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A Source Book in Medieval Science
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Biographical SummaryJohn Pecham (ca. 1230–1292) Although he is known to be an Englishman, Pecham’s year and place of birth are very uncertain. After studying in the faculties of arts at Paris and Oxford, he entered the Franciscan Order at Oxford, perhaps around 1250. Returning to Paris sometime between 1257 and 1259, Pecham began the study of theology and received his doctorate in that subject from the University of Paris in 1269. For the next two years he lectured in theology to Franciscans in Paris. During his stay at Paris, Pecham was not only active in philosophical and theological disputes against the Thomists, and a defender of the mendicants against the seculars, but he also composed many theological treatises. He returned to Oxford sometime during 1271–1272 and again lectured to the Franciscans. In 1275 he became Provincial Minister of the English Franciscans, continuing his opposition to Thomism and Averroism. In 1279 he became Archbishop of Canterbury, a post he held until his death on December 8, 1292. In the course of a busy administrative life Pecham found time to compose a number of scientific treatises, the most famous being his enormously popular optical treatise, Perspectiva communis. He also commented on Sacrobosco’s Sphere (Tractatus de sphera), and wrote Theorica planetarum, Tractatus de numeris, Tractatus de anima, Questiones de anima, and perhaps a Tractatus de animalibus.
Critical SummaryAlthough Robert Grosseteste greatly stimulated European interest in optics, his own investigations were hampered by the lack of many important sources. Ptolemy’s Optica was just becoming known in the West, and it is doubtful that Grosseteste was familiar with it; Alhazen’s Perspectiva, although translated late in the twelfth or early in the thirteenth century, had not come to Grosseteste’s attention by the time he composed his optical works. Consequently, Grosseteste’s knowledge of optics, though more complete than that possessed by any Western predecessor or contemporary, was primitive by comparison with the optical achievements of Islam; thus his works lack the scope and depth of such a work as Alhazen’s great optical treatise, as even the most casual inspection will reveal. However, by the second half of the century, the most advanced treatises of Greek antiquity and medieval Islam had been rendered into Latin. The most important of these for the development of optics were the Perspectiva of Alhazen, the Optica of Ptolemy, a number of works of Avicenna, and (toward the end of the period) the Catoptrica of Hero of Alexandria. These new riches, especially Alhazen’s Perspectiva, occasioned a dramatic surge in the study of optics, which found its best expression in the works of Roger Bacon, Witelo, and John Pecham. Thus, whether in Alhazen’s Perspectiva (which not only served as the principal source for Western writers but also circulated widely itself) or in the works of Bacon, Witelo, and Pecham which it inspired, the West possessed for the first time treatises in which almost the entire gamut of problems now classified as optical was systematically treated; moreover, in these treatises we find an enormous increase in the sophistication of mathematical techniques employed. Indeed, we find what must be considered a grand synthesis of optical knowledge, comprehensive in scope and incorporating the very best learning of Greece, Islam, and the Latin West. It speaks for the vigor and excellence of this synthesis, that the progress of optics throughout the remainder of the Middle Ages came about as scientists extended the application of principles set forth late in the thirteenth century or as questions raised in the thirteenth century, but incompletely or unsatisfactorily answered, became the objects of inquiry and debate. The selections appearing in this chapter are an attempt to convey the principal doctrines and techniques of this late thirteenth-century synthesis. They are drawn from the works of Roger Bacon, Witelo, and John Pecham, all of whom wrote on optics during the 1260’s and 1270’s. In addition, it has been deemed essential to include selections from the Latin text of Alhazen’s Perspectiva to illustrate further the optical knowledge available in Europe after about 1250 and the origin of many of the ideas expressed by Bacon, Witelo, and Pecham. Since Alhazen and his three thirteenthcentury followers were in such complete agreement on most fundamental issues, it has been unnecessary to present the view of each individual on every question; rather, those passages have been selected that most clearly and concisely present the shared theory. In cases of major disagreement, as on the question of visual rays, alternative views are presented. Finally, it should be noted that the magnitude of the thirteenth-century optical synthesis has made it both possible and necessary to omit all but two selections illustrating optical progress during the later Middle Ages: possible, because the thirteenth-century synthesis provided the framework within which later optics was pursued, so that the views presented here largely represent later medieval views as well; necessary, because late medieval discussions were of a highly particular sort impossible to treat adequately in a source book.
Late Thirteenth-Century Synthesis in Optics
Translations, introduction, and annotation by David C. Lindberg1
29. John Pecham: Image Formation by Refraction
PERSPECTIVA COMMUNIS, III, PROPOSITION 4
Proposition 4. The image is located at the intersection of the pyramid under which the object is seen and the perpendiculars that one can imagine dropped from the visible object to the surface of the adjacent transparent medium.163
As was shown above,164 everything that is viewed appears [as though] in a straight line; and by the apprehension of the ray through which the eye perceives the object, the object is judged to be at the end of the straight-line extension of the ray. Therefore, just as the appearance of the object at the intersection of the perpendicular and [the rectilinear extension of] the ray is considered basic to mirrors, so in the case at hand it [that is, the image] is at the intersection of the ray and the perpendicular dropped from the visible object. For example, let A be the eye, B the visible object, BC the bent ray (refracted at C, from which [point] proceeds [ray] CA) that presents the object to the eye, and BLD the perpendicular [Fig. 17]. I say that point B appears at L.
 Fig. 17
1. Except for section 18, which was translated by Robert B. Burke.
2. Set forth, that is, by Alhazen’s Perspectiva as well as by those thirteenth-century treatises based upon it. One could legitimately argue that this synthesis was actually Islamic and occurred in the eleventh century in the works of Alhazen and Avicenna. Nevertheless, their works did not become available to the West until the thirteenth century, whereupon they inspired further efforts by Bacon, Witelo, and Pecham; thus, so far as the optical knowledge of the West is concerned, the synthesis occurred in the late thirteenth century.
3. Unless otherwise noted, the selections have been translated or reprinted from the following editions: Alhazen, Perspectiva, from Opticae thesaurus Alhazeni Arabis libri septem, edited by Friedrich Risner(Basel, 1572); Witelo, Perspectiva, bound with Alhazen’s Perspectiva in the Opticae thesaurus, but separately paginated; Roger Bacon, The Opus Majus of Roger Bacon, edited by J. H, Bridges (London, 1900); Roger Bacon, De multiplicatione specierum, included in Volume II of Bridges’ edition of the Opus maius. The propositions from John Pecham’s Perspectiva communis (both revised and unrevised versions) are reprinted by permission of the copyright owners, the Regents of the University of Wisconsin, from John Pecham and the Science of Optics: Perspectiva communis edited with an introdution, English translation, and critical notes by David C, Lindberg (Madison, Wis.: University of Wisconsin Press, 1970). The order in which the propositions appear in this source book and their page numbers in my Pecham volume are as follows: Part I, Proposition 27, revised version (p. 109); Propositions 29–34 (pp. 111– 119); Propositions 43, 28, 37, 33, 38 (pp. 127, 109–110, 121, 119, 121–123); Propositions 44–46 (pp. 127–131); Part II, Propositions 6, 20, 30 (pp.161–163, 171–173, 183–185); Part III, Proposition 4 (p.215); Proposition 16 (pp.229–231). Henceforth abbreviated citations will be used.
4. On the history of late medieval optics, see Graziella Federici Vescovini, Studi sulla prospettiva medievale (Turin: Giappichelli, 1965).
163. As in the case of reflection, the image of any given point is located at the intersection of the ray under which the point is seen and the perpendicular dropped from the point to the refracting surface. However, an object is composed of many points, and the collection of the rays under which those points are seen constitutes a pyramid. Consequently, in the enunciation of this proposition, Pecham speaks of the intersection of the pyramid and the perpendiculars.
164. See Perspectiva communis, II, proposition 20, in section 19 above.
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Chicago: John Pecham, "Late Thirteenth-Century Synthesis in Optics," A Source Book in Medieval Science in A Source Book in Medieval Science, ed. Edward Grant (Cambridge: Harvard University Press, 1974), 426. Original Sources, accessed May 11, 2025, http://www.originalsources.com/Document.aspx?DocID=H441B8DJYNKGVZG.
MLA: Pecham, John. "Late Thirteenth-Century Synthesis in Optics." A Source Book in Medieval Science, in A Source Book in Medieval Science, edited by Edward Grant, Cambridge, Harvard University Press, 1974, page 426. Original Sources. 11 May. 2025. http://www.originalsources.com/Document.aspx?DocID=H441B8DJYNKGVZG.
Harvard: Pecham, J, 'Late Thirteenth-Century Synthesis in Optics' in A Source Book in Medieval Science. cited in 1974, A Source Book in Medieval Science, ed. , Harvard University Press, Cambridge, pp.426. Original Sources, retrieved 11 May 2025, from http://www.originalsources.com/Document.aspx?DocID=H441B8DJYNKGVZG.
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