- The basic studies of Leonardo in this regard are those of Ackerman James S. Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 108 146 Martin Kemp, ‘Leonardo and the Visual Pyramid’, ibid., 40 (1977), 128–49; and Donald Sanderson Strong, ‘Leonardo da Vinci on the Eye: the Ms.D. in the Bibliothèque de l'Institut de France…’ (unpublished Ph.D. dissertation, University of California, Los Angeles, 1967).
- Alhazen . 1572 . De aspectibus Edited by: Risner , Friedrich . 24 – 27 . Basel (Ibn al-Haytham),
- Lindberg , David C. 1976 . Theories of Vision from al-Kindī to Kepler 154 – 168 . Chicago Strong (footnote 1), p. 301.
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 67 – 74 . Chicago 80–4, gives a careful summary, although my account does not agree in all particulars with his. For a detailed discussion see A. I. Sabra, ‘Sensation and Inference in Alhazen's Theory of Visual Perception’, in Studies in Perception, edited by Peter K. Machamer and Robert G. Turnbull (Columbus, 1978), pp. 160–85.
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 28 – 30 . Chicago 72–3. I follow Lindberg's implication that Alhazen knew and used al-Kindī on this matter. A. I. Sabra has reminded me in a private communication that there is no proof of this knowledge and use.
- A recent account of Hunayn's visual theory appears in Eastwood Bruce The Elements of Vision…Hunayn ibn Ishāq Philadelphia 1982 (American Philosophical Society Transactions, 72, pt 5 especially pp. 21–46 on the visual pneuma. Not only did Alhazen limit the visual spirit to this interior container defined by Hunayn, but he also limited its presence within this container. In De aspectibus, I, iv, 4 (p. 4), the final sentence does not say what it at first appears to say. The text is as follows: ‘Et dicitur, quod spiritus visibilis emittitur ex anteriori parte cerebri, et implet duas concavitates duorum nervorum primorum coniunctorum cum cerebro, et pervenit ad nervum communem, et implet concavitatem eius, et venit ad duos nervos secundos opticos, et implet ipsos, et pervenit ad glacialem, et dat ei virtutem visibilem’. In this passage there are four pairs of verbs applied to the spiritus visibilis. First, ‘emittitur’ and ‘implet’; second, ‘pervenit’ and ‘implet’; third, ‘venit’ and ‘implet’; last, ‘pervenit’ and ‘dat’. In all but the last case, the spiritus both arrives at and fills, while in the case of the glacialis there is arrival but no filling. The glacialis receives a virtus visibilis from the spiritus, but is not pervaded by the spirit itself. Finally, Alhazen uses glacialis, not humor glacialis; the glacialis here is best understood as the composite corpus glacialis, as will be shown below. My interpretation of the limits of the spiritus visibilis is brought out and developed at various points below. Cf. I, vi, 33 (p. 21) for the same vocabulary with regard to the visual spirit and the glacial: ‘spiritus visibilis…perveniat ad glacialem et det ipsi virtutem sensibilem successive…’
- Alhazen . 17 – 17 . I, v, 30 ‘Glacialis ergo alteratur a luce et coloribus tantum ut sentiat’.
- Alhazen . 15 – 15 . I, v, 25 ‘Et etiam glacialis est praeparatus ad recipiendum istas formas et ad sentiendum ipsas. Formae ergo pertranseunt in eo propter virtutem sensibilem recipientem’.
- Alhazen . 15 – 15 . I, v, 25 ‘…et ex ordinatione partium formae in sua [glacialis] superficie et suo toto corpore erit sensus eius ex ordinatione partium operantis’, II, i, 1 (p. 25): ‘…extensio formarum a superficie glacialis intra corpus glacialis est secundum rectitudinem linearum rectarum radialium tantum, quoniam glacialis non recipit istas formas, nisi secundum verticationem linearum radialium tantum’.
- Alhazen . 25 – 26 . II, i, 3 The following points exhaust the prescriptions he makes for the forward surface of the vitreous humour. (a) The surface, in order to preserve the same relationship of points as exists on the surface of the glacial, should be either plane or spherical. (b) The surface cannot have the same centre of curvature as the anterior surface of the glacial. (c) The surface cannot be part of a small (parva) sphere, because this would cause a distorted (monstruosa) form. (d) Therefore the surface will be either planar or part of a sphere of some good size (alicuius bonae quantitatis).
- Alhazen . 28 – 28 . II, i, 7 Edinburgh Royal Observatory, MS Cr 3. 3, f. 25r.
- This is not to say that Alhazen was unconcerned with the truth of the matter but rather that he was concerned first to present a geometrically consistent model. In this vein he presented the theory of extramission of rays on the one hand as theoretically otiose (I, v, 23) but on one other hand not simply and totally incorrect or useless (I, v, 24; p. 15). He retained his stand that extramission is simply unnecessary when he argued yet more persuasively that comprehension occurs only after mental distinction and reason; therefore, something must come from object to brain (II, ii, 23). As A. I. Sabra has remarked, for Alhazen, ‘A hypothesis was not to be accepted simply (my emphasis) because it saved the phenomena’; see his, ‘The Physical and the Mathematical in Ibn al-Haytham's Theory of Light and Vision’, in The Commemoration Volume of the Bīrūnī International Congress in Tehran Tehran 1976 439 478 especially 454. While Alhazen allotted the study of vision to both physics and mathematics, with neither subordinated to the other, he also said, ‘Mathematicians, for their part, have paid more attention to this science [of optics] than others. They have pursued its investigation, paying attention to its details and divisions. They have distinguished objects of vision, assigning causes to their particular properties and stating reasons for each of them’. (Bk. I, ch. 1, paragraph 3; translation kindly offered by A. I. Sabra). See Eilhard Wiedemann, ‘Zu Ibn al Haitams Optik’, Archiv für die Geschichte der Naturwissenschaften und der Technik, 3 (1910), 1–53, especially 18–9 for a slightly different translation of the passage. Mattias Schramm, ‘Zur Entwicklung der physiologischen Optik in der arabischen Literatur’, Sudhoffs Archiv, 43 (1959), 295–6, points generally to the scientific model of Ptolemaic astromony and optics as the fundamental pattern followed by Alhazen.
- Alhazen . 25 – 25 . II, i, 2 It is not made explicit whether the density of the vitreous is greater or less than that of the glacial humour, although the answer is suggested by what follows in II, i, 6.
- Alhazen . 26 – 27 . II, i, 6
- Alhazen . 25 – 25 . II, i, 2 ‘Et debet ista superficies esse consimilis ordinationis, quoniam, si non fuerit consimilis ordinationis, apparebit forma monstrousa propter refractionem’.
- Alhazen . 25 – 25 . II, i, 3
- Alhazen . 26 – 26 . II, i, 5
- Alhazen . 27 – 27 . II, i, 6
- Alhazen . 8 – 8 . I, v, 16 More precisely, Alhazen says at one point: ‘apud membrum istud [i.e. glacíalem] principium est sensus’. (II, i, 3; p. 26). Here principium means ‘the beginning’.
- Alhazen . 15 – 15 . I, cf. I, v, 25 ‘Formae ergo pertranseunt in eo [corpore glaciale] propter virtutem sensibilem recipientem… ex ista operatione [formae] et passione [virtutis sensibilis] erit sensus glacialis ex formis rerum visibilium, quae sunt in superficie sua et pertranseunt per totum suum corpus’.
- The term sensus alone does not refer simply to what happens in the glacialis, as is evident when, in the process of describing binocular vision, Alhazen says, ‘Et etiam sensus non extenditur a membris ad ultimum sentiens nisi in nervis continuatis membris et cerebro’. Alhazen 16 16 I, v, 27
- Alhazen . 26 – 26 . II, i, 4
- Alhazen . 26 – 26 . II, i, 4 ‘Pars ergo anterior tantum glacialis est appropriata receptioni formarum ex verticationibus linearum radialium; posterior autem pars, quae est humor vitreus, et virtus recipiens, quae est in illo corpore, non est appropriata cum suo sensu istarum formarum, nisi ad custodiendum eorum ordinationem tantum’. However, he later says that the vitreous senses as well as receives the form (II, i, 5).
- Alhazen . II, i, 5 ‘refractio ergo formarum apud superficiem vitrei non est nisi propter diversitatem qualitatis receptionis sensus inter ista duo corpora. Formae ergo refringuntur apud vitreum duabus de causis, quarum altera est diversitas diaphanitatis duorum corporum et altera diversitas qualitatis receptionis sensus inter ista duo corpora’.
- Alhazen . 27 – 27 . II, i, 6
- Alhazen . 16 – 16 . II, ii (p. 34).
- Alhazen . 6 – 6 . II, i (p. 26).
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 209 – 210 . Chicago nicely summarizes the situation.
- On Jordanus see Grant Edward Jordanus de Nemore Dictionary of Scientific Biography 1973 7 171 179 Barnanas Hughes, ‘Biographical Information on Jordanus de Nemore to Date’, Janus, 62 (1975), 151–6; Ron B. Thomson, ‘Jordanus de Nemore: Opera’, Mediaeval Studies, 38 (1976), 97–144. On Jordanus' proposed use of the Perspectiva, see Marshall Clagett. Archimedes in the Middle Ages, I: the Arabo-Latin Tradition (Madison, 1964), pp. 668–9; this attribution to Jordanus has been re-evaluated and contradicted by Marshall Clagett, Archimedes in the Middle Ages, V: Quasi-Archimedean Geometry in the Thirteenth Century (Philadelphia, 1984), pp. 297–301, 303–4, 594.
- Albertus Magnus seems to signal the new awareness with his evident ignorance of De aspectibus in the 1240s and explicit reference to the work of Alhazen in the late 1250s. See Lindberg Theories of Vision from al-Kindī to Kepler Chicago 1976 106 106 n. 16 for the evidence.
- Lindberg , David C. 1975 . A Catalogue of Medieval and Renaissance Optical Manuscripts 17 – 19 . Toronto lists 21 manuscripts, of which one is a fourteenth-century Italian translation, two are short fragments, one is brief excerpts, and one is a list of propositions derived from Risner's edition. Of the sixteen manuscripts remaining, all of which are complete or nearly complete, the distribution by centuries is: s. XIII, 7 (6 dated in Lindberg's catalogue, Vat. Palat. lat. 1355 dated tentatively by myself to s. XIIIex.); s. XIV, 6; s. XV, 2; s. XVI, 1. Of these sixteen, one (London Royal College of Physicians MS 383, s. XIII) lacks a significant portion of Book I, beginning only at I, 31, according to Risner's numbering, and thereby omits the anatomical section fundamental to our topic. If we omit as well Paris BN 16199, s. XVI, because of its late date, we have 14 manuscripts to consider in discussing the medieval Latin tradition of Alhazen's account of vision in the eye.
- A nice example of how these geometrically conceived anatomies of the eye were naturalized in the Renaissance without any change in anatomical doctrine appears in Murdoch John E. Album of Science. Antiquity and the Middle Ages New York 1984 238 239
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 145 – 146 . Chicago
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 126 – 126 . Chicago neatly summarizes Henry's contentions. I would interpret these arguments differently from Lindberg, as I see them relating directly to what the Latin text of Alhazen says or implies, as explained in Section 2 of this study. Lindberg considers Henry's first point flawed, because Henry assumed the anterior vitreous convex; I believe Henry understood correctly, pace anything in Roger Bacon. Lindberg's suprise (p. 129) at Henry's location of the visual power in the vitreous also seems to me needless, for the real problem is the location of conjoined sensitivity and non-rectilinear transmission, which Alhazen placed completely beyond the corpus glacialis.
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 127 – 127 . Chicago Figure 16, gives a good reconstruction of the very rough diagram in the Florentine MS, f. 72v left margin, upper diagram. At p. 258 n. 18 (ref. p. 126) Lindberg comments on the issue of convexity vs. concavity of the glacial-vitreous interface, ‘only a concave surface would prevent intersection of the rays’. Since I disagree with this interpretation, I should say that the distances, curvatures, and density gradients are not quantified, so that a concave surface simply is not the ‘only’ possibility.
- The MS is described in most laconic fashion in Coxe H.O. Catalogus … Oxford 1852 II 59 59 iv ‘codex membr., fol. min., ff. 114, s. XIII’. I have no further information on origin or early provenance. There seem to have been two main glossators, the earlier s. XIIIex.(?), the later responsible for the diagram under discussion.
- Alhazen . 1 – 1 . II, i (pp. 24–5), ends at line 32, some seven lines below the diagram.
- Alhazen . 2 – 2 . II, i (p. 25): ff. 12v, 32–13r, 9.
- Alhazen . 1 – 1 . II, i (p. 25, line 2).
- Strong . 1978 . Leonardo's Eye . Journal of the Warburg and Courtauld Institutes , 41 : 212 – 212 . Strong's dissertation includes a translation of this text, known as MS D in the Institut de France, as well as a detailed commentary on its contents.
- As examples Lindberg Kemp Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 212 212 Ackerman's article seems to me to stray too far in the direction of modernizing Leonardo in this regard.
- A useful summary of main points in Leonardo's theory appears in Lindberg Theories of Vision from al-Kindī to Kepler Chicago 1976 164 168
- Regarding these ‘pinhole images’ and the decline in proper understanding during the fourteenth century, see Lindberg's David C. The Theory of Pinhole Images from Antiquity to the Thirteenth Century Archive for History of Exact Sciences 1968 5 154 176 three consecutive articles ‘A Reconsideration of Roger Bacon's Theory of Pinhole Images’, ibid., 6 (1970), 214–23; ‘The Theory of Pinhole Images in the Fourteenth Century’, ibid., 6 (1970), 299–325.
- MS D, f. 2v Strong Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 47 48
- Kemp . 1978 . Leonardo and the Visual Pyramid . Journal of the Warburg and Courtauld Institutes , 41 : 144 – 145 . remarks on Leonardo's reasoning with regard to this point, but Leonardo does not require the aperture to be close to the eye as does Kemp.
- For my purposes it is not so important to determine whether Leonardo meant something close to the modern ‘pupil’ by ‘popilla’ or something much more ambiguous. Kemp Leonardo and the Visual Pyramid Journal of the Warburg and Courtauld Institutes 1978 41 140 140 n. 43, thinks the former, noting that in MS D ‘popilla’ means ‘gateway’ of the eye. Ackerman (footnote 1), p. 130 n. 73, thinks the latter and translates ‘popilla’ as ‘cornea’. While it is true that Leornardo locates the visual power at more places than this forward surface, whether pupil or cornea, he explicitly states that it is to be found here also.
- MS D, f. 2v. Strong Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 48 49 The same experiment is described again at f. 4v (Strong, pp. 60–1) with the explicit purpose of showing that the visual power, or virtue, covers the surface of the pupil.
- MS D, f. 6v. Strong Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 68 70
- MS D, f. 10v. Strong Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 91 92
- MS D, f. 8r; Strong p. 77. As remarked by Kemp Leonardo and the Visual Pyramid Journal of the Warburg and Courtauld Institutes 1978 41 140 140 n. 43. Also at MS D, f. 3v; Strong, p. 54. At least provisionally, Leonardo explicitly rejects the option of placing the visual power in the crystalline humour: MS D, f. 7v; Strong, pp. 73–4. Antonio Borsellino and Corrado Maltese, ‘Leonardo, un' agucchia e un foro: uno studio sull' ottica leonardiana’, Physis, 18 (1976), 221–44, at pp. 238–9 argue unconvincingly that Leonardo reached a final conclusion at MS D, f. 8r-v that the visual power is localized at the end of the optic nerve. (The historical part of the article is by Maltese alone.) The argument is unconvincing, because Leonardo returns again at f. 10v to his earlier statement that the virtù is present across the whole front of the pupil. Borsellino and Maltese are far too concerned to show how perceptive and forward-looking Leonardo was.
- While there is some ambiguity about the properties of Leonardo's visual virtus, there is none about Alhazen's. In a description of the properties of the glacial humour, Alhazen describes the passive nature of the humour's virtus sensibilis, which receives the visible forms: ‘appareat virtuti sensibili forma lucis et coloris, quae figebantur in eo. Nam si esset [humor] diaphanus in fine diaphanitatis, pertransirent formae in eo, et non pateretur a formis passione, quae est ex genere doloris; et sic non comprehenderet formas’. See Alhazen 21 21 I, vi, 33
- The former at MS D, f. 7v Strong 74 74 The latter at MS D, f. 10v; Strong, p. 91.
- The only pattern in which Leonardo delays initial intersection until the crystalline is at f. 3r Strong 50 51 The preferred alternative is also on f. 3r; Strong pp. 51–2.
- In only one of the five hypothesized (unrejected) patterns does Leonardo name the central, refracting sphere ‘crystalline’; see MS. D, f. 10r Strong 88 89 At f. 8v (Strong, p. 79) no name is given to the central sphere. In all the other patterns, he calls this sphere ‘vitreous’; see ff. 3r, 3v (twice), 8r; Strong, pp. 51–2, 54–7, 76–7. Leonardo may have been influenced by Lorenzo Ghiberti's imprecise ocular anatomy here. Ghiberti depicted a single body with the labels ‘spera gratialis’ and ‘humor vitreus’, having no division or demarcation. While this can be correct in Alhazen's scheme, the labelling is also misleading and can suggest that the two names are quite interchangeable. See Firenze BN Centr. MS. II, i, 333 (Magl. XVII, 33), f. 18v; edited by Julius von Schlosser, Lorenzo Ghilbertis Denkwürdigkeiten (I Commentarii) (Berlin, 1912), I, 79. At f. 48r–v (I, 180–3), Ghiberti discusses refracted and unrefracted rays in the visual pyramid using a simple three-layer model of the eye, exactly like Leonardo's, with a central glacial sphere surrounded by the albugineous humour, which is in turn enclosed by the cornea and its extension.
- The second intersection of rays is placed within the crystalline in MS D at ff. 3v, 10r Strong 54 55 88–9
- A location posterior to the crystalline is given in MS D at ff. 3r, 3v, 8r, 8v; respectively in Strong 51 52 56–7, 76–7, 79.
- Refraction of the rays leaving the central sphere is posited in MS D at ff. 3r, 3v, 8r Strong 51 52 56–7, 76–7.
- Rectilinear exit of the rays from the central sphere is posited in MS D at f. 8v Strong 79 79 At f. 10r (Strong, pp. 88–9) the optic nerve abuts the central, or crystalline, sphere, so that no path is shown for exiting rays (Figure 16). At f. 3v (Strong, pp. 54–5) there is not geometrical definition of the rays leaving the central, or vitreous, sphere, though it would be reasonable to assume refraction in this case, because of the location of the visual power at the optic nerve.
- The locations of the alternative namings are given above, n. 66. The following arrangement discussed in detail appears at MS D, f. 3r; Strong, pp. 50–1. A preferable arrangement is given immediately after Strong 512 512 where the only refractions are by the ‘vitreous sphere’.
- For the manuscripts of Henry of Langenstein, see above, n. 43. Henry's Quaestiones were published as an appendix to Pecham's Perspectiva communis adjoined to Thomas Bradwardine's arithmetic and geometry in Praeclarissimum mathematicarum opus in quo continentur perspicacissimi mathematici… (Valencia, 1503). Leonardo also seems to have known Pecham's Perspectiva communis; see Lindberg Theories of Vision from al-Kindī to Kepler Chicago 1976 266 266 n. 41, on Leonardo's medieval sources.
- Revising older opinions to the effect that Leonardo developed his ideas without notable influence of medieval Latin writings 155 – 156 . Lindberg as well as Kemp and Ackerman find numerous connections between Leonardo's writing on vision and medieval works.
- Ackerman . 1978 . Leonardo's Eye . Journal of the Warburg and Courtauld Institutes , 41 : 139 – 139 .
- Ackerman . 1978 . Leonardo's Eye . Journal of the Warburg and Courtauld Institutes , 41 : 141 – 141 .
- Ackerman . 1978 . Leonardo's Eye . Journal of the Warburg and Courtauld Institutes , 41 : 138 – 138 .
- It is ironic that Ackerman associates such voluntaristic notions with the medieval tradition, which is not a single tradition anyway, when Leonardo employs such language so often himself. For example, in Codice Atlantico, f. 270rb, Leonardo writes, ‘That water which is in the light that surrounds the black centre of the eye serves the same purpose as the hounds in the chase, for these are used to start the quarry and then the hunters capture it. So also with this, because it is a humour that derives from the power of the imprensiva and sees many things without seizing hold of them, but suddenly turns thither the central beam which proceeds along the line to the sense, and this seizes on the images and confines such as please it within the prison of the memory’. Translation by Edward MacCurdy The Notebooks of Leonardo da Vinci New York 1958 237 237 I see also Carlo Pedretti, The Literary Works of Leonardo da Vinci. Commentary (Oxford, 1977), I, 135.
- Ackerman . 1978 . Leonardo's Eye . Journal of the Warburg and Courtauld Institutes , 41 : 140 – 140 . comments that one of Leonardo's schemes, which places the imprensiva in the eye itself, was a ‘conclusion to which Leonardo apparently arrived independently, [that] happened to bring his thinking into line with that of Alhazen’. In so far as the imprensiva is the organ of perception, not sensation, this conclusion is unlike Alhazen's, which clearly places perception, involving judgment, in the brain and nowhere prior to it. On the other hand, there is an interplay between Leonardo's scheme at this point and Alhazen's theory, and I doubt that the scheme was conceived altogether independently.
- Alhazen summarizes this in De aspectibus II 34 34 ii, 16 referring to the limited function of the corpus sentiens, which is simply a sensate transmitter. ‘Et ita corpus sentiens extensum a superficie membri sentientis usque ad concavum nervi communis, scilicet spiritus visibilis est sentiens per totum, quoniam virtus sensitiva est per totum istius corporis. Cum ergo forma extenditur a superficie membri sentientis usque ad concavum nervi communis, quaelibet pars corporis sentientis sentiet formam, et cum pervenerit forma in concavum nervi communis, comprehendetur ab ultimo sentiente, et tunc erit distinctio et argumentatio’.
- MS D, f. 2v Strong 47 47 Leonardo begins at the top of this page by remarking that the virtù visiva always sees things as they are, and then proceeds to show that as soon as the species are righted, in this case at the posterior crystalline surface, they are received by the imprensiva; see Figure 18, taken from f. 10r. If we understand Leonardo to mean that the imprensiva is encased in the optic nerve, then Figure 18, minus the reflected rays (which Leonardo says are ineffective) between crystalline and uvea, is a good representation of what Leonardo means here at f. 2v. See footnote 78.
- MS D, f. 2v Strong 47 47 pursuing the same text a bit further.
- Codex Arundel, f. 171 v Ackerman Leonardo's Eye Journal of the Warburg and Courtauld Institutes 1978 41 140 140
- Lindberg . 1976 . Theories of Vision from al-Kindī to Kepler 155 – 156 . Chicago 266 n. 41.
- 1976 . Theories of Vision from al-Kindī to Kepler 268 – 269 . Chicago n. 78.
- Vat. lat. 4595. Federici Vescovini Graziella Contributo per la storia della fortuna di Alhazen in Italia: Il volgarizzamento del MS. Vat. 4595 e il ‘Commentario terzo’ del Ghiberti Rinascimento 1965 5 17 49 series 2 shows that Ghiberti (1381–1455) used this manuscript. Many of the labelled diagrams are in Latin, not Italian, and by another hand than the text. While it says nothing about Leonardo's use of Vat. 4595, it is interesting to note that the diagram for ocular anatomy is much closer to that in London BL MS Roy. 12. G. VII, f. lr, than to any other extant diagram of Alhazen's eye anatomy. There is similarity in the choice of other diagrams and the nature of those diagrams across the two manuscripts.
- See Strong 88 89 Both Ghiberti and Vat. lat. 4595, f.lr, show in their diagrams a blending and confusion of the spera glacialis and humor vitreus.
Annals of Science
Volume 43, 1986 - Issue 5