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Additional resources for Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i

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Sit ergo piramis abg [Fig. 5], cuius basis est circulus bg, et secetur 80v / superficie transeunte per eius sagittam, que faciat in ipsa piramide tri­ angulum abg. Et protrahamus latus eius ba usque ad d, et protrahamus a io puncto d ad basim bg lineam dez, et protrahamus a puncto e perpendicu­ larem supra triangulum abg, que sit eh, et protrahamus superficiem deh, que secet piramidem super duas lineas dez et eh, et sit communis sectio huius superficiei et superficiei piramidis linea existens in superficie pira­ midis, que sit linea eok, eritque per tercium theorema perpendicularis eh 15 contingens sectionem eok, et est superficies deh stans perpendiculariter supra triangulum abg, et communis earum sectio est linea ez, et hec linea ez cum eo quod iungitur ei in infinitum sit inter lineas ab et ag cum ipse protracte fuerint in infinitum.

G. , Hildesheim, 1966), pp. 39-63, 432-55 and passim ', T. L. Heath, Apollonius o f Perga: The Treatise on Conic Sections (Cambridge, 1896; repr. 1961), pp. xli-lxvii, and E. J. Dijksterhuis, Archimedes (Copen­ hagen, 1956), pp. 55-118. 63 64 ARCHIMEDES IN THE MIDDLE AGES Let us now turn directly to Witelo’s treatment of conic sections in the Perspectiva, first observing some generalities. It will be clear as our analysis unfolds that Witelo most probably had some direct access to the Conics of Apollonius, either through the Greek text itself, which Moerbeke may have helped him read, or, what is more likely, through a Latin trans­ lation prepared by his friend.

Of Unguru, pp. 269-70: ‘‘[Propositio] 91. Omnis pyramidis rotunde vel laterate linee longitudinis super axem in vertice tantum se intersecant; producte quoque aliam similem pyramidem principiant cuius linee longitudinis, secundum positionem et situm, priori pyra­ midi modo contrario se habent. ) omnes linee longitudinis pyramidis cuiuscunque producte se super axem in vertice secent evidens est, quoniam concurrent omnes in illo puncto verticis. Et quoniam omnes sunt equales. per 89am huius, patet quia citra verticem nulla ipsarum aliam intersecat.

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