TAILIEUCHUNG - Project Gutenberg’s Researches on curves of the second order, by George Whitehead Hearn

Project Gutenberg’s Researches on curves of the second order, by George Whitehead Hearn This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at Title: Researches on curves of the second order Author: George Whitehead Hearn Release Date: December 1, 2005 | Project Gutenberg s Researches on curves of the second order by George Whitehead Hearn This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at Title Researches on curves of the second order Author George Whitehead Hearn Release Date December 1 2005 EBook 17204 Language English Character set encoding TeX START OF THIS PROJECT GUTENBERG EBOOK RESEARCHES ON CURVES Produced by Joshua Hutchinson Jim Land and the Online Distributed Proofreading Team at http . This file was produced from images from the Cornell University Library Historical Mathematics Monographs collection. RESEARCHES ON CURVES OF THE SECOND ORDER ALSO ON Cones and Spherical Conics treated Analytically IN WHICH THE TANGENCIES OF APOLLONIUS ARE INVESTIGATED AND GENERAL GEOMETRICAL CONSTRUCTIONS DEDUCED FROM ANALYSIS ALSO SEVERAL OF THE GEOMETRICAL CONCLUSIONS OF M. CHASLES ARE ANALYTICALLY RESOLVED TOGETHER WITH MANY PROPERTIES ENTIRELY ORIGINAL. By GEORGE WHITEHEAD HEARN A GRADUATE OF CAMBRIDGE AND A PROFESSOR OF MATHEMATICS IN THE ROyAL MILITARy COLLEGE SANDHURST. LONDON GEORGE BELL 186 FLEET STREET. MDCCCxLVI. Table of Contents PREFACE. 1 INTRODUCTORY DISCOURSE CONCERNING GEOMETRY. . 2 CHAPTER I. 6 Problem proposed by Cramer to Castillon. 6 Tangencies of Apollonius. 10 Curious property respecting the directions of hyperbola which are the loci of centres of circles touching each pair of three circles. 15 CHAPTER II. 17 Locus of centres of all conic sections through same four points . 18 Locus of centres of all conic sections through two given points and touching a given line in a given point. 18 Locus of centres of all conic sections passing through three given points and touching a given straight line . 19 Equation to a conic section touching three given straight lines . 19 Equation to a conic section .

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