By Gerald J. Toomer
With the ebook 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 available basically in Halley's Latin translation of 1710 (and translations into different languages completely 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 contemporary scholarship. specifically, it doesn't include the Arabic textual content. i'm hoping that the current variation won't merely therapy these deficiencies, yet also will function a beginning for the examine of the impact of the Conics within the medieval Islamic international. I recognize with gratitude assistance from a few associations and folks. the toilet Simon Guggenheim Memorial beginning, via the award of 1 of its Fellowships for 1985-86, enabled me to commit an unbroken yr 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 traveling Fellowship in Trinity time period, 1988, which allowed me to make reliable use of the wealthy assets of either the college 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
Here, and usually, maxima are associated with the ellipse, being drawn from the minor axis or its extension, and are intimately related to the minima drawn from the major axis, as is shown in V 23 (and is obvious, since both minima and maxima are normalsl. However, a local maximum (to a restricted part of the curvel is found for parabola and hyperbola in Prop. 72. The general case is enunciated in V 20, but various special cases are dealt with first. V 16-18 correspond to V 6. If a point is taken on the minor axis or its extension such that its distance from the (fartherl vertex of the minor axis is equal to half the latus rectum, then the maximum line from that point to the curve is the distance to the farther vertex, the minimum is the distance to the nearer vertex, the lines in between decrease from maximum to minimum, and the difference in length between the maximum and any other line from the point taken is given by a formula analogous to that for the minimum in V 6 (see (3al in V 6 on p.
All such lines will cut the hyperbola. This is used in V 43. II 3 The converse of II 1. See Fig. 1 *. e. ~B = BE. (1) Furthermore, if AB is the transverse diameter corresponding to tangent BE, and BZ the latus rectum of the llfigure", (2) The latter is used in V 37 &. 42. II 4 Problem: given the asymptotes to a hyperbola and a point on the curve, to construct the hyperbola. See Fig. 4. The given asymptotes are rA and AB, and the given point ~. Solution: join ~A and extend it to E, making AE = ~A.
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.