Geometrical Conics Including An Harmonic Ratio And Projection With Numerous Examples

This book provides a thorough explanation of geometrical conics with examples. It covers anharmonic ratio and projection in depth This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Excerpt from Geometrical Conics: Including Anharmonic Ratio and Projection, With Numerous Examples This work contains elementary proofs of the principal properties of Conic Sections, together with Chapters on Projection and Anharmonic Ratio. The term Conic, elsewhere frequently employed as an abbreviation, is here formally adopted, with reference to the fact that it is no longer usual to define the curves in question as sections of a surface. The term Conic Section is introduced in Chapter XI. In Chapter II., some fundamental propositions are proved by methods applicable to all Conics, a Conic being considered as the locus of a point whose distance from a fixed point bears a constant ratio to its perpendicular distance from a fixed straight line. The propositions of this Chapter have been selected as either important in themselves or useful in their application. To the latter class belong Props. VII., VIII. which are useful in proving the Anharmonic Properties of Conics. Prop. XII., in which the fundamental property of diameters is established, leads to important simplifications. Prop, XIII., which follows immediately from it, has been applied to prove that, in the ellipse, CV.CT = CP2, (p. 81). The Lemma is shown, in the Appendix, to be closely connected with some important properties of central Conics. 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.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.