained above.⁑ The reason it blocks none of the wall beyond it from view at such a close position is that, as far as the needle’s [capacity] to block vision is concerned, such a tiny distance is inordinate. For if the needle is brought a little farther away from the eye, a portion of the wall that is larger than the needle itself will be blocked from view.

7.47 ◉ Et huius rei causa plenius deinceps explanabitur.

7.47 ◉ But the reason for this phenomenon will be explained more fully later.⁑

7.48 ◉ Ex superhabundantia longitudinis accidit error soliditatis. Si quis a longe intueatur corpus rarum, et statuatur post ipsum corpus coloratum aut quid tenebrosum, non reputabitur corpus illud rarum sed solidum. Et est error quoniam post corpus illud non percipit aliud. Cum natura rari sit ut post ipsum possit videri solidum, concludetur corpus illud non esse rarum sed solidum.

7.48 ◉ An error in [the perception of] opacity occurs on the basis of excessive distance. If someone looks at a transparent body from afar, and a colored body or something dark is placed behind it, that body will not be judged as transparent, but as opaque. And this error stems from the fact that [sight] perceives no other body behind that body. Since it is in the nature of a transparent object that an opaque object can be seen behind it, it will be concluded that the body is not transparent but opaque.

7.50 ◉ Ex superfluitate remotionis oritur error in umbra. Si a tali longitudine opponatur visui corpus album in quo sit pars tenebrosa, luce solis super corpus illud descendente, apparebit umbra in parte corporis tenebrosa.

7.50 ◉ On the basis of excessive distance an error in [the perception] of shadow arises. If a white body with a dark area faces the eye at such an [inordinate] distance, and if sunlight shines upon that body, there will seem to be a shadow on the dark area of the object.

7.51 ◉ Et hoc pro constanti habito, si circa corpus illud videatur aliud, fiet conclusio quod umbra apparens proiciatur ab illo alio. Et palam quod accidit error iste ex nimia remotione.

7.51 ◉ Moreover, if another body is seen near that one, it will be concluded on the basis of longstanding habit that the apparent shadow is cast by the other body. And it is obvious that this error is due to an excessive distance.

7.52 ◉ Propter distantie excessum se ingerit error tenebrarum. Si a longe videatur corpus album in quo pars nigra multum sit, existimabuntur fortassis in parte illa tenebre, unde fiet conclusio quod in directo illius partis sit foramen corporis per quod appareat tenebrarum egressio post corpus illud existentium.

7.52 ◉ An error [in the perception] of darkness is induced by excessive distance. If a white body with a pitch-black section is seen from afar, that section may be judged to consist of darkness, so it will be concluded that right where that section lies there is a hole in the body through which the darkness behind [the surface of] that body seems to show.

7.54 ◉ Remotio excedens modum causa est erroris speciei et deformitatis. Cum a longe inspicitur res aliqua, si fuerint in ea macule parve ipsam deformantes, quia occultantur ex longitudine, iudicatur formosa. Quoniam ex solis apparentibus fit conclusio, et quia latent macule, apparent vero partes formose.

7.54 ◉ A distance that exceeds the limits of moderation causes an error [in the perception] of beauty or ugliness. If something is looked at from afar, and if there are small blemishes in it that deform it, it is judged beautiful because those blemishes are rendered invisible by the distance. For the final perception [of beauty] is reached on the basis of appearances alone, and since the blemishes are invisible, the parts really do appear beautiful.

7.56 ◉ Similiter, si a tanta longitudine videatur res in qua sunt picture, sed minute rei totali, decorem conferentes, cum lateant visum cause decoris, iudicabitur res illa deformis, cum ex apparentibus tantum iudex sumat iudicium.

7.56 ◉ Similarly, if an object with designs on it that render it beautiful is seen from afar, and if those designs are tiny with respect to the object as a whole, then, since the features that confer beauty on the object are invisible to sight, that object will be judged ugly, because the [viewer] who is judging [the object] bases his judgment exclusively on appearances.

7.58 ◉ Ex superflua elongatione accidit error in similitudine corporum et dissimilitudine. Si dirigantur visus in corpora longe remota in colore similia, si fuerint in eis note vel protractiones minute sibi dissimiles et diverse, cum visus pretereant, iudicabuntur corpora ex toto similia.

7.58 ◉ An error in [the perception of] similarity or dissimilarity among objects arises from an excessive distance. If the eyes are directed toward bodies of a similar color that lie far away, and if there are tiny marks or lines drawn on them that are dissimilar and varied, then, if sight fails to notice [those features], the bodies will be judged to be similar overall.

7.60 ◉ Econtrario, si diversitas fuerit in totalibus corporum coloribus, sed in eis sunt note minute inter quas adinvicem sit similitudo, iudicabuntur dissimilia ex toto. Et accidet error quoniam ex solis apparentibus fiet conclusio.

7.60 ◉ On the other hand, if the colors of the bodies are altogether different, but there are identical tiny marks on them, then they will be judged to be dissimilar overall. And this error will arise because the conclusion will be drawn on the basis of appearances only.

Distinctio 2 ◉ Situs egreditur a temperamento et errorem inducit in quolibet eorum quorum fit comprehensio per sillogismum.

7.63 ◉ In longitudine, si videantur duo corpora quorum unum sit post aliud directe, ita quod unum cooperiat partem alterius, et pars posterioris emineat, et hoc in longitudine temperata, non tamen multum certa, nec inter ea fuerint alia corpora, non plene existimabitur longitudinis unius ad aliud mensura, et forsitan iudicabit videns ea sibi esse valde propinqua.

7.63 ◉ In [regard to] distance, if two bodies are seen, one of them being directly behind the other so that the one occludes part of the other, and part of the rear body juts out, and if the distance is moderate but not quite determinate, and if there are no other bodies between them, then the measure of the distance of one from the other will not be gauged clearly, and the observer may judge them to be very near one another.⁑

7.64 ◉ Et est error iste in sillogismo, cum per sillogismum tantum comprehendatur longitudo per situm, quoniam, si non occultaret unum alterius partem, sed utrumque totum exponeretur visui, ut via inter ipsa in diversos non in eundem incideret radios, discerneretur distantia unius ab alio. Et est error ex sola situs intemperantia, quoniam situ ad temperantiam reducto, ceteris partibus non mutatis, non accidit error.

7.64 ◉ This error involves deduction, because distance is deductively perceived on the basis of spatial disposition alone, for, if part of one of the bodies were not occluded by the other, but, rather, both were completely exposed to view so that the gap between them fell not on the same ray but on different rays, then the distance of one from the other would be discerned. And this error is due entirely to an inordinate spatial disposition, for if the spatial disposition is restored to moderation while everything else remains the same, the error does not arise.

7.65 ◉ Situs extra temperantiam situs visui errorem invehit. Cadente axe visuali in corpus a temperata longitudine oppositum visui, sumpto alio corpore multum elongato ab axe declinato modicum super lineam intellectualem super quam cadit axis perpendiculariter, non comprehendit videns corporis illius declinationem propter situm a temperamento egressum. Quoniam non plena fit comprehensio corporum longe ab axe positorum, et in hoc errore declinatum iudicabitur rectum.

7.65 ◉ An inordinate spatial disposition causes an error in the visual perception of spatial disposition. When the visual axis meets a body that faces the eye at a moderate distance, if another body that is far removed from the axis and somewhat inclined to the imaginary line to which the [visual] axis falls orthogonally is taken, then the viewer does not perceive the inclination of that body because its spatial disposition has fallen outside [the range of] moderation. For bodies that lie far away from the [visual] axis are not clearly perceived, so in the case of this error something that is inclined will be judged to face the eye directly.

7.67 ◉ In figura accidit error per situm. Si corpus circulare, ut ciphus vel scutella, ab axe elongetur et modicum super lineam intellectualem quam diximus declinetur, quoniam occultatur eius declinatio, et unus eius dyameter sub maiori angulo comprehenditur quam alius, qui enim apparet rectus maiorem respicit angulum quam declinatus, et quia notabilis est excessus unius anguli ad alium, iudicatur dyameter rectus maior declinato, unde circularis figura corporis iudicabitur oblonga.

7.67 ◉ In [regard to] shape, an error occurs on account of [an inordinate] spatial disposition. If a round body, such as a goblet or bowl, is situated far away from the [visual] axis and somewhat inclined to the imaginary line we [just] mentioned, then, because its inclination is imperceptible, and because one of its diameters is perceived under a greater [visual] angle than the other diameter, for whatever is seen from a facing disposition subtends a larger [visual] angle than it does when it is inclined, and because there is a marked difference in size between the angles, the facing diameter is judged to be longer than the inclined one, so the round body will be judged to have an oval shape.

7.68 ◉ Pari errore figura quadrangula existimabitur oblonga, cum latus eius directe oppositum oculo maius appareat latere declinato.

7.68 ◉ Through the same error a square figure will be judged to be rectangular, since the side of it facing the eye directly appears longer than the side that is inclined.

7.70 ◉ Et est error in sillogismo, premittit enim propositiones in quibus falsitas est—scilicet neutrum laterum esse declinatum; et visa ab eadem longitudine sub eodem situ et inequalibus angulis sunt inequalia; et oblonga est forma cuius unum latus inequale alii—inde concluditur error non veritas figure. Ex eadem causa palam esse errorem in quantitate cum dyameter circularis corporis maior videtur alio eiusdem dyametro cui est equalis.

7.70 ◉ And this is an error in deduction, for it depends on premises that are false—i.e., that neither of the sides is inclined; that, if they subtend unequal [visual] angles, things seen at the same distance according to the same spatial disposition are [invariably] unequal in size; and that when one side is unequal to the other, the form of the object is [invariably] oblong—so the shape is interpreted incorrectly, not as it actually is. For the same reason it is clear that there is an error in [the perception of] size if one diameter of a circular body appears longer than another diameter of the same body, since they are actually equal.

7.71 ◉ Amplius alio modo accidit error in magnitudine ex situ intemperato et solo cum aliquis in altum positus intuetur sub altitudine illa incedentes et inter se equales eis in ordine uno post alium dispositis, radius cadens super primum absque dubio demissior erit radio cadente super secundum. Et secundum quod augmentabitur elongatio alicuius eorum a primo, maior erit radii super ipsum cadentis altitudo, unde altior erit radius cadens in postremum quam in aliquem alium. Iudicabitur ergo a vidente postremus maior omnibus ita, dico, si terre spatium inter quoslibet duos situm lateat visum ne in collatione ad terram apparentem facta comprehendi possit altitudinis homini mensura.

7.71 ◉ Another way, moreover, in which an error in [the perception of] size arises exclusively from an inordinate spatial disposition comes about when someone who is high up looks down on objects of equal size that are placed in a row, one after the other [away from the viewer, for in that case] the ray that falls on the first of these objects will certainly be lower [with respect to the center of sight] than the ray falling on the second. And the height of the rays falling on any of those objects will depend on how far that object lies from the first in line, so the ray falling on the last object in line will be higher than a ray falling on any other of those objects. Accordingly, the last object will be judged by the observer to be taller than all the rest, provided, that is, that the ground lying between any of the two objects is invisible to sight so that the altitude of the person [who is observing from on high] cannot be measured relative to the ground that appears.

7.72 ◉ Et erit error in sillogismo, quoniam errat in antecedentibus quorum unum est quecumque apparent altiora sunt maiora, et hoc non invenitur in omnibus sed in pluribus. [7.73] Et est error ex situs immoderatione respectu comprehensionis magnitudinis rei sic disposite, si enim radius cadens in primum sit equidistans terre, et idem radius cadat in quemlibet alium processu suo, non habebit locum error iste.

7.72 ◉ And this will be an error in deduction, because the observer errs according to the presupposition that whatever appears higher is taller, which applies in most, but not all, cases.

7.75 ◉ In distinctione provenit error ex excessu situs. Si magna fuerit corporis alicuius super radios declinatio, et fuerint in eo puncta sensibilia nigra vel valde tenebrosa, putabuntur forsitan esse foramina, et ita inter partes huic tenebrositati affines iudicabitur divisio, licet ibi sit continuitatis unio. Si vero in hoc corpore fuerint linee sensibiles tenebrose, iudicabuntur conterminales divise cum sint continue, et ita error accidit ex corporis declinatione.

7.75 ◉ An error regarding disjunction arises from an inordinate spatial disposition. If the inclination of some body with respect to the rays is great, and there are perceptible black or very dark areas on it, they may be taken to be interstices, and so it will be assumed that there is a disjunction between the parts bounded by [any] such darkened area, even though there is continuity at this point. Moreover, if dark lines are perceptible on this body, the parts on each side will be judged to be disjoined when they are continuous, and so an error arises on the basis of the body’s inclination.

7.77 ◉ In continuitate erit error ex situ. Si apponatur visui plurium parietum dispositio quorum unus sit ordinatim post alium modicum distans ab eo, et omnes cadant super eundem radium, occultabitur forsitan videnti spatium quod inter eos fuerit.

7.77 ◉ There will be an error in [the perception of] continuity on the basis of [an inordinate] spatial disposition. If several walls are positioned facing the eye so that one lines up behind another at a slight distance from it, and if all of them lie along the same line-of-sight, the interval between them may be hidden from the viewer.⁑

7.78 ◉ Unde putabuntur continui cum sint divisi, quod non accidet situ parietum immutato ut non comprehendantur sub eodem radio.

7.78 ◉ In that case they will be judged to be continuous when they are disjoined, an error that would not arise if the spatial disposition of the walls were changed so that they were not perceived by the same ray.

7.79 ◉ Error inducitur in numero ex situ immoderato quando corpus aliquod videtur duo, et hoc accidit cum respectu duorum visuum corpori diversitas situs fuerit. Pari modo et in corpore uno iudicabitur pluralitas cum inter duos axes corpus visum ceciderit, sicut supra patuit.

7.79 ◉ An error in [the perception of] number is prompted by an inordinate spatial disposition when some object is seen double, and this occurs when there is a difference in the body’s spatial disposition with respect to the two eyes. So, too, as was explained above, a single body will be judged double when that body falls between the two [visual] axes.⁑

7.80 ◉ Et est error in sillogismo, premittit enim videns esse diversa corpora exterius visa. Cum forma interius in diversa visus ceciderit loca, inde diversitatem ubi ydemptitas est concludit.

7.80 ◉ And this is an error in deduction, for the viewer supposes that he has seen different bodies outside. When the form reaches to different locations inside the eyes, the viewer concludes on this basis that what is actually identical is different.

7.81 ◉ In motu oritur error ex situ, ut navem currentem in flumine aliquo inspiciente, si fuerint in littore fluminis arbores ab axe multum elongate, putabuntur moveri.

7.81 ◉ An error in [the perception of] motion arises from [an inordinate] spatial disposition, as [happens] when someone looks out from a boat floating with the current on a river, [for in that case] if there are trees on the riverbank that lie far to the side of the [visual] axis, they will be judged to be moving.⁑

7.82 ◉ Et si fiat directio axium super eas, videbuntur immote.

7.82 ◉ But if the [visual] axes are focused directly upon those trees, they will appear immobile.

7.83 ◉ In quiete error ex situ se ingerit. Intuita re aliqua, et tota que citissimo motu volvatur ab axe elongata, apparebit immota.

7.83 ◉ An error in [the perception of] rest arises from [an inordinate] spatial disposition. If some object is seen far to the side of the [visual] axis, and if that entire object revolves swiftly, it will appear motionless.

7.84 ◉ Et planum est per situm esse errorem, quoniam, situ mutato, percipietur eius motio, unde error ex situ solo intemperato.

7.84 ◉ So it is obvious that this error involves spatial disposition, for, if the spatial disposition were restored [to moderation], the body’s motion would be perceived, so the error is due solely to an inordinate spatial disposition.

7.85 ◉ In asperitate situs errorem facit. Si a capillis expresse depictis fiat reflexio lucis, et non fuerit visus in loco reflexionis, fiet in eis comprehensio asperitatis cum sola sit in eis lenitas.

7.85 ◉ [An inordinate] spatial disposition causes an error in [the perception of] roughness. If light reflects from a painting that represents hair, but the eye does not lie where the reflection occurs, there will be a perception of roughness in the painted hair when there is only smoothness there.

7.86 ◉ Et est error ex situ solo, quoniam visu sub luce reflexa sito non comprehenditur asperitas in corpore viso.

7.86 ◉ And this error is due solely to an inordinate spatial disposition, for when the eye is placed in line with the reflected light, no roughness is perceived in the body that is seen.

7.87 ◉ In lenitate erit error ex situ. Cum aliquid elongatum fuerit ab axe, si modica fuerit in eo asperitas, apparebit lene cuius quidem asperitatem.

7.87 ◉ An error in [the perception of] smoothness will be due to [an inordinate] spatial disposition. If something that lies far to the side of the [visual] axis is slightly rough, it will appear smooth.

7.88 ◉ Situ ad temperantiam reducto, posset videns comprehendere.

7.88 ◉ If the spatial disposition were returned to moderation, the viewer would be able to perceive its roughness.

7.89 ◉ In raritate et soliditate fiet error ex situs immoderamine. Si descenderit lux declinata in vitrum vino plenum, et lateat visum transitus lucis per vitrum, et magna sit declinatio illius a radiis, et videntem lateat vinum esse in vase vitreo, existimabitur a vidente vinum esse corpus solidum unum cum vase. Et non accidit error iste in transitu lucis per vas vitreum patente, unde error ex situ in raritate et soliditate.

7.89 ◉ In [the perception] of transparency or opacity an error will occur on the basis of an inordinate spatial disposition. If light shines at a slant on a glass that is full of wine, and if sight fails to see the light pass through the glass, then, if the inclination of the glass with respect to the rays is extreme, and the observer fails to see that there is wine in the glass, the wine will be judged by the observer to be an opaque body that is continuous with the glass. But this error does not occur when the passage of light through the glass is evident, so this error in regard to transparency and opacity is due to [an inordinate] spatial disposition.

7.92 ◉ In umbra et tenebris: Corpore aliquo ab axe elongato, si fuerit in eo pars tenebrosa, putabitur fortassis umbra, et corpore aliquo circa posito, existimabitur umbram procedere ab illo.

7.92 ◉ In [regard to] shadow and darkness: if some object lies far to the side of the [visual] axis, and if it has a dark section on it, that section may be taken for shadow, and if there is some body nearby, it will be assumed that the shadow is cast by it.

7.9495 ◉ Si autem in corpore illo fuerit pars multum nigra, existimabitur forsitan in loco nigredinis perforatio per quam egrediatur tenebra, quod non accidet in corpore statuto in situs temperantia.

7.96 ◉ In specie et deformitate autem error accidit ex situ. Cum corpus aliquod remotum fuerit ab axe, et sint in eo macule minute ipsum deturpantes, occultabuntur, et iudicabitur in corpore species, unde facies lentiginosa in hoc situ videtur speciosa. Similiter in hoc situ latet videntem lune adherens umbra, unde ascribitur decor lune sic inspecte.

7.96 ◉ Furthermore, in [the perception of] beauty and ugliness an error occurs on the basis of [an inordinate] spatial disposition. When some body lies far to the side of the [visual] axis, and there are tiny blemishes in it that disfigure it, they will be invisible, and the body will be judged to possess beauty, so in this situation a freckled face appears beautiful. Likewise, in this situation the shadow inherent in the moon is invisible, so when it is viewed in such a way [perfect] beauty is attributed to the moon.⁑

7.98 ◉ Si autem in corpore viso fuerint picture ei speciem redentes, nec sit corpus decorum nisi ex pretentu earum, cum ipse in hoc situ lateant visum, iudicabitur corpus deforme.

7.98 ◉ On the other hand, if there are designs on the object that render it beautiful, and if the object is beautiful only when these designs are apparent, then, since they are invisible in this situation, the object will be judged to be ugly.

7.99 ◉ Et est error in sillogismo quia per apparentiam tantum sit deformitatis vel decoris conclusio.

7.99 ◉ And this error involves deduction, because the conclusion that something is ugly or beautiful depends entirely on appearance.

7.100 ◉ In similitudine et dissimilitudine ex situ error oritur. Si longe ab axe stabiliantur duo concordantia in specie, figura, et colore, sed in eis sint modice et dissimiles note, iudicabitur in ea similitudo omnimoda, cum note ille videnti sint ignote.

7.100 ◉ In [the perception of] similarity and dissimilarity an error arises on the basis of [an inordinate] spatial disposition. If two objects are set up far to the side of the [visual] axis [and if they are] of the same kind, color, and shape but possess some small features that are dissimilar, they will be judged to be perfectly identical since those features have escaped the viewer’s notice.

7.102 ◉ Si autem fuerit diversitas inter ea in specie, et colore, et figura, sed in eis sint note similes, putabuntur ex toto dissimilia, cum aliqua dissimilitudo sit inter ea. Et ita est error in similitudine et dissimilitudine propter conclusionem ex apparentibus tantum factam.

7.102 ◉ On the other hand, if those objects are not of the same kind, color, or figure but possess some identical features, they will be judged to be wholly dissimilar, since there is some dissimilarity between them. Accordingly, the error in [perceiving] similarity and dissimilarity is due to the fact that the final judgment [of similarity or dissimilarity] is based solely on appearances.

7.103 ◉ Et in omnibus predictis procreatur error ex solo situ intemperato, quoniam eo intra temperamentum sito, aliis sicut sint manentibus, non accidet erronea estimatio.

7.103 ◉ In all of the foregoing cases the error arises exclusively from an inordinate spatial disposition, for if the spatial disposition falls within [the range of] moderation, all other things remaining as they are, the erroneous judgment will not occur.

Distinctio 3 ◉ Lux a temperantie finibus egreditur, et ob hoc solum in omnibus quorum fit adquisitio per sillogismum error procreatur.

7.104 ◉ In longitudine ex lucis parvitate: Si in longitudine temperata non multum circa fiat hominum dispositio ut sit unus post alium, et visu huic dispositioni de nocte adhibito, videbuntur sibi coherere incomprehensa inter eos distantia propter debilitatem lucis, que pateret si lux esset fortis. Qui homines, si in eandem partem moveantur equali motu, simul semper moveri putabuntur.

7.104 ◉ In [the perception of] distance [an error arises] from a deficiency of light. If people are arranged in a line, one after another, at a moderate distance and not too near one another, then, if sight is directed toward them at night while they are so disposed, they will appear to coalesce because the separation between them is imperceptible on account of the deficiency of light, although that separation would be evident in strong light. And if these people move in the same direction at the same velocity, they will invariably be judged to move as one.

7.106 ◉ In situ: Si in nocte non obscura aliquid modicum a visu declinatum opponatur visui, existimabitur in eo situs rectitudo propter debilitatem lucis egressam a temperamento.

7.106 ◉ In [regard to] spatial disposition: If something faces the eye at a slight inclination at night, when it is not too dark, the object will be judged to face the eye directly because of the inordinate weakness of the light.

7.107 ◉ Similiter figura multorum laterum equalium circularis apparebit de nocte inspecta, quoniam occultat angulos lux nimium debilis.

7.107 ◉ Likewise, a figure with several equal sides will appear circular when viewed at night, for the excessive weakness of the light hides the corners [from sight].

7.108 ◉ Pari modo, spera sic visa reputatur superficies plana, quia occultatur visui partium eminentia.

7.108 ◉ By the same token, a sphere viewed under these circumstances is taken to have a flat surface, because its outward bulge is hidden from sight.

7.109 ◉ ???????? @author {kew}

7.110-111 ◉ In magnitudine: De nocte inspecto homine, et viso nemore aut remoto ab eo pariete, videbitur propinquitas hominis ad nemus vel parietem, cum lateat visum distantia eorum, licet sit plurima. Et forsan exibit idem radius super caput hominis ad altitudinem nemoris secundum quantitatem distantem a nemore, et in hoc situ videbuntur eiusdem esse altitudinis, aut forsitan homo videbitur maioris, quod non accideret si lux in temperamento esset, quoniam distantia hominis ad nemus etiam discerneretur, et altitudo uniuscuiusque secundum terram apparentem mensuraretur.

7.110-111 ◉ In [regard to] size: If a person is viewed at night, and a grove of trees or a wall that is far away from him is seen, the person will appear to be near the grove or the wall, since sight fails to perceive their distance from each other, even though it is considerable. Moreover, the same ray may pass over the head of the person to the top of the grove according to how far away the grove is, and in this case they will appear to be of the same height, or else the person may appear taller. This would not happen if the light were moderately intense, for the distance between the person and the grove would be discerned, and the height of each would be gauged according to the [intervening] ground that is perceived.

7.112 ◉ In distinctione, numero, continuitate erit error ex lucis debilitate. Si de nocte videatur tabula in qua sit linearum obscurarum protractio, ut sit ad mensuras capiendas, putabit forsan videns divisiones esse vel fissura; et ita error in distinctione, quia continuum apparet divisum, et in numero, quia pluralitas in uno.

7.112 ◉ An error in [the perception of] disjunction, number, and continuity will arise from an insufficiency of light. If a plank with dark lines drawn on it along its full length is seen at night, an observer may assume that these lines represent junctures or gaps; and so there will be an error in [perceiving] disjunction, because something that is continuous appears disjoined, and [there will also be an error] in [perceiving] number, because something that is single will be taken to be multiple.

7.114 ◉ Similiter, existente visu in lucis fortis reflexione, si adhibeantur corpora modicum distantia, apparebunt continua; et ita error in continuitate propter lucem nimium, aut fortem, aut debilem.

7.114 ◉ Likewise, when the eye is placed where strong light is reflected, if it looks at bodies that are somewhat distant, they will appear continuous; so there is an error in [the perception of] continuity on account of light that exceeds limits, whether of intensity or of weakness.

7.116 ◉ In motu aut quiete accidit error in luce. Si de nocte comprehenderit visus hominem et remotum ab eo nemus, occultabitur distantia hominis ad nemus. Et si moveatur videns ad hominem illum, quanto magis ad eum accesserit distantiam illam certius videbit, unde, cum prius, simul cum nemore appareret ei homo visus. Et quanto ad eum accedit plus videtur a nemore remotus, et cum certum sit ei nemus immotum manere, sillogizabit hominem visum a parte nemoris incedere, licet veritas habeat ipsum immotum esse, quod non accideret in temperata luce.

7.116 ◉ In [regard to] motion or rest an error occurs in light [that falls outside the range of moderation]. If a person and a grove of trees that is far away from him are perceived at night, the distance between the person and the grove will be imperceptible. But if the observer moves toward the person, the closer he gets to him the more determinate that distance will appear, so, as before, the person who is seen will appear conjoined with the grove. But the closer the viewer gets to that person, the farther away from the grove the person appears to get, and since the viewer is certain that the grove remains immobile, he will deduce that the person who is seen is moving away from the grove, even though he is actually immobile, but this error would not occur in moderate light.

7.117 ◉ In quiete: Homo de nocte visus non plene comprehenditur, unde si modicum moveatur, non discernetur motus, et putabitur quiescere.

7.117 ◉ In [regard to} rest: A person who is seen at night is not clearly perceived, so if he moves slowly, his motion will not be discerned, and he will be judged to be immobile.

7.118 ◉ In asperitate et lenitate erit error. De nocte visi enim asperitas iudicabitur forsitan erit lenitas, aut econtrario secundum quod fuerit rei vise qualitas.

7.118 ◉ In [regard to] roughness or smoothness an error will occur [on the basis of light that falls out of the range of moderation]. For a rough object that is seen at night may be judged to be smooth, or vice versa, depending on the nature of the visible object.

7.119 ◉ In raritate et densitate: De nocte enim remissa iudicabitur in corpore multum raro raritas, quia, cum post ipsum non plena fiat comprehensio solidi, existimabitur remissionem raritatis eius viam negare visui. Corpus vero modicum rarum iudicabitur solidum.

7.119 ◉ In [regard to] transparency or opacity: At night the transparency of a body that is highly transparent will be judged to have decreased, for, since an opaque object cannot be clearly perceived behind it, the viewer will judge that its lessened transparency prevents sight from seeing through it. An object that is [only] somewhat transparent will in fact be judged to be opaque.

7.121 ◉ In umbra et tenebris: Si in pariete albo fuerint partes obscure, et cadat super parietem illum lux candele, iudicabit forsitan videns obscuritatem illam esse umbram, et videbitur ei forsitan quod procedat apparens umbra a vicino pariete; et ita error in umbre estimatione.

7.121 ◉ In [regard to] shadow or darkness: If there are dark areas on a white wall, and candlelight shines on that wall, an observer may judge such dark areas to be shadows, and it may appear to him that the shadow he sees is projected by a neighboring wall; and so [there is] an error in the judgment of shadow.

7.122 ◉ Similiter, si fuerit in parte parietis nigredo multum intensa, existimabitur forsitan vacuitas foraminis iter prebens egredientibus tenebris. Et si tota parietis superficies afficiatur intensa nigredine, totus forsitan putabitur tenebre, ut accidit in pariete cooperto ignis fuligine, viso sub debili luce.

7.122 ◉ Likewise, if there is a pitch-black area on the wall, it may be judged as the space of an opening through which the [inner] darkness [of the wall] shows forth. And if the entire surface of the wall is tinged with a pitch-black color, the entire wall may be taken for darkness, as happens in the case of a wall that is covered with soot when it is seen in faint light.

7.124 ◉ In specie et deformitate: Palam quod de nocte videtur facies formosa, licet in ea sint macule, sicut lentiginosa.

7.124 ◉ In [regard to] beauty and ugliness: It is clear that a face appears beautiful at night, even if there are blemishes, such as freckles, in it.

7.125 ◉ Et si fuerint in re visa picture subtiles totalis speciei cause, cum in nocte visum lateant, videbitur res deformis.

7.125 ◉ And if there are subtle designs in the visible object that are entirely responsible for its beauty, then, since they are invisible to sight at night, the object will appear ugly.

7.127 ◉ In similitudine et dissimilitudine: In corporibus eiusdem speciei, coloris, et figure in quibus partialis diversitas per latentes notas in debili luce omnimoda iudicabitur similitudo.

7.127 ◉ In [regard] to similarity and dissimilarity: In the case of objects of the same kind, color, and shape, when differences among certain of their features are rendered invisible in faint light, those objects will be judged altogether alike.

7.128 ◉ Et si diversa fuerint corpora in specie, colore, et figura, sed ex aliquibus notis conformitas partialis propter occultationem notarum ex remissione lucis iudicabitur omnimoda diversitas corporum.

7.128 ◉ If, however, the objects are different in kind, color, and shape but share certain features, then, since those features are imperceptible because of the decreased light, the objects will be judged to be altogether dissimilar.

7.130 ◉ Et palam in omnibus predictis errorem accidere ex sola debilitate lucis, cum enim ipsa inter terminos temperantie fuerit sita, error non accideret aliis immotis.

7.130 ◉ So it is clear in all the foregoing cases that the error arises from the weakness of light alone, for if the light fell within the limits of moderation, the error would nor occur, assuming that everything else remained the same.

Distinctio 4 ◉ Quantitas egreditur a temperantia, et ille egressus causa est erroris in omnibus quorum fidem facit sillogismus.

7.131 ◉ Error erit in longitudine ex causa predicta. Si videantur duo homines a longitudine temperata, et si in suo genere maxima, et unus paululum fuerit ante alium, non discernetur via inter eos sita, unde unus eorum apparebit circa alium. Et accidit error quoniam distantia eorum, cum multum sit parva, non est proportionalis totali eorum a visu elongationi, licet elongatio sit temperata.

7.131 ◉ An error in [the perception of] distance will arise for the reason just given. If two people are seen from a moderate distance, but that distance extends to the limit of moderation, and if one of the people stands a little in front of the other, the gap between them will not be discerned, so one will appear to be right next to the other. And the error arises from the fact that, since the distance between them is quite small, it is not proportional to their overall distance from the eye, even though that [overall] distance is moderate.

7.133 ◉ Est autem error in longitudine quoniam homines illi iudicabuntur ab oculo eque remoti, et ita quantitas unius longitudinis maior quam sit in veritate, unde est error in longitudine.

7.133 ◉ Furthermore, it constitutes an error in [the perception of] distance because those people will be judged by sight to be equidistant [from the eye], and thus one distance [is judged] greater than it actually is, so there is an error in [the perception of] distance.

7.134135 ◉ In situ propter quantitatis parvitatem est error. Quoniam si granum sinapis fuerit ab oculo declinatum, tamen videtur rectum, quoniam pro parvitate nimia non potest deprehendi declinatio huius grani super lineam intellectualem in quam axis communis cadit ortogonaliter, quoniam non plene discernitur longitudo inter hanc lineam et extremitates grani, cum sit minima, et secundum hanc longitudinem consideratur declinatio eius super lineam illam. Et secundum hanc lineam consideratur semper declinatio rei vise respectu visus utriusque, et ita error in situ ex quantitate immoderata.

7.137 ◉ In figura: Cum res visa fuerit multum parva, si fuerint in ea anguli, occultabuntur visui, unde fortassis eius forma, cum non sit, existimabitur rotunda aut longa.

7.137 ◉ In [regard to] shape: When the visible object is extremely small, and there are corners on it, those corners will be invisible to sight, so that, even though it is not actually [round], its form may be judged to be round or oblong.

7.138 ◉ Et si fuerit in ea aliqua incurvatio modica, latebit visum, et existimabitur superficies eius plana, unde palam quod error in figura.

7.138 ◉ And if there is some slight curvature to it, that curvature will be imperceptible to sight, so its surface will be judged to be flat; hence, there is clearly an error in [the perception of] shape.

7.140 ◉ In quantitate quantitas errorem invehit. Propositis visui duobus corporibus quorum unum modicum excedat aliud, aut in longitudine sola aut in latitudine, forsan iudicabuntur equalia in omni dimensione. Et est error iste quoniam excrementum unius dimensionis super aliam evasit fines temperantie respectu visus cum sit ei insensibile pre nimia sui diminutione. Ob hoc necessarie sunt mensure ut verificentur quantitates corporum cum non adquiratur certitudo per visum.

7.140 ◉ In [regard to the perception of] size, [an inordinate] size induces an error. If two objects are set before the eyes, one slightly larger than the other in length alone or in breadth, they may be judged to be identical in every dimension. And this error arises because the excess of one dimension over the other has passed the limits of moderation with respect to sight since that excess is imperceptible to sight by virtue of its inordinate smallness. Thus, in order for the sizes of objects to be correctly determined, these measurements are necessary, because size cannot be apprehended with certainty by sight [under such conditions].

7.142 ◉ In divisione error accidit. Capillo adherente vasi vitreo, apparebit divisio esse in vitro et fissura cum ibi sit continuitas vera. Et provenit hoc ex capilli tenuitate, quoniam, si adheserit vitro quantitas corpulenta, non existimabitur in eo fissura.

7.142 ◉ In [the perception of] disjunction an error occurs [if the size is inordinate]. If a hair is stuck on a glass, there will appear to be a disjunction or crack in the glass when, in reality, there is absolute continuity in it. And this error arises from the thinness of the hair, for, if something thick[er] were to adhere to it, the glass would not be judged to be cracked.

7.143 ◉ In continuitate: Si pretendantur visui folia pargameni tenua, equalis altitudinis, bene compressa, et ignoret videns esse folia, iudicabit ipsa esse continua et unum corpus efficere. Et est erroris causa quantitas vie interiacentis folia que pre sui parvitate non percipitur a vidente. Et eadem erit causa erroris numeri que continuitatis.

7.143 ◉ In [regard to] continuity: If thin sheets of parchment that are of equal length are stacked tightly together, and if the viewer does not know that it is a stack of sheets, he will assume that it forms a single, continuous body. And the reason for this error is that the size of the gaps between the sheets is not perceived by the viewer because of their smallness. Moreover, the same thing that causes an error in [the perception of] continuity will cause an error in [the perception of] number.

7.145 ◉ In motu: Si moveantur duo quorum unum paululum velocius alio, putabit videns equalem esse motum eorum, quod est cum insensibile sit videnti unius super alium excrementum.

7.145 ◉ In [regard to] motion: If two things move, and one of them moves a bit more quickly than the other, an observer will judge their speeds to be equal, because the excess of one over the other is imperceptible to the observer.

7.146 ◉ Similiter quantitas excessus vie quam incedit unus super eam quam incedit alius imperceptibilis est visui, unde iudicatur equalitas viarum et motuum.

7.146 ◉ Similarly, the difference in size between the path that one follows and the path that the other follows is imperceptible to sight, so both the paths and the speeds are judged to be equal.

7.147 ◉ In quiete: Cum offertur visui animal multum parvum, forsitan movebitur pars eius aliqua, et ipsum iudicabitur immotum, cum motus partis lateat visum.

7.147 ◉ In [regard to] rest: When a very small animal is presented to sight, one of its members may move, but the animal will be judged to be motionless, because the member’s movement is invisible to sight.

7.149 ◉ In asperitate et lenitate: Cum enim occurrerit visui res multum parva, iudicabitur forsitan lenitas ubi fuerit asperitas, aut econtrario. Quoniam, ut dictum est, asperitas non comprehenditur in corpore nisi ex umbra quarumdam partium super alias, vel eminentia earum et depressione aliarum, quod totum occultatur iudicio videntis pre nimia parvitate corporis.

7.149 ◉ In [regard to] roughness and smoothness: Indeed, when a very small object is seen, it may be judged to be smooth where it is rough, and vice-versa. For, as has been said, roughness is perceived in an object only through the shadow cast by certain parts on others, or the protrusion of such parts and the depression of others,⁑ all of which escapes the viewer’s scrutiny on account of the inordinate smallness of the body.

7.151 ◉ In raritate et soliditate: Si quis intueatur corpus valde parvum politum, ut ab eo possit lux reflecti, margarite simile, rarum esse iudicabit cum non sit.

7.151 ◉ In [regard to] transparency and opacity: If someone looks at a very small, polished object, like a pearl, from which light can reflect, he will judge it to be transparent when it is not.

7.152 ◉ Similiter, viso corpore raro multum parvo, quia post ipsum non sit corporis solidi comprehensio, simulatur esse solidum.

7.152 ◉ By the same token, when a very small, transparent object is seen, it may seem to be opaque because no opaque body is perceived behind it.

7.154 ◉ In umbra et tenebris: Si in pariete albo visui opposito fuerit punctorum valde nigrorum distinctio, adhibita solis luce, sed directe in pariete cadente vel prope, existima buntur a vidente singula puncta singula esse foramina postquam erumpant tenebre, unde error cum tenebrarum estimatione ex sola punctorum parvitate, que non accideret si nigredo quantumcumque intensa magnam partem parietis inficeret.

7.154 ◉ In [regard to] shadow and darkness: If there are separate spots of a pitch-black color on a white wall facing the eye, and if it is exposed to sunlight that falls directly on the wall, or nearly so, then the individual spots will be judged by the viewer to be individual holes behind which darkness shows forth, so there is an error with regard to the judgment of darkness on account solely of the smallness of the spots, and that error would not occur if the blackness, no matter how intense, were to be painted on a sizeable portion of the wall.

7.155 ◉ Si autem fuerit in punctis illis nigredo non adeo intensa, reputabuntur quidem puncta illa foramina in quibus sit umbra cum lux non penetret ea, sicut solet accidere luce super multorum foraminum superficiem cadente, unde error umbre ex sola punctorum diminutione.

7.155 ◉ On the other hand, if the blackness in these spots is not so intense, those spots will be judged to be openings filled with shadow, since light will not penetrate into them, as often happens when light shines on a surface with many openings in it, so there is an error in [the perception of] shadow on the basis solely of the smallness of the spots.

7.156157 ◉ In specie et deformitate: Cum pre sui parvitate occultentur visui deturpantes corpus visum macule, accidit erroneum speciei iudicium, quia sumitur ex apparentibus tantum, sicut est error in deformitate cum propter parvitatem latent picture decorem ingerentes rei vise.

7.159160 ◉ In similitudine et dissimilitudine: Cum note minutissime inter aliqua corpora similitudinis aut dissimilitudinis fuerint cause, quia pretereunt visum pre parvitate sua, iudicabitur similitudo aut dissimilitudo omnimoda. Et sumetur iudicium ex apparentibus tantum.

7.162 ◉ In omnibus predictis est error in sillogismo ex parvitate corporis; cum ea temperata, non accidit error, aliis immotis.

7.162 ◉ In all the foregoing cases the error in deduction is based on the smallness of the body; if the size is moderate, all other things being equal, the error does not occur.

Distinctio 5 ◉ Soliditas aliquando egreditur temperamentum et errorem inducit in quolibet eorum que comprehenduntur per sillogismum.

7.163 ◉ In longitudine: Si minima fuerit corporis soliditas, et est ut sit valde rarum sicut est cristallus purus, et sit post ipsum lucidum luce forti corpus, non plene comprehenditur cristallus; sed quasi non esset intermedium comprehendetur corpus per ipsum. Unde, cum quasi non sit fiat rari acquisitio, non plena erit longitudinis eius ab eo comprehensio, unde error in longitudine, quare, si corporis rari situs fuerit declinatus, occultabitur videnti declinatio, et iudicabitur forsitan rectitudo, unde error in situ et etiam in longitudine, quoniam una eius extremitas eiusdem longitudinis reputabitur cum alia, cum sint diverse.

7.163 ◉ In [regard to] distance: If the opacity of a body is minimal so that it is exquisitely transparent, like pure crystal, and if some intensely luminous body lies behind it, the crystal is not clearly perceived; rather, the [other] body will be perceived through it as if there were no intermediate body [between it and the eye]. Therefore, since the transparent body is apprehended as if it did not exist, there will not be a clear perception of its distance on that basis, so there is an error [in the perception of] distance, whereby, if the transparent body is disposed at a slant, its inclination will be invisible to the viewer, and it may be judged to face the eye directly, so there is an error in [the perception of] spatial disposition as well as in [the perception of] distance, for one of its extremities will be judged to lie the same distance [from the eye] as the other, although they lie at different distances.⁑

7.164165 ◉ Verum quoniam quantitas corporis comprehenditur ex longitudine et anguli sub quo videtur capacitate, ignorata longitudine, accidit error in quantitate. Modo consimili accidit error in figura, si enim in corpore fuerint anguli, occultabuntur videnti, unde sexquiangula forma putabitur sperica. Et si modica fuerit incurvatio in corpore, latebit, et iudicabitur corpus planum esse.

7.166169 ◉ In divisione: Si fuerit per corpus hec linea nigra, apparebit enim corpus divisum in loco in quem cadit linea, unde existimatur plura. Si vero fuerint duo corpora talia modicum a se distantia, reputabuntur continua, unde error in continuitate. Et palam quod ex hiis error erit in numeri comprehensione, cum unum plura vel plura unum appareant.

7.170 ◉ In motu erit error ex immoderamine raritatis. Si opponatur foramini corpus valde rarum, ut cristallus, et huius corporis extremitates lateant visum, et post corpus hoc moveatur aliud, putabit videns corpus rarum moveri cum sit immotum, quod non accideret ipso temperate solido.

7.170 ◉ There will be an error in [the perception of] motion on the basis of inordinate transparency. If an exquisitely transparent body, such as crystal, is placed before an opening, and if the edges of this body are invisible to sight, then, if some other object moves behind this body, an observer will judge the transparent body to be moving when it is actually motionless, but this would not happen if the body were moderately opaque.⁑

7.171 ◉ In quiete accidet error ex eadem intemperantia. Si includatur in manu corpus valde rarum coniunctum manui, et ab ea recedat, et moveatur intra manum revolutionis motu, immota manu, ita tamen quod appareat divisio aliqua inter ipsum et manum, iudicabitur corpus illud immotum. Quoniam non potest in eo comprehendi motus nisi mutatione situs partis alicuius respectu manus vel partis eius, et quia omnimoda est similitudo in partibus vel pretenditur propter raritatem, non potest discerni alicuius partium situs, quare nec motus.

7.171 ◉ An error in [the perception of] rest will occur on the basis of the same inordinate [transparency]. If an exquisitely transparent object is held snugly in the hand, and if it recedes from the hand or is rotated inside it⁑ while the hand remains immobile, provided that it appears distinct from the hand, the body will be judged to be motionless. For its motion cannot be perceived unless each of its parts changes its spatial disposition with respect to the hand or with respect to part of it, but since its parts are completely identical or seem to be according to its transparency, the spatial disposition of none of its parts can be discerned, nor on that account can its motion.

7.173 ◉ In asperitate: Si in corpore multum raro fuerit asperitas non magna, putabitur forsitan lene. Si vero fuerit lene et post ipsum statuatur corpus asperum aut corpus diversorum colorum, existimabitur hoc rarum asperum, unde error in lenitate.

7.173 ◉ In [regard to] roughness: If a highly transparent body has some roughness, but not too much, it may be judged to be smooth. On the other hand, if it is smooth, but a rough object or an object of various colors is placed behind it, the transparent body will be judged to be rough, so there will be an error in [the perception of] smoothness.

7.175 ◉ In raritate: Si post corpus valde rarum sit aliud corpus rarum non multum et colore forti coloratum, apparebit primum non multum rarum; sed existimabitur eius raritas secundum raritatem postpositi, unde vitrum alii vitro superpositum non apparet ita rarum sicut apparet eo solo visui adhibito, unde error in raritate.

7.175 ◉ In [regard to] transparency: If a body that is not very transparent but intensely colored lies behind an exquisitely transparent body, the body in front will not appear very transparent; instead, its transparency will be judged according to the transparency of the body placed behind it, so a glass placed behind another glass does not appear as transparent as it does when it is exposed to sight on its own, so there is an error in [the perception of] transparency.

7.176 ◉ Si autem post primum rarum statuatur corpus solidum, iudicabitur primum solidum, unde error in soliditate. Pari modo, si vas valde rarum contineat vinum, cum post illud non percipiatur lux aut corpus aliud, iudicabitur forsitan totum cum vino vitrum esse unum corpus solidum.

7.176 ◉ If an opaque object is placed behind the first transparent body, though, the first body will be judged to be opaque, so there will be an error in [the perception of] opacity. By the same token, when a highly transparent glass contains wine, if neither light nor some other body is perceived behind it, the glass may be judged to form an opaque body along with the wine.

7.178179 ◉ In umbra erit error ex raritate. Luce solis in domum aliquam per foramen aliquod descendente et super fenestram vitream cadente, tamen domus illa sit umbrosa, apparebit super fenestram illam umbra, licet in veritate lux super ipsam incidat, que quidem lux comprehenderetur si solidum esset fenestre corpus, quoniam non transiret, et ita super solidum appareret, unde error in umbra.

7.180 ◉ In tenebris: Luce solis in aquam fluminis non descendente, aut in mare, sicut accidit hora matitutina et vespertina, si fuerit claritas in aqua, apparebit tenebrosa. Et quanto fuerit clarior, tanto putabitur tenebrosior.

7.180 ◉ In [regard to] darkness: If sunlight does not shine on the water of a river, or on the sea, as happens in [the early] morning or evening, and if the water is clear, it will appear dark. And the clearer the water is, the darker it will be judged to be.

7.182 ◉ Et accidit hoc quoniam pars aque superior umbram iacit super proximam partem inferiorem, et illa proxima super aliam inferiorem propinquam, et ita per singulas usque ad fundum.

7.182 ◉ And this happens because the upper stratum of the water casts shadow on the stratum just below, and that stratum casts shadow on the one just below it, and so on in order to the bottom.

7.183 ◉ Et licet singularum partium umbra in se sit modica, tamen coniuncte unam efficiunt maximam, sicut palam est in colore vini accidere. In modica enim quantitate vini color est debilis, et in multa, licet eiusdem modi, fortis. Causa autem quare in mari umbra iaciente videantur esse tenebre in maris claritate est quoniam intensa claritas intensam redit raritatem, unde visui maiorem pretendit penetrationem. Unde fit acquisitio plurium maris partium umbram facientium quarum umbrarum aggregatarum perceptio inducit fidem tenebrarum.

7.183 ◉ And even though the shadow in any of the individual strata is minimal, taken as a whole they form an intense shadow, as clearly happens in the color of wine. For the color in a tiny amount of wine is faint, but when such amounts are multiplied, even though they are the same in kind, the color deepens. Moreover, the reason there seems to be darkness in a clear sea when shadow is cast upon it is that extreme clarity produces transparency, so it can be seen through to a considerable depth. Accordingly, many of the strata that cast shadows can be seen, and in the aggregate these shadows, when perceived, lead to the conclusion that there is darkness [in the water].

7.184 ◉ Si vero mare fuerit turbulentum, propter diminutam raritatem penetrabit visus paululum, et comprehendet modicam aque partem. Et licet faciat umbram, cum ipsa sit remissa, color illius partis vincit umbram, in turbida enim color apparet, in clara nullus. Unde et propter apparentem turbide colorem et propter umbre partis apparentis remissionem non comprehenduntur in aqua tenebre, unde ipsa turbida apparebit clara, et clara tenebrosa. Solis autem radio cadente super faciem maris, cum ei per raritatem ipsius pateat transitus, abicietur omnis tenebra et umbre apparentia.

7.184 ◉ On the other hand, if the sea is roiled [and muddy], then sight will penetrate only a little because of the water’s diminished transparency, and it will perceive [only] a narrow stratum of the water. And even though it casts shadow, since that shadow is attenuated, the color of that stratum overcomes the shadow, for in muddy water the color is apparent, whereas in clear water there is none. Hence, according to both the color that is seen in the muddy water and the attenuated shadow that is seen in the [narrow] stratum [through which sight penetrates], darkness is not perceived in the water, so roiled water will appear clear, whereas clear water will appear dark. Moreover, when a ray of sunshine strikes the surface of the sea, since the ray’s passage [into the water] is evident because of the water’s transparency, every appearance of darkness or shadow will vanish.

7.185187 ◉ In decore et deformitate: Si in vase multum raro sint particule vel incisure ipsi decorem inferentes, et imponatur vasi illi vinum turbidum et turpe, occultabuntur decoris cause, et iudicabitur vas deforme, ut aliquando accidit in vitreo vase. Econtrario, si vas tale deforment alique eius particule, et imponatur ei vinum clarum lucidum et in colore formosum, occultabuntur deformitatis cause, et reputabitur vas speciosum cum sit deforme.

7.189 ◉ In similitudine et dissimilitudine: Si duo vasa multum rara conveniant in forma, specie, raritate, sed discrepant in aliquarum partium dispositione, vino eiusdem coloris eiusdem claritatis implenta, latebunt cause diversitatis, et reputabuntur omnino similia.

7.189 ◉ In [regard to] similarity and dissimilarity: If two highly transparent glasses are identical in form, kind, and transparency, but if they differ in the arrangement of certain of their features, then, when they are filled with wine of the same color and clarity, what causes them to differ will be invisible, and they will be judged to be perfectly identical.

7.190 ◉ Si vero inter ea fuerit diversitas in specie et forma, sed in aliquibus partialibus convenientia, vino simili plena, putabuntur omnino dissimilia, unde error in similitudine et in dissimilitudine, quia sumitur iudicium ex apparentibus tantum.

7.190 ◉ On the other hand, if they differ in kind and form but are identical in certain [other] features, then, when they are filled with the same kind of wine, they will be judged to be entirely different, so there is an error in [the perception of] similarity and dissimilarity because such a judgment is based on appearances alone.

7.192 ◉ Et in omnibus predictis accidit error ex sola soliditatis intemperantia, quoniam, aliis in esse suo manentibus, non accidit error ea ad temperantiam revocata.

7.192 ◉ In all of the preceding cases the error arises solely from an inordinate opacity, for, if everything else remains the same, the error does not arise when the opacity is restored to moderation.

Distinctio 6 ◉ Raritas aeris visum et rem visam intercidentis egreditur temperamenti proprii metas et errorem generat in omnibus quorum fidem visus efficit et sillogismus.

7.193194 ◉ In longitudine: Si fuerit aer pruinosus et obscurus, sicut in horis matutinis solet accidere, turre aliqua visui opposita in longitudine temperata, existimabitur plus a visu elongata quam habeat veritas, unde error in longitudine est, quoniam non comprehenditur longitudo inferioris terre secundum quam elongationis turris conviciatur mensura, et occultatur terra ex raritate aeris diminuta, unde raritas est erroris causa.

7.195 ◉ Si autem in hoc aere declinetur modicum corpus visum, occultabitur declinatio que pateret in aere claro, unde error in situ.

7.195 ◉ Moreover, if a body that is under scrutiny is somewhat inclined with respect to the eye in this kind of air, the inclination, which would be evident in clear air, will be hidden, so there will be an error in [the perception of] spatial disposition.

7.196 ◉ Et si fuerit in corpore gibbositas modica, apparebit planum in tali aere, et si fuerint in corpore anguli, latebunt, unde erroneum erit figure iudicium.

7.196 ◉ In addition, if there is a slight bulge in the object, that object will appear flat in such air, and if the object has corners, they will be invisible, so there will be an erroneous judgment of shape.

7.197 ◉ In quantitate erit error ex tali aere, quoniam visum maius apparebit quam in temperato aere, sicut accidit in corporibus post aque raritatem comprehensis.

7.197 ◉ An error in [the perception of] size will arise in such air, for a visible object will appear larger than it would in moderate[ly transparent] air, as happens in the case of bodies that are perceived through transparent water.⁑

7.198 ◉ Et si fuerit in corpore quasi linea nigra, putabitur esse partium divisio, unde error in divisione.

7.198 ◉ If, moreover, there is a black line in an object, that line will be judged to represent a split between segments, so there is an error in [the perception of] disjunction.

7.199 ◉ Et si fuerint duo corpora modicum a se disiuncta, apparebunt in hoc aere continua, unde error erit in continuitate. Et ex hiis palam quod error est in numero.

7.199 ◉ But if two bodies are barely separated, they will appear continuous in such air, so there will be an error in [the perception of] continuity. And it is clear from these [two] cases that there is an error in [the perception of] number.

7.202 ◉ In motu: Si in hoc aere duo videantur quorum unum alio paululum velocius moveatur, iudicabuntur forsitan equales esse eorum motus, cum in temperato aere discerni posset unius ad alium excessus. Et est error propter latens excrementum vie unius super viam alterius.

7.202 ◉ In [regard to] motion: If two things are seen in such air, and if one of them moves a bit faster than the other, they may be judged to move at equal speeds, whereas in moderate[ly transparent] air the difference in speed between them could be discerned. And this error occurs because the difference between the length of the path one follows and the length of the path the other follows is imperceptible.⁑

7.204 ◉ In quiete: Si quis post talem aerem a longitudine temperata non parva videat aquam fluentem, aut iudicabit eam immotam, aut, si fuerit fortis eius fluxus, minus quam moveatur motam.

7.204 ◉ In [regard to] rest: If someone looks at flowing water through such air from a distance that is moderate but not short, either he will judge it to be motionless, or, if it flows swiftly, he will judge it to move less vigorously than it actually does.

7.206 ◉ In asperitate et lenitate: Quia in hoc aere videbitur asperum lene propter latentes asperitatis causas, et visa re polita, cum non discernatur reflexio in ea, existimabitur aspera.

7.206 ◉ In [regard to] roughness and smoothness: [It follows] that in this kind of air a rough object will appear smooth because the reason for its roughness will be invisible, whereas if the visible object is polished, since there is no reflection discerned in it, it will be judged to be rough.

7.207209 ◉ In umbra: Si post hunc aerem videatur corpus album in quo sint particule rotunde nigre, luce ignis in corpus illud cadente ita tamen ut sit interpositio huius aeris, apparebit in locis illis umbra, aut forsitan reputabuntur foramina viam tenebris erumpentibus prestantia, unde error in tenebris, quare post hunc aerem corpus rarum apparebit minus rarum, et forsan putabitur solidum, et ita error in soliditate et raritate.

7.211 ◉ In specie et deformitate per causas particulares corpus decorantes vel deformantes in hoc aere latentes.

7.211 ◉ In [regard to] beauty and ugliness [an error in perception will arise] because the specific things that render the object beautiful or ugly are invisible in such air.

7.213 ◉ In similitudine et dissimilitudine propter partiales diversitatis aut convenientie causas inter duo corpora non apparentes.

7.213 ◉ In [regard to] similarity and dissimilarity [an error in perception will arise] because the features that cause two bodies to differ or to be identical are not apparent [in such air].

7.216 ◉ In hiis omnibus provenit error ex raritate aeris sola immoderata, cum, aliis immotis, in aere temperato non accideret.

7.216 ◉ In all these cases the error is due to solely to the inordinate transparency of the air, for, if everything else remained the same, that error would not occur in moderate[ly transparent] air.

Distinctio 7 ◉ Tempus extra temperamenti sui fines locatum causa est erroris per singula quorum fides in visu sumitur ex sillogismo.

7.217 ◉ In longitudine: Si subito intueatur quis aliquod remotum a turre quod statim visui subripiatur, non poterit plene discernere longitudinem inter illud et turrem, et iudicabitur forsan aut minus remotum a turre quam esset in veritate, aut magis. Et est quoniam in illa temporis instantia non percipitur a vidente terra turri et rei vise intermedia secundum quam sumatur distantie mensura, aut quoniam in tam brevi tempore non potuit axis viam intermediam discurrere, unde nec plene comprehendere, et ita error in longitudine.

7.217 ◉ [In [regard to] distance: If, from a tower, someone glimpses a distant object that is immediately snatched away from view, he will not be able to determine its distance from the tower properly, so he may judge it to be nearer or farther away from the tower than it actually is. And this happens because, in that brief period of time, the ground between the tower and the visible object according to which the distance is measured is not [properly] perceived by the observer, or else it happens because in such a brief time-span the [visual] axis could not scan the intermediate ground, so it could not apprehend it properly, and there will thus be an error in [the perception of] distance.

7.218 ◉ In situ: Cum aliquid subito occurrit visui et statim recedit, reputabitur forsitan rectum declinatum, aut econtrario.

7.218 ◉ In [regard to] spatial disposition: When something is glimpsed and then immediately removed, it may be judged to face the eye directly when it is inclined, or vice versa.

7.221 ◉ In figura: Si fuerit modica gibbositas in re subito visa latebit, et reputabitur res plana, aut latebunt anguli si fuerint in ea.

7.221 ◉ In [regard to] shape: if there is a slight bulge in an object that is [merely] glimpsed, that bulge will go unseen, so the object will be judged to be flat, or the corners it possesses will be invisible [to sight].

7.222 ◉ In quantitate: Si quis tirsum ardentem moveat motu citissimo et intra viam modicam ut sepius vadat et revertatur per eam, apparebit via motus ignea, quoniam motus tirsi ab uno vie termino ad alium sit quasi instanti.

7.222 ◉ In [regard to] size: If someone waves a flaming torch quickly over a short distance so that it oscillates back and forth many times [during a brief time-interval], the path of its motion will appear fiery, because the movement of the torch from one side to the other is almost instantaneous.

7.223 ◉ Unde propter temporis brevitatem non potest discerni vel quantitas vel motus tirsi, unde et hic error in motu.

7.223 ◉ Accordingly, neither the size nor the motion of the torch can be [properly] discerned because of the brevity of the time, so in this case there will also be an error in [the perception of] motion.

7.226 ◉ In divisione: Si aliquid subito visum a visu divertatur, et fuerit in eo linea nigra, putabitur esse divisio partium illa nigredo.

7.226 ◉ In [regard to] disjunction: If something that is glimpsed by sight is [immediately] taken away, and if there is a black line on it, that black [line] will be taken to mark a split between segments [of the object].

7.227228 ◉ Et si corpora contigua aut valde propinqua subito videantur, existimabuntur continua, sicut accidit in scanni tabulis subito inspectis, unde error in continuitate.

7.230 ◉ In motu: Cum duorum unum paulo velocius alio movebitur, motus in tempore modico comprehensi equales iudicabuntur, cum non tam subito comprehensibilis sit excessus.

7.230 ◉ In [regard to] motion: When one of two objects moves a bit faster than the other, their motions will be judged to be equal when they are perceived over a brief time-span, because the difference [in speed] is not perceptible in such a short amount of time.

7.232 ◉ In quiete: Si aliquid modicum moveatur subito visum, moveri non videbitur, quoniam via quam percurrit in tempore perceptionis sue imperceptibilis est visui pre sui parvitate. Superius autem explanatum est quod non comprehenditur motus in corpore nisi in sensibili tempore.

7.232 ◉ In [regard to] rest: If a slowly moving object is [merely] glimpsed, it will not appear to move, for the path it follows during the time it is perceived is imperceptible to sight because of its brevity. But it was explained above that the motion of a body is perceived only during a perceptible time-span.⁑

7.233 ◉ Similis error accidit in rota modica. Cum citiissime volvatur, apparet immota cum non possit fieri comprehensio revolutionis eius in tempore tam parvo quam parvum est in quo fit una eius revolutio.

7.233 ◉ The same sort of error happens in the case of a small disk. When it revolves swiftly, it appears motionless because its revolution cannot be perceived in the small amount of time during which it makes a single revolution.

7.234 ◉ Idem error accidit in troco, unde error in quiete, quoniam non potest discerni mutatio situs partium troci, quare nec motus eius. Et si unius coloris fuerit trocus, palam quod non comprehenditur motus. Si vero plurium et diversorum colorum nec sic etiam apparebit motus, cum lateat colorum diversitas et pretendatur ex nimia festinatione confusa quedam colorum unitas.

7.234 ◉ The same error occurs in the case of a top, so there will be an error in [the perception of] rest, since the change in spatial disposition of the parts of the top cannot be discerned, which is why its motion cannot be discerned either. Now if the top is of one color only, it is clear that its motion is not perceived. If it consists of several different colors, its motion will still not be seen, because the difference among the colors is invisible, and they are presented as a sort of uniform blend of the colors on account of the inordinate speed [of rotation].⁑

7.237 ◉ In asperitate: Cum subito videatur asperum, putabitur forsitan lene. Et si hoc modo videatur lene, non poterit in eo discerni lenitas aut asperitas, unde dubitatio et error.

7.237 ◉ In [regard to] roughness: When something rough is [merely] glimpsed, it may be judged to be smooth. Moreover, if something smooth is glimpsed the same way, neither smoothness nor roughness can be discerned in it, so there will be uncertainty and error [in such perception].

7.239 ◉ In raritate. Luce declinata super corpus rarum descendente subito visum, cum non percipiatur declinatio lucis, putabitur forsitan quod finis raritatis sit apparens raritas corporis. Quod, si in tempore modicum maiori adhibeatur visui, percipietur declinatio causa apparentie raritatis remisse.

7.239 ◉ In [regard to] transparency: If light shines on a transparent object at a slant, and that object is [merely] glimpsed, since the inclination of the light is not perceived, the transparency of the object as it appears may be judged absolute. But if the object is exposed to view a bit longer, the [light’s] inclination will be perceived as the cause of the apparent decrease in transparency.⁑

7.240 ◉ In soliditate: Si quis instanter videat corpus rarum et post ipsum non discernat lucis transitum, putabitur esse solidum.

7.240 ◉ In [regard to] opacity: If someone sees a transparent object very briefly and does not discern light passing through it from behind, the object will be judged to be opaque.

7.241242 ◉ In umbra: Si in albo pariete sint partes sub nigredine, descendente super ipsum ignis luce, subito vise, putabuntur esse umbre. Si vero nigredo visa fuerit intensa, existimabuntur foramina tenebris plena.

7.244246 ◉ In specie et deformitate: Quoniam in tam parvo tempore non sunt comprehensibiles minute decoris vel deformitatis cause, sicut accidit cum aliquis movens per foramen intuetur faciem iudicat aliquando fedam formosam, vel econtrario. Et idem error accidit mota re visa, oculo immoto.

7.247 ◉ In similitudine et dissimilitudine. Quoniam latent particulares similitudinis aut dissimilitudinis cause.

7.247 ◉ In [regard to] similarity and dissimilarity: For the particular features that cause similarity or dissimilarity are invisible to sight.

7.249 ◉ Et in hiis omnibus ex solo tempore non moderato accidit error, cum in predictis nulla accideret eo ad temperantiam reducto.

7.249 ◉ In all these cases an error occurs on the basis solely of an inordinate[ly short amount of] time, since none of those errors would occur if the time-interval were restored to moderation.

Distinctio 8 ◉ Visus debilitas et immoderatio errorem invehit singulis per sillogismum in visu comprehensis.

7.250 ◉ In longitudine: Si opponantur visui duo corpora quorum unum coloris fortis et remotius aliud coloris debilis et oculo propinquius, cum non fiat comprehensio longitudinis nisi facta collatione inter aliqua, incertam faciet collationem debilitas visus.

7.250 ◉ In [regard to] distance: If two objects face the eye, one being of an intense color and lying farther from the eye, the other being of a faint color and nearer the eye, since the perception of their distance [from the eye] depends entirely on comparing the two, weak sight will produce an inconclusive comparison.

7.251 ◉ Et quia certum est homini quod ex propinquioribus certior fit fides visui quam ex remotioribus, concludit illud quod apparet ei certius ex hiis corporibus esse propinquius. Et planum quod visui debili certior fit fides coloris fortis quam debilis, licet modicum plus elongati.

7.251 ◉ But since it is certain to everyone that sight has a clearer apprehension of nearer things than it does of farther things, the viewer concludes that, between these two objects, the one that is seen more distinctly is the nearer. And it is obvious that weak sight has a clearer apprehension of an intense color than it does of a weak one, even though [the intensely colored object] lies somewhat farther away.

7.252 ◉ Idem error accidit etiam in temperantia visus, quoniam in longitudine magna propinquius iudicatur corpus cuius color fortis quam cuius color debilis, licet non sit multum remotius.

7.252 ◉ The same error arises when the visual power lies within [the range of] moderation, for at a great distance a body that is more intensely colored is judged to be nearer than one that is faintly colored, provided that it does not lie much farther away.⁑

7.254 ◉ In situ errat visus debilitas. Si ab aliquanta longitudine, licet temperata, declinetur corpus, et sit modica declinatio, ignorabitur cum plene comprehenditur longitudo.

7.254 ◉ Weak sight errs in [the perception of] spatial disposition. If an object at some moderate distance is slightly inclined, the inclination will not be apprehended [even] when the distance [of the object] is properly perceived.

7.255 ◉ Et incertitudo longitudinis et situs errorem ingerit quantitatis.

7.255 ◉ Moreover, an indistinct perception of distance and spatial disposition produces an error in [the perception of] size.

7.256 ◉ In figura: Quia gibbus corporis modicus et multiplex angulus latet debilitatem visus.

7.256 ◉ In [regard to] shape: For a slight bulge or a multiplicity of corners in a body is invisible to weak sight.

7.257 ◉ Et si in corpore linea nigra fuerit, existimabitur divisio vel fissura, et existimabitur unum continuum corpora contigua, unde error in divisione, continuitate, numero.

7.257 ◉ Moreover, if there is a black line on an object, it will be judged as a juncture or crack, whereas contiguous bodies will be judged to form a single continuum, so there will be an error in [the perception of] disjunction, continuity, and number.

7.258 ◉ Eadem erroris causa strabo unum iudicat duo si fuerit informitas in uno tantum oculo, quoniam tenebit res visa diversitatem situs respectu duorum oculorum eius.

7.258 ◉ For the same reason someone who suffers from a squint judges a single object to be double if there is a deformity in one eye only, for the visible object will occupy noncorresponding places with respect to his two eyes.

7.259 ◉ Si autem in duobus oculis eius sit deformatio, cum accidit eos moveri, forsitan accidet ei diversitas situs respectu vise rei, et ita in uno pluralitas.

7.259 ◉ Moreover, if the deformity extends to both of his eyes, then, when he chances to move them, they may happen to be oriented differently with respect to the visible object, and so one thing [will be taken as] more than one thing.

7.261 ◉ In motu: Si quis sepius in circuitu volvatur, cum quiescit putat quod parietes moveantur. Et est quoniam, moto vidente, movetur interius vis visibilis. Et licet videns steterit, non statim vis visibilis stabit, sed motus eius in videntis quiete durabit, et ob hoc motus visarum rerum estimatio insurgit. Et huiusmodi motus exemplum in troco videmus, quoniam diu post manus moventis quietem volvitur trocus. Est etiam infirmitas in qua videntur patienti omnia volvi.

7.261 ◉ In [regard to] motion: If someone spins around several times, when he stops he supposes that the walls are moving. And this happens because, when the viewer is moving, the visual spirit within him moves [too]. So even though the viewer has stopped, his visual spirit will not come to rest immediately, but its motion will continue in the motionless viewer, and on this basis a judgment that the [surrounding] visible objects are moving arises.⁑ We see an example of this sort of motion in the case of a top, for the top revolves for awhile after the hand that moves it stops. There is also a disease according to which everything seems to the sufferer to revolve [about him].

7.264 ◉ In quiete: Quando corpus similium partium volvitur revolutione pauca, visus debilis non percipit eius motum quem quidem percipiet visus temperatus.

7.264 ◉ In [regard to] rest: When a body with identical parts revolves slowly, weak sight does not perceive its motion, whereas moderately strong sight will perceive it.

7.265 ◉ Si autem multa sit revolutio, non percipitur etiam a temperato. Si vero sit dissimilium partium corpus motum, ut in rota, visus debilis comprehendet motum. Si autem festina fuerit revolutio, occultabitur visui debili motus. Quoniam partes rote non multum sunt dissimiles, non plene comprehendetur dissimilitudo in festinatione, et per dissimilitudinem partium fit comprehensio motus earum.

7.265 ◉ On the other hand, if its rotation is swift, its motion is not even perceived by moderately strong sight. If, however, the moving body consists of dissimilar parts, e.g., in the case of a wheel,⁑ weak sight will perceive its motion. But if the rotation is swift, the motion will be hidden to weak sight. Since the parts of the wheel are not completely dissimilar, their dissimilarity will not be properly perceived in swift motion, but it is by a dissimilarity of parts that their motion is perceived.

7.266? ◉ ?????? @author {kew}

7.267-268 ◉ In asperitate et lenitate: Quia forsan reputabitur modicum lene asperum, vel econtrario si inter formas asperi et lenis fuerit dissimilitudo.

7.267-268 ◉ In [regard to] roughness and smoothness: For something that is [only] moderately smooth will be judged to be rough, or vice versa if there is a difference between the forms of the rough and smooth objects.

7.269 ◉ In raritate. Cum fuerit in corpore raro soliditas pauca, existimabitur a visu debili maior vera.

7.269 ◉ In [regard to] transparency: When there is a bit of opacity in a transparent body, it will be judged by weak sight to be more opaque than it actually is.

7.270 ◉ In soliditate: Cum fuerit in corpore raro color fortis, aut post ipsum, et raritas non magna, putabit illud esse solidum.

7.270 ◉ In [regard to] opacity: When a transparent body is intensely colored, or when an intensely colored body lies behind it, if its transparency is not too great, [weak] sight will judge it to be opaque.

7.272 ◉ In umbra: Note parietis albi sub nigredine descendente super ipsum luce, apparent etiam huic visui umbre.

7.272 ◉ In [regard to] shadow: When light shines on a white wall with small marks that are black, but not intensely so, those marks appear to weak sight as shadows.

7.273 ◉ Et si fuerint multum nigre, apparebunt foramina in quibus tenebre.

7.273 ◉ If, however, those marks are intensely black, they will look like holes through which darkness appears.

7.274? ◉ ?????? @author {kew}

7.275-276 ◉ In decore, deformitate, similitudine, et dissimilitudine [error accidit] per particulares decoris vel feditatis et similitudinis causas visum latentes.

7.275-276 ◉ In [regard to] beauty, ugliness, similarity, and dissimilarity [an error arises] because the specific features that render objects beautiful, or ugly, or similar are hidden to [weak] sight.

7.278 ◉ Et est error in predictis omnibus ex sola debilitate visus.

7.278 ◉ So there is an error in [the perception of] all of the things we discussed on account, solely, of weak sight.

7.279 ◉ Iam diximus quomodo accidit error in sillogismo secundum unamquamque causarum erroris visus in qualibet partium que adquiruntur per sillogismum. Iam incessimus super quemlibet erroris modum, et cuiuslibet supposuimus exemplum. Et licet in erroribus visus sit copiosa multitudo, tamen omnium ad modos dictos fiet reductio, et ad exempla ordinatim proposita. Et assignavimus errores secundum quod singuli eorum accidunt ab unica tantum causa.

7.279 ◉ We have now explained how an error of [visual] deduction arises according to each of the causes of visual errors in each of the things that are apprehended through deduction. We have now dealt with each kind of error and have adduced an example of each. And even though there is a plethora of visual errors, they have nonetheless all been distilled down to the kinds that have been described and arranged according to the examples adduced. And we have presented each of these errors according to a single cause that produces it.

7.280 ◉ Et aliquando error infertur non ab una tantum sed duabus causis vel pluribus. Verbi gratia, si moveatur aliquid a longitudine magna motu lento subito visum, videbitur immotum, et percipi posset motus ille in temperata longitudine visus instantia manente. Et etiam in longitudine temperata non occultaretur motus si temperatum esset inspectionis tempus.

7.280 ◉ Now [visual] error sometimes arises not from a single cause, but from two or more causes. For instance, if something that is [merely] glimpsed from afar moves slowly, it will appear to be motionless, whereas its motion could be perceived at a moderate distance in the same brief time-span. So too, the motion would not be imperceptible at a moderate distance if the time during which it was viewed were moderate.

7.281 ◉ Provenit igitur error ex duabus intemperantiis quarum neutra per se sufficit.

7.281 ◉ This error thus arises on the basis of two inordinate conditions, neither one of which suffices by itself [to produce the error].

7.282 ◉ Trium aggregatio errorem efficit. Si a magna longitudine, sub debili luce, in modico tempore opponatur visui corporis diversorum colorum revolutio non cita, existimabitur corpus stare.

7.282 ◉ A convergence of three [inordinate conditions] produces [visual] error. If a body of various colors that rotates, but not very fast, is seen in faint light from afar for a brief moment, the body will be judged to be at rest.

7.283 ◉ Et si ab eadem longitudine, sub eadem luce, tempore temperato adhibeatur intuitus, comprehendetur motus, qui similiter non latebit in temperata longitudine sub eadem luce et modico tempore. Et etiam percipi poterit in eadem longitudine sub forti luce.

7.283 ◉ Yet if [the same body] is looked at from the same distance in the same light, but during a moderate amount of time, the motion will be perceived, and by the same token it will not be imperceptible [if seen] in the same light for a brief moment, but at a moderate distance. And it could also be perceived at that same distance [for a brief moment but] in strong light.

7.286 ◉ Et generaliter ex omnibus erroribus visui accidentibus nec unus nec plures aggregati evadunt causas quas diximus. Quelibet autem rei vise forma ex eis que numeravimus est compacta, et cum visus non adquirat ex rebus visis nisi aliquas istarum, non accidet error in visu nisi in aliqua istarum. Et omnis error qui accidit in scientia est quoniam intellectus similia efficit que percipit cum eis que percepit in modo aliquo aut dissimilia.

7.286 ◉ In general, then, among all the errors that occur in sight, whether singly or in conjunction, every one is subject to the causes that we described. Moreover, every form of a visible object is a composite of the [visible] attributes we have listed, and since sight apprehends nothing about visible objects except these specific attributes, no error will occur in sight that does not involve one of them. And every error that occurs in recognition occurs because the intellect either assimilates things it perceives [at the moment] with things it somehow perceived [earlier] or distinguishes between them.

7.287 ◉ Et omnis error in particularibus erit aut in sensu, aut in scientia, aut in sillogismo, nec potest esse quin sit in aliquo istorum, aut duobus, aut ipsis tribus. Et quicumque error accidit in huiusmodi tribus non erit nisi per errorem visus in partibus.

7.287 ◉ And every error concerning individuals will occur either in [brute] sensation, in recognition, or in deduction, and error can occur in no other way than according to one, two, or three of these. Moreover, whatever error occurs in any of these three ways will occur only by means of an error of sight concerning particular aspects.

7.288 ◉ Et iam patuit quod error visus in partialibus non erit nisi per causas quas assignavimus, aut ex una earum tantum aut ex pluribus.

7.288 ◉ So now it has been shown that an error of sight concerning particular aspects will be due only to the causes we have listed, either from one of them alone or from several of them.