Read e-book online 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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By Marshall Clagett

ISBN-10: 087169137X

ISBN-13: 9780871691378

Show description

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

Sample text

Similarly the plane in which tl and so lie forms a circle in the cone whose diameter is line sto. Hence let the circle be slo. Therefore, line mn is the diameter of circle mkn; and line hk is perpendicular to mn. Therefore [from the property of a circle], (1) mh ■hn = hk2, and similarly, (2) st -to = tl2. And (3) dh -he / mh -hn — {dh / mh)-(eh / hn). But (4) dh / mh = dt / ts [by similar triangles], and (5) eh / hn = et / to [by similar triangles]. Therefore, (6) dh -he / mh -hn = (dt / ts)-(et / to) =dt-te / st-to.

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 . . duplicata mg.

1 See M. Clagett, Archimedes in the Middle Ages, Vol. 2: The Translations from the Greek by William o f Moerbeke (Philadelphia, 1976). , 17rA-20vD, 20vE-22vH, 34rA-44vP, 45rA-52vO, 53rA-55rW, 55vA-60rA. Also see below the various passages given in note 6 from Moerbeke's translations of Euto­ cius’ two commentaries. For summaries of Archimedean conics, see J. L. Heiberg, “ Die Kenntnisse des Archimedes iiber die Kegelschnitte,” Zeitschriftfiir Mathematik undPhysik, XXV. Jahrg. -lit. Abtheilung, pp.

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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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