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Get Archimedes in the Middle Ages, Vol. 4: A supplement on the PDF

By Marshall Clagett

ISBN-10: 087169137X

ISBN-13: 9780871691378

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Read or Download Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part i PDF

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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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LEMMA] * Modus inveniendi lineam ad cuius quadratum se habeat quecunque superficies rectangula secundum proporcionem cuiuscunque dati quadrati ad aliud quadratum datum est iste. Inveniatur latus tetragonicum superficiei date, quo invento procedatur 5 sic. Superficies data est equalis quadrato sui lateris tetragonici; ergo per 7a[ml quinti ambo habent eandem proporcionem ad quodlibet tercium, ergo 8lr ad quadratum linee quam querimus; non habemus igitur aliud / querere nisi invenire quoddam quadratum ad quod se habeat unum quadratum datum secundum proporcionem cuiuslibet alterius quadrati tercii dati ad 10 quartum quadratum datum.

Dico tunc quod proporcio superficiei contente sub dh et he ad quadratum hk est sicut proporcio superficiei contente sub dt et te ad quadratum tl et dico iterum quod tl est maior hk. Protrahantur enim in triangulo abg due linee mhn et sto equidistantes linee bzg, et intelligatur superficies secans piramidem in qua sint due linee hk et hmn, eritque per secundam communis sectio curve superficiei pira­ midis et superficiei secantis linea continens circulum que sit mkn, cuius diameter erit mn. Similiter intelligatur alia superficies secans piramidem in qua sint due linee tl et sto, eritque similiter linea sio continens circulum et eius diameter so, et erit superficies que continetur sub hm et hn equalis quadrato hk, et superficies contenta sub st et to equalis quadrato tl.

Add. m. 2 / [illud . . addit] addidi; cf. Vers. A 57-58 [nq . . est] addidi; cf. Vers. A 64-65 de Quia . . mn mg. inf. scr. m. 2 Nota quod linea ucx est maior quam linea qmn, similiter linea eh que comparatur seu correspondet linee ucx est maior quam linea eh que correspondet linee qmn, sicut enim crescit linea ucx super lineam qmn similiter crescit linea eh correspondens linee ucx super lineam eh correspondentem linee qmn [Lemma] 4 supra Inveniatur scr. m. 2 per 14 secundi 12-13 de Eadem . .

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


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