Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

Abzj proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Bnhzj from (...) Ibn Sinān seems to support this last interpretation. (shrink)

This paper presents the Arabic text, the French translation and an analysis of al-Sijzīʼs treatise, the Book of Measurement of Spheres by Spheres. In this text, al-Sijzī divides the cube into several sub-cubes and parallelopipedes, thus offering us a stereometric interpretation of algebraic identities of the third degree usually credited to mathematicians of the sixteenth and seventeenth centuries. However, this was not al-Sijzīʼs motivation for writing this treatise; rather it was his theoretical interest in the Euclidian concept of the “power” (...) of a segment, an interest which is clearly geometric rather than algebraic. This has led al-Sijzī to the notion of dimension, at least in outline. Cet article contient l'édition du texte arabe, la traduction françhise et une analyse d'un traité d'al-Sijzī, le Livre de la mesure des sphéres par les sphères. Dans ce texte, al-Syzī expose plusieurs décompositions du cube en réunions de cubes et de parallélépipédes, donnant ainsi une interprétation stéréométrique d'identités algébriques de degré 3 qu'on avait coutume d'attribuer à des mathématiciens des XVT e et XVII e siècles. Pourtant, ce n'est pas cette interprétation qui, pour l'auteur, semble avoir motivé la rédaction du traité, mais bien une réflexion théorique sur le concept euclidien de “puissance” d'un segment, réflexion de nature clairement géométrique et non pas algébrique, et qui a conduit le mathématicien à dégager, au moins en filigrane, la notion de dimension. (shrink)

We apply a physical and historical analysis to a passage by the medieval scholar Michael Scot concerning multiple rainbows, a meteorological phenomenon whose existence has only been acknowledged in recent history. We survey various types of physical models to best decipher Scot’s description of four parallel rainbows as well as a linguistic analysis of Scot’s special etymology. The conclusions have implications on Scot’s whereabouts at the turn of the 13th century.

Quand on compare l' Optique d'Ibn al-Haytham à celle de Ptolémée, on rencontre des innovations à coup sûr capitales, et qui chacune mériterait une analyse particulière: étude expérimentale de la propagation rectiligne de la lumière, nouvelle théorie de la vision fondée sur la réception dans l'œil de rayons lumineux, recherche du lien entre l'anatomie de 1'œil et sa fonction optique, preuve expérimentale que la réfraction joue un rôle important dans la vision, et j'en passe: les dimensions d'un article de revue (...) n'y suffiraient pas. Aussi bien mon but est-il plus global et plus synthétique. Il consiste à tenter de faire le point sur ce qu'est devenue, après Ibn al-Haytham, l'insertion de l'optique dans le système des savoirs qui lui sont connectès, en comparant cette insertion à ce qu'elle était au temps de Ptolémée, c'est-à-dire dans l'œuvre de référence reçae et travaillée par lui. (shrink)

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena, “henceforth the [visible] representations of objects should be considered as paintings [ picturae ] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization, this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs (...) – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot. (shrink)

This version has been superseded by the one published in Spring, 2014.