Download Apollonius: Conics Books V to VII: The Arabic Translation of by Gerald J. Toomer PDF

By Gerald J. Toomer

With the ebook of this e-book I discharge a debt which our period has lengthy owed to the reminiscence of a superb mathematician of antiquity: to pub­ lish the /llost books" of the Conics of Apollonius within the shape that's the nearest we need to the unique, the Arabic model of the Banu Musil. Un­ til now this has been obtainable in basic terms in Halley's Latin translation of 1710 (and translations into different languages solely depending on that). whereas I yield to none in my admiration for Halley's version of the Conics, it truly is faraway from pleasant the necessities of contemporary scholarship. specifically, it doesn't comprise the Arabic textual content. i'm hoping that the current version won't simply treatment these deficiencies, yet also will function a beginning for the learn of the impression of the Conics within the medieval Islamic global. I recognize with gratitude the aid of a few associations and other people. the loo Simon Guggenheim Memorial origin, via the award of 1 of its Fellowships for 1985-86, enabled me to commit an unbroken 12 months to this undertaking, and to refer to crucial fabric within the Bodleian Li­ brary, Oxford, and the Bibliotheque Nationale, Paris. Corpus Christi Col­ lege, Cambridge, appointed me to a vacationing Fellowship in Trinity time period, 1988, which allowed me to make reliable use of the wealthy assets of either the collage Library, Cambridge, and the Bodleian Library.

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Additional info for Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā

Example text

40, but, as noted above, is implicit in the core theorems of the book, V 44 ff. Apollonius does not discuss the general problem of whether the meeting-point of two minima is inside or outside of the conic; however, he does treat this question for the particular case of the ellipse in V 39 &. 40, but only as lemmas preliminary to determining the number of minima that can be drawn from one point in an ellipse in V 46 &. 47. V 39 Two maxima in an ellipse meet on the side of the minor axis in which they are drawn.

This is used for the ellipse in V 71. 132 If a straight line is drawn through the vertex of a conic section parallel to an ordinate, it will be tangent to the section (d. I 17 p. xxxii), and no other straight line can be drawn between it and the section. Proven by reductio ad absurdum. This is used for the parabola in V 64, for the ellipse in V 73 and (implicitly) for all three sections in VI 6. 1 Apollonius also proves the corresponding theorem for the circle, as he does for a number of propositions involving the central conics.

Then it is easily shown, by V 40, that no third minimum can be drawn to the same quadrant from the point of intersection of the original two minima. As it stands, however, the enunciation and proof are incomplete: see n. 563. This is used in Props. 47, 54, 57, 76 &. 77. V 47 considers minima drawn to an ellipse, not just to one quadrant (as in V 45), but to the whole semi-ellipse,. The theorem states that no four minima can meet in a single point. Apollonius uses reductio ad absurdum, considering three possibilities: (1) One of the lines coincides with the minor axis.

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