(b. Poland, ca. 1230/1235; d. after ca. 1275)
optics, natural philosophy.
Life. Very little is known of Witelo’s life. His homeland and national origins must be inferred from scattered remarks in his Perspectiva. There he refers to “our homeland, namely Poland” and mentions the city of Vratizlavia (Wroclaw) and the nearby towns of Borek and Liegnitz,1 thus revealing an intimate knowledge of the environs of Breslau (Wroclaw) in Silesia, which suggests that he probably was born and raised there. In the preface to the Perspectiva, Witelo refers to himself as “the son of Thuringians and Poles,” from which it may be gathered that on the paternal side he was descended from the Germans of Thuringia who colonized Silesia in the twelfth and thriteenth centuries, while on the maternal side he was of Polish descent.
Witelo’s education and adult life likewise must be reconstructed from the most fragmentary evidence. It may be surmised, from a reference to time spent in Paris and a description of a nocturnal brawl that occurred there in 1253, that he received his undergraduate education at the University of Paris in the early 1250’s. He must, therefore, have been born in the early or middle 1230’s. In the 1260’s Witelo was studying canon law at Padua, as revealed by his reference to an event that occurred in Padua in 1262 or 1265.2 His presence in Padua also is indicated by the explicit of his Tractatus de primaria causa penitentie et de natura demonum (written during his stay in Padua), in which he is referred to as “Witilo, student in canon law.’3 it is evident, however, that at Padua he was not totally preoccupied with his legal studies, for he wrote the Tractatus during an Easter recess, and, according to Birkenmajer, it reflects the teachings of Plato, Galen, Ibn Sīnā, Aritotle, Ibn Rushd, Euclid, and Ibn al-Haytham (Althazen).4
Late in 1268 or early in 1269, Witelo appeared in Viterbo, where he became acquainted with William of Moerbeke, papal confesssor and translator of philosophical and scientific works from Greek to Latin, to whom Witelo later dedicated the perspectiva. We know nothing further of Witelo’s movements unless he is to be identified with the person of that name who served as chaplain to King Ottocar II of Bohemia and who was sent on a mission to Pope Gregory X in 1274.5 The Bern manuscript of Witelo’s Perspectiva refers to the author as “Magister Witelo de Viconia,” which has given rise to speculation that Witelo retired to the Premonstratensian abbey of Vicogne during his declining years.6
It is apparent that Witelo’s Perspectiva was not composed before 1270. since it draws on Hero of Alexandria’s Catoptrica, the translation of which was completed by Moerbeke on 31 December 1269. Because such an immense work probably was not written in less than several years, it is unlikely that Witelo died before the mid- 1270’s.
There continues to be a good deal of confusion regarding Witelo’s name. In the printed editions of the Perspectiva, the author’s name is spelled “Vitellio” or “Vitello” and a number of historians have adopted this orthography. Maximilien Curtze and Clemens Baeumker have demonstrated, however,that early manuscripts of the Perspectiva give orerwhelming support to the form “Witelo.”7 They have argued, further, that “Witelo” is a diminutive of “Wito” or “Wido,” a given name commonly encountered in Thuringian documents of the thirteenth century. Family names were uncommon in thirteenth-century Poland, and there is no evidence to suggest that Witelo had one.
Works. Witelo’s known extant works are Perspectiva and De primaria causa penitentie et de natura demonum. In addition he refers in the Perspectiva to several other treatises of his, none of which can now be identified: De elementatis conclusionibus,Philosophia naturalis, Scientia motuum celestium, Naturales anime passiones, and De ordine entium.8 these titles reveal the range of Witelo’s interests in natural philosophy. Nevertheless, since only the Perspectiva has been the object of detailed study, his reputation rests almost solely on his work in optics.
Optics in the latter half of the thirteenth century was hardly (if at all) an experimental endeavor;9 the principal task was to master zan abundance of literature on the subject. By far the most important optical treatise in Witelo’s day was Ibn al-Haytham’s Optics or De aspectibus, rendered into Latin by an unidentified translator late in the twelfth or early in the thirteenth century. Although Witelo never refers to Ibn al-Haytham by name, there can be no doubt that the latter was his chief source: Witelo normally treats the same topics in the same fashion and sometimes even in the same words; occasionally he omits or inserts a topic, and often he seeks to clarify or supplement one of Ibn al-Haytham’s points by further elaboration or an improved demonstration, but in very few respects does he escape the general framework inherited through the latter’s Optics.10
Yet other influences are evident. It is beyond dispute that Witelo used the Optica of Ptolemy, whose table of refraction he reproduces; the Catoptrica of Hero, whose principle of minimum distance he employs to explain reflection at equal angles: and the De speculis comburentibus (anonymous in the thirteenth century. but now attributed to Ibn al-Haytham), from which he drew his analysis of paraboloidal mirrors. There can be little doubt that he also was familiar with the widely circulated Optica (De visu) of Euclid, Catoptrica (De speculis of Pseudo-euclid, De aspectibus of al-Kindī, and the physiological and psychological works of Galen, Hunayn ibn Ishāq, Ibn Sīn0101; and Ibn Rushd. As for Latin authors, Alexander Birkenmajer has argued that Witelo was strongly infuenced by Robert Grosseteste’s De lineis angulis et figuris and Roger Bacon’s De multiplicatione specierum.11 In addition, it is certain that he knew Bacon’s Opus maius and possible that he knew John pecham’s Perspectiva communis.12 Witelo also relied on a number of ancient mathematical works. including those of Euclid and Apollonius of Perga, and perhaps of Eutocius, Archimedes. Theon of Alexandria, and Pappus.
Witelo’s Perspectiva is an immense folio volume of nearly five hundred pages in the three printed editions, and no detailed analysis of its contents has ever been made. It will be possible, in the remainder of this articale, only to trace its most significant features. The scope of the Perspectiva is revealed by the following outline of its contents: Book I consists of definitions, postulates, and 137 geometrical theorems, which provide the mathematical principles required for the optical demonstrations of the remaining nine books. In this book Witelo skillfully summarizes the aspects of the geometrical achievement of antiquity that are relevant to his own geometrical optics. Book II deals with the nature of radiation, the propagation of light and color in straight or refracted lines, shadows, and the problem of pinhole images, Book III is concerned with the physiology, psychology, and geometry of monocular and binocular vision by means of rectilinear radiation.
Book IV treats the perception of the twenty visible intentions other than light and color, including size, shape, remoteness, corporeity, roughness, darkness, and beauty. It also deals with errors in the perception of these intentions- principally errors in judging distance, shape, and relative size. This book is thus largely psychological in tone, although it includes a number of matters that fall into the realm of traditional geometriacal perspective. In book V, Witelo considers vision by reflected rays, beginning with the natre and geometrical laws of reflection and proceeding to a detailed analysis of plane mirrors. Image formation in cured mirrors occupies books VI through IX of the Perspectiva–convex spherical mirrors in book VI. convex cylidrical and conical mirrors in book VII. concave spherical mirrors in book VIII, and concave cylindrical, conical, and paraboloidal mirrors in book IX. Book X is concerned with vision by rays refracted at plane or spherical interfaces; it also includes a discussion of the rainbow and other meteorological phenomena.
The most essential feature of any optical system might seem to be its theory of the nature of light. Witelo’s concerns were principally geometrical,however, and he formulated no systematic account of the nature of light. From scattered remarks throughout the Perspectiva (particularly its preface)one can hope at the very most to classify him within a broad tradition on this question. He writes in the preface: “Sensible light is the intermediary of corporeal influences” ; “Light is a corporeal form”; and “Light is the first of all sensible forms.” It is apparent from such remarks that light is regarded as the intermediary in certain natural actions–an instance of the multiplication of fromas. Light is thus one particular manifestation of a more general phenomenon, the propagation of force of influence from one natural body to another, But although light is only one instace of natural action, it is the instance most accessible to the senses and most amenable to analysis; therefore it serves, for Witelo, as the paradigm for the investigation of all natural actions. Thus he writes, at the conclusion of his quantitative analysis of refraction, “These are the things that occur to lights and colors and universally to all forms in their diffusion through transparent bodies and in the refraction that occurs in all of them.”13 And in the preface he remarks, “The investigation [in general, of the action of one body on another] properly proceeds by means of visible entities.” It is evident, then, that Witelo falls very generally into the Neoplatonic tradition traceable fro plotinus through Ibn Gabirol to Grosseteste and Bacon. Fro Witelo, as for these predecessors, every natural body propagation light is the principal example. Moreover, Witelo would seem to follow Grosseteste and Bacon in perceiving that optics thus becomes the fundamental science of nature.
A second essential feature of any optical system, about which Witelo says somewhat more, is the propagation of light or visible forms. According to Witelo, light is always propagated rectilinearly unless it enconunters a reflecting or refracting surface. This fact, he claims, can be verified experimentally; and he even describes the required apparatus. The same apparatus had already been described by Ibn al-Haytham, however, and there is no reason to believe that Witelo personally verified the rectilinear propagation of light by experimental means. Witelo is uninformative on the physical mechanism of propagation, but one can surmise from his use of terms like “multiplication” and “diffusion” that his view was not far from that of Roger Bacon. He departs from Ibn al-Haytham and Bacon and most of the ancient optical tradition on the temporal aspects of propagation, arguing that light requires no time for popagation through an extended medium. He proceeds on logical grounds, reducing to absurdity the claim that the propagation of light requires time. Witelo is unable to maintain this position, however, and later admits that “every light passing through a transparent body tranverses it with an exceedingly swift and insensible motion. And yet the motion occurs more swiftly through more transparent bodies than through less transparent bodies.”14
The applicability of geometry to optical problems follows from the principle of rectilinear propagation: light proceeding along staight lines, subject only to the rules of reflection and refraction, clearly is amenable to geometrical analysis. Witelo draws a careful distinction, however, between the one-dimentsional lines employed in a geometrical analysis of optical phenomena and actual rays (or radial lines) of light. The latter are real physical lines traversed by the smallest visible light, and “in the least light that can be supposed, there is width . . . Therefore in a radial line alone which light is diffused, there is some width.”15 Nevertheless, “in the middle of that [radial line] is an imaginary mathematical line, parallel to which are all the other mathematical lines in that natual line.”16 And since the mathematical lines always fall within the natual readial lines, the former adequately represent the actual path of light, and it is proper to employ them in optical demonstrations.17
It was still a matter of debate in the thirteenth century whether rays issue only from the visible object or whether, in addition, there is an emission from the observer’s eye that assists in the act of sight. Witelo follows Ibn al-Haytham (and departs from Grosseteste, Bacon, and Pecham) in acknowledging no emission of visual rays from the eye; sight is due solely to the forms of light and color issuing in all direction from every point (or small part) of the visible object and entering the observer’s eye to produce visual sensations.
Witelo also follows Ibn al-Haytham (and the entire ancient and medieval optical tradition) in declaring that the sensitive organ of the eye is the glacial humor (or crystalline lens), which occupies the central position. Sight occurs, therefore, when the forms of light and color are arranged on the surface of the crystalline lens in the same order as the points of the visible object from which they issued: on the surface of the crystalline lens there is a “union of the visible forms and the soul’s organ,”18 which constitutes the act of sight, But how is it possible for light to be arranged on the surface of the lens exactly as on the surface of the object, since light issues in all directions from every point of the object? Witelo supplies precisely the same answer as Ibn al-Haytham, Bacon, and Pecham:only unrefracted lighty is strong enough to be efficacious in sight, and there is but one unrefraced ray issuing from each point of the visible object–the ray proceeding toward the center of curvature of the humors and tunics of the eye. The collection of all such unrefracted rays maintains its configuration between the visible object and the glacial humor and consequently forms, on the surface of the latter, an exact image (albeit reduced in size) of the visible object. Yet the act of sight is not completed in the galcial humor; the forms it receives pass through to the optic nerve and thence to the anterior part of the brain, where the nerves from the two eyes intersect to form the “common nerve,” the residence of the visual power or ultimum sentiens, where a final judgement is made.
The geometrical structure that Witelo builds upon the conception of rays and mathematical lines naturally encompasses problems of geometrical perspective and image formation by reflection and refraction, but it also extends to the anatomy of the eye and the act of sight. He describes the eye in traditional terms, as a compostie of three humors–glacial or crystalline, vitreous, and albugineous (aqueous)–and four tunics–uvea, cornea, conjunctiva or consolidativa, and aranea or retina. Geometrical considerations predominate in Witelo’s descriptions of these tunics and humors: all are spherical in form; all tunics and humors anterior to the glacial humor must have concentric surfaces. so that a ray perpendicular to one is perpendicular to the rest and passes through all of them without refraction; and the glacial and vitreous humors have precisely the necessary shapes and relative densities to refract the rays converging toward the center of the eye before they actually intersect, and to conduct them through the vitreous humor and optic nerve without alteration or inversion.
Books V-IX of the perspectiva are devoted to the science of catoptrics. The foundation of this science is the law of reflection, which Witelo drives from the principle of minimum distance: since nature does nothing in vain, it “always acts along the shortest lines.”19 Following Hero of Alexandria, Witelo demonstrates that the shortest lines connecting two points and a reflecting surface are those that make equal angles with the surface.20 He also argues that the plane formed by the incident and reflected rays is perpendicular to the surface of reflection (or, in the case of curved mirrors, its tangent), and that an object seen by reflection appears to be located where the backward extension of the ray incident on the eye intersects the perpendicular dropped from the visible object to the reflecting surface.
Employing these three rules and the principles of geometry, Witelo proceeds to solve a series of very abstruse problems in reflection, drawn primarily (but not entirely) from ptolemy an Ibn al-Hay-tham. This is the most substantial section of the Perspectiva, occupying much of books V-IX and some 200 pages in the printed editions. Witelo deals skillfully with such problems as inversion and reversal of images, determination of precise size and location of images formed by concave and convex mirrors of various shapes, and computation of the number of images of a given object visible in a concave spherical mirror. Not until the seventeenth century was his catoptrics excelled in the West.
Book X of the Perspectiva deals with the refraction of light. In book II. Witelo had described an instrument for gathering quantitative data on the propagation of light, and in book X he claims to have used the same instrument in the formulation of tables of refraction. In fact, there is ample evidence that this claim is untrue. In the first place,the upper half of the table is taken directly from ptolemy’s Optica.21 Second, the values appearing in the table are not those given by experiment’, but sets of numbers conforming to a regular progression–the differences between successive angles of refraction (corresponding to angles of incidence taken at 10°intervals) form an arithemtic progression with a common difference of one-half degree. Finally, the lower half of the table was computed by Witelo from the values in the upper half by erroneous application of the reciprocal law; consequently it includes preposterous results, such as angles of refraction (measured from the perpendicular)greater than 90° and no recognition whatsoever of total internal reflection.
Nevertheless, at the qualitative level Witelo is fully cognizant of the principal phenomena of refraction:light passing obliquely from a less dense to a more dense medium is refracted toward the perpendicular, while light passing in the reverse direction is refracted away from the perpendicular. But Witelo is not content with a quantitative or qualitative description of the geometrical phenomena of refraction: he also presents a mechanical explanation based on the varying resistance offered to the passage of light by different transparent substances, the idea that ease of traversing a medium is associated with proximity to the perpendicular, and the principle that light is so refracted at a transparent interface as to most nearly preserve uniformity of strength or action in the two media. In the course of this analysis, Witelo resolves the oblique motion of light into components perpendicular and parallel to the refracting interface.22
Influence. It is difficult to separate Witelo’s influence on the history of late medieval and early modern optics from that of Ibn al-Haytham, particularly after their works were published in a single volume in 1572. One can affirm in general that their writings, along with John pecham’s Perspectiva communis, served as the standard textbooks on optics until well into the seventeenth century. More specifically, it is possible to establish Witelo’s influence on Henry of Hesse, Blasius of Parma, and Nicole Oresme in the fourteenth century; Lorenzo Ghiberti, Johannes Regiomontanus, and Leonardo da Vinci in the fifteenth century; Giambattista della porta, Francesco Maurolico, Giovanni Battista Benedetti, Tycho Brahe, William Gilbert, Simon Stevin, and Tycho Brahe, William Gilbert, Simon Stevin, and Thomas Harriot in the sixteenth century: and kepler, Galileo, Willebrord Snell, Descartes, and Francesco Grimaldi in the seventeenth century.23
1. Bk. X, theor. 74; bk. IV, theor. 28
2. The former date is in Alexander Birkenmajer’s “Witelo e lo studio di padova,” 156; the latter is in Lynn Thorndike’s History of Magic and Experimental Science, V, 86.
3. Birkenmajer, op. cit., 160. Thorndike regards this as a single work, while Birkenmajer treats it as two separate treatises.
6. Alternatively, it has been suggested that “Viconia” may be a misreading of “Vitovia,” a Polish village (which is not, however, near Wroclaw): see Clemens Baeumker, “Zur Biographie,” 360.
7. Maximilien Curtze, “Sur l’orthographe,” 49–66: Baeumker, Witelo, 190–200.
8. Some of these titles are less than certain: in several cases one cannot be sure that Witelo is claiming authorship; in others it is not clear whether the title applies to a chapter or to an entire treatise. For more detail, see Baeumker, Witelo, 239–244. De intelligentiis, formerly ascribed to Witelo, is now generally attributed to Adam Pulchare Mulieris (fl. 1225). On the possibility that certain MSS of Euclid’s De visu actually contain Witelo’s recension of this treatise, see Wilfred R. Theisen, “The Medieval Tradition of Euclid’s Optics” (Ph. D. diss., Univ. of Wis., 1972), 58–60; David C. Lindberg, intro. to face. repr. of Risner ed., xi, xxvii.
9. If there is an exception to this generalization, it seems to be in the science of the rainbow, where both Witelo and Dietrich von Freiberg claim to have used spherical containers filled with water to simulate a raindrop.
10. The appellation “Alhazen’s ape,” later applied to Witelo by Giambattista della porta, is unfortunate, since it ignores Witelo’s frequent attempts to revise or supplement Ibn alHaytham and the constant use of his own critical powers.
12. In bk. X, theor. 78, Witelo refers to those who maintain that the sum of the altitudes of the sun and rainbow is 42°, the precise value given by Bacon in pt. VI of the Opus mains. As I have argued in my ed. of Pecham’s Perspectiva communis and elsewhere, it is possible that Witele borrowed from pecham, but more likely that pecham borrowed from witelo.
13. Bk. X, theor. 8.
14. Bk. II, theor. 47.
15. Bk. II, theor. 3.
17. Yet Witelo recognizes that not only the imaginary mathematical lines. but even radial lines. are fictions and that radiation is actually continuous; see, for example, bk. X, theor. 3. Nevertheless, analysis into rays and imaginary lines is a legitimate technique for the solution of most optical problems.
18. Bk. III, theor.6.
19. Bk. V.theor.5.
20. Bk. I,theor. 17–18; bk. V, theor 18.
21. Witelo’s table appears in bk. X. theor. 8, a trans. of which appears in Edward Grant, A Source Book in Medieval Science (Cambridge, Mass., 1974). 424–426.
22. Bk. II, theor. 47.
23. Witelo’s influence is treated more fully in the intro. to the facs. repr. of the Risner ed., xxi–xxv.
I. Original Works. Witelo’s most important extant work is the Perspectiva, first published under the title Optica (Nuremberg, 1535; 1551) and, with Ibn al-Haytham’s Optics, in a volume edited by Friedrich Risner, entitled Opticae thesaurus (Basel, 1572; facs. repr., New York, 1972). There is no modern ed. except for a few sections edited by Clemens Baeumker in his Witelo and a critical ed. and English trans. of bk. I (with analysis and commentary) by Sabetai Unguru, “Witelo as a Mathematician: A Study in XIIIth Century Mathematics” Ph.D. diss., Univ. of Wis., 1970). The extant MSS of the Perspectiva are listed in the intro. to the facs. repr. of Risner’s Opticae thesaurus. A comparison of early MSS with the three printed eds. reveals that the latter are quite accurate.
Witelo’s De primaria causa penitentie et de natura demonum (regarded as two separate works by Birkenmajer)is extant in British Museum, MS Sloane 2156(15th century), fols. 148r–154v; and Paris, B.N. MS Lat. 14796 (15th century), fols. 86v-97v (abbreviated version). Birkenmajer has edited the latter MS in his “ÉEacue;tudes sur Witelo, I” (see below).
II. Secondary Literture. The major studies of Witelo are Clemens Baeumker, Witelo, ein Philosoph und Naturforscher des XIII. Jahrhunderts, which is Beiträge zur Geschichte der philosophie des Mittelalters,III, pt. 2(Münster, 1908); and Aleksander Birkenmajer. “Études sur Witelo,” which appear in his études d’historie des sciences en pologne (Wroclaw, 1972), 97–434. Portions of Baeumker’s analysis are vitiated by his erroneous attribution of De intelligentiis to Witelo, and it is absolutely essential that close attention be paid to Birkenmajer’s cautions, reservation, and corrections. The first and fourth of Birkenmajer’s “Études sur Witelo” were previously published as “Studja and Witelonem. I,” in Archiwum komisji do badania historji filozofji w polsce, 2, pt. 1 (1921), 1–149; and “Witelo e lo studio di padova,” in Omaggio dell’ Accademia polacca di scienze e letter all’Università di padova nel settimo centenario della sua fondazione (Cracow, 1922), 147–168.
On Witelo’s life, in addition to Baeumker’s Witelo and Birkenmajer’s “Études sur Witelo,” see Baeumker, “Zur Biographie des philosophen und Naturforschers Witelo” in Histroisches Jahrbuch der Görres-Gesellschaft,33 (1912), 359–361: Maximilien Curtze, “Sur l’orthographe du nom et sur la patrie de Witelo (Vitellion),” in Bullettino di bibliografia e di storia delle scienze matematiche e fisiche,4 (1871), 49–77 and David C. Lindberg, “Lines of Influence in Thirteenth-Century Optics: Bacon, Witelo, and pecham” in Speculum,46 (1971), 72–75, 77–83; and intro. to the facs. repr. of the Risner ed. (New York, 1972), vii-xiii.
Studies of particular aspects of Witelo’s thought appear in Carl B.Boyer, The Rainbow: From Myth to Mathematics (New York, 1959), ch. IV; A.C.Crombie, Robert Grosseteste and the Origins of Experimental Science 1100–1700 (Oxford, 1953), 213–232; David C. Lindberg. “The Theory of pinhole Images From Antiquity to the Thirteenth Century,” in Archive for History of Exact Sciences,5 , pt. 2 (1968), 154–176; and “The Cause of Refraction in Medieval Optics,” in British Journal for the History of Science,4 (1968–1969), 23–38; and Sabetai Unguru, “Witelo and Thirteenth-Century Mathematics: An Assessment of His Contributions,” in lsis.63 (1972), 496–508. Witelo’s De natura demounm has been summarized briefly by Lynn Thorndike in A History of Magic and Experimental Science, V (New York, 1941), 86–89.
David C. Lindberg