A Source Book in Medieval Science

Author: John Pecham

Show Summary

Late Thirteenth-Century Synthesis in Optics

Translations, introduction, and annotation by David C. Lindberg1

29. John Pecham: Image Formation by Refraction


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.


Related Resources

None available for this document.

Download Options

Title: A Source Book in Medieval Science

Select an option:

*Note: A download may not start for up to 60 seconds.

Email Options

Title: A Source Book in Medieval Science

Select an option:

Email addres:

*Note: It may take up to 60 seconds for for the email to be generated.

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 28, 2023, 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. 28 May. 2023. 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 28 May 2023, from http://www.originalsources.com/Document.aspx?DocID=H441B8DJYNKGVZG.