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By Marshall Clagett

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Additional info 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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Ha scr. m. 1 per secundam 6li DE DUABUS LINEIS (VERSION B) AD SUPERFICIEM TRANSEUNTEM PER ILLUD PUNCTUM ET PER SAGITTAM PIRAMIDIS, ILLA PERPENDICULARIS EST 5 CONTINGENS OMNEM SECTIONEM QUAM FECERIT IN SUPER­ FICIE PIRAMIDIS OMNIS SUPERFICIES PROTRACTA PER IPSAM, HOC EST DICTU QUOD DE ILLA PERPENDICULARI NON EST IN SUPERFICIE PIRAMIDIS NISI SOLUM PUNCTUM SIGNATUM. Verbi gratia, sit piramis rotunda abg, cuius basis circulus bg, et ipsius io circuli centrum est e, et in eius superficie sit signatus punctus d [Fig.

Si igitur per B circa asymptotas T[K]M descripserimus yperbolam, transibit per Z et erit positione data propterea quod et signum B positione datum est et utraque ipsarum AB, BM et propter hoc circa asymptotas T[K]M. Sit descripta et sit ut que XB. Ergo signum X tangit positione datam yperbolam; tangebat autem et positione datam ellipsim. Datum est ergo X. Et ab ipso per­ pendicularis que XE; datum est ergo E. Et quoniam est ut que MB ad BE ita que ZA ad AE, et data est que AE, data est ergo et que AZ.

Ipsum ergo K tangit positione datum parabolam. Sit igitur descripta ut dictum est et sit ut que HK. ’’ 40vK -L (see Fig. 2): “ Equale ergo est quod ab HM ei quod sub HZN. Si ergo per Z circa axem ZH descripserimus parabolam ut protracte possint penes ZN , veniet per M. Sit descripta et sit que MXZ. " 40vQ-U (see Fig. ) ipsi TG equedistanti existenti diametro sectionis propter 27. theorema primi libri elementorum conicorum Apollonii. Sit educta et concidat apud N, et per B circa asymptotas NGH sit descripta yperbola.

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