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

By Gerald J. Toomer

With the e-book of this publication I discharge a debt which our period has lengthy owed to the reminiscence of a very good 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 merely 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 enjoyable the necessities of recent scholarship. particularly, it doesn't comprise the Arabic textual content. i'm hoping that the current variation won't merely therapy these deficiencies, yet also will function a starting place for the research of the effect of the Conics within the medieval Islamic global. I recognize with gratitude the aid of a couple of associations and other people. the toilet 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 venture, 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 traveling Fellowship in Trinity time period, 1988, which allowed me to make strong use of the wealthy assets of either the college Library, Cambridge, and the Bodleian Library.

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

With the e-book of this publication I discharge a debt which our period has lengthy owed to the reminiscence of an excellent mathematician of antiquity: to pub­ lish the /llost books" of the Conics of Apollonius within the shape that is the nearest we need to the unique, the Arabic model of the Banu Musil. Un­ til now this has been obtainable simply in Halley's Latin translation of 1710 (and translations into different languages fullyyt depending on that).

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

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Xlii Summary of V 8, V 9 &. V 10 V 8 The basic theorem on minima in the parabola. See Fig. 8. For a point E on the axis [where Er > l/lR), the minimum is found by marking off half the latus rectum, EZ, towards the vertex and erecting a perpendicular from Z, ZH, to cut the section in H. g. e. the difference between the squares on the two lines equals the square on the intercept on the axis between the perpendiculars from the two points. Using the basic property of the parabola [I 11) and the "geometrical algebra" familiar from early propositions of Euclid's Book II [see pp.

5) on p. xxxii). II 27 Two tangents to an ellipse or circle will be parallel if the line joining the points of tangency passes through the center of the section; otherwise they will meet on the side of the center on which that line lies. Used for the ellipse in V 71. II 28 The line bisecting two parallel chords in a conic section is a diameter to that section. This follows from II 5-6 and the definition of a diameter. Used in VI 19, VI 20 & VI 25. II 30 If two tangents are drawn from a point to a conic section, the dia- meter through that point (where the tangents intersect) will bisect the line joining the points of tangency.

284-309, where it is treated from a modern viewpoint. Here I give only a brief analysis of the content and interconnections of the individual propositions. 342). Book V; summary of V 1-3 xxxix the book may be stated as follows. For a given conic section and a given point P: (1) to construct all minimum and/or maximum straight lines from P to the conic; (2) to determine how the distance between P and a variable point X on the conic changes as PX moves away from the position of minimum or maximum.

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