By David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry

ISBN-10: 0821808958

ISBN-13: 9780821808955

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Extra resources for Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2)

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Hence, to you we owe the discovery that the [two] books are conjoined; that the problems in [Book] eight are allotted their determination from the theorems on diorisms (διοριστικο ς)74 in [Book] seven. Indeed, having weighed the matter carefully, this seemed to me to be indicated not only by probable conjecture but also by certain [concrete] vestiges: with that, and with you showing the way, I undertook, as far as I could, to restore the loss. Therefore, I pray, please accept whatever I have managed to accomplish.

See, for example, the note 153 problem 13 in the translation. 67 I might emphasize, however, that Halley’s consistency of approach is particularly striking given the fact that when he worked on the Cutting-off of a Ratio and the Cutting-off of an Area, he was still working closely with David Gregory. But David Gregory died in 1708. So Halley’s work on the extant books of the Conics and the reconstruction of Book VIII was done largely on his own. This suggests that Gregory’s influence on Halley’s general approach to the Greek mathematical works was either minimal or so complete that Halley continued in the same vein after Gregory’s death.

70 In a way, albeit a qualified way, Halley acted in this dispute as an ambassador from the new to the old. In the end of course the new would win out, and yet Halley could give a fair chance to the old and learn from it. To be a good mediator means to be an agent of dialogue between the sides, to look closely at both, and represent one to the other faithfully and fairly. It is in this role that we should understand Halley’s work on ancient mathematical texts in general and on his reconstruction of Book VIII in particular.

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Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2) by David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry


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