A Treatise On Some New Geometrical Methodes

Author : James Booth
Publisher : Forgotten Books
ISBN 13 : 9781330409633
Total Pages : 484 pages
Book Rating : 4.4/5 (96 download)

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Download or read book A Treatise on Some New Geometrical Methods, Vol. 2 of 2 written by James Booth and published by Forgotten Books. This book was released on 2015-06-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Treatise on Some New Geometrical Methods, Vol. 2 of 2 After the lapse of nearly four years, in the face of many hindrances, untoward events, and difficulties, I have succeeded in bringing through the press this second and concluding volume of my mathematical and physical researches. An outline of the following researches on the Geometrical Properties of Elliptic Integrals was published in the Philosophical Transactions of the Royal Society for 1852, p. 311, followed by a Supplement 'printed in the volume for 1854, p. 53. Ample time and unbroken leisure have enabled me to recast and enlarge those essays. Though the work was onerous, it was also, I may say, a labour of love, lightened by the discovery, sometimes unexpected, of new truths of great geometrical beauty. Amongst these researches not the least important is the discovery of three curves of double eurvature whose rectification may be effected by elliptic integrals of the first and third orders. These arc the geometrical types of those transcendental expressions due to Legendre and Lagrange. The algebraical relations discovered by these illustrious geometers arc the exponents of the geometrical properties of those curves. Those versed in the subject will not need to be told how the simplicity of these relations contrasts with the abortive attempts of the most illustrious mathematicians to devise, on a plane, curves whose quadrature or rectification might represent those expressions. I do not here propose to give an analysis of the work; but, for the sake of the few who care to inquire into those matters, I would call attention to Chapter VIII. on conjugate amplitudes, and to Chapter X. on derivative hyperconic sections. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.