Synopsis
The digital edition of all books may be viewed on our website before purchase. Excerpt from An Introduction to Projective Geometry (Classic Reprint)
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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 text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.The digital edition of all books may be viewed on our website before purchase.
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Présentation de l'éditeur
Conic Sections on modern lines. During recent years increasing space has been allowed, in University syllabuses and courses of instruction, to the more powerful and general projective methods, as opposed to the more special methods of what is still known as Geometrical Conies. The line of cleavage between the two has, however, been sharply maintained, with the result that the already much overworked matiiematical student has to learn his theory of Conic Sections three times over: (1) analytically; (2) according to J]uclidean methods; (3) according toP rojective methods. The difficulty has been to reconcile theE uclidean and Projective definitions of the curve; in fact to bring in tlie focal properties into Projective Geometry at a sufficiently early stage. The practice has usually been, in order to pass from the projective to the focal definitions, to introduce the theory of involution. But the latter requires for its fullest and cleare.st treatment the employment of imaginary elements. It seems undesirable that the more fundamental focal properties of the conies, e.g. tlie sum (r ditference of the focal distances and the angles made by tlie.sc with the tangent and normal, should appear to depend upon properties of imaginary points and lines, even though this might introduce greater rapidity of treatment. The University of London has recognized thi.s, for, while admitting Projective Geometry into its syllabuses for the Final Examination for a Pass Degree, it has excluded involution. Many teacliers iiave felt that this exclusion amounted to a rigorous enforcement of the line of cleavage mentioned above. In the present book the difficulty has been met, it is hopcil, successfully.
(Typographical errors above are due to OCR software and don't occur in the book.)
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An Introduction to Projective Geometry (Classic Reprint)
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Paperback. Etat : New. Print on Demand. This book explores conic sections, a geometric shape created by the intersection of a plane and a cone, which is a profound and versatile concept with applications reaching far beyond pure mathematics. The author aims to unify classical Euclidean and projective treatment of the subject using the tools of cross-ratio. Historically, the study of conic sections has its roots in ancient Greece, but through the author's work, it undergoes a significant transformation, revealing its power as an organizing principle in the geometry of curves and surfaces. The book demonstrates that conic sections can be viewed as transformations of other conic sections, opening up new perspectives on the subject. Through the unifying lens of cross-ratio, this book provides a profound understanding of conic sections and their wider geometrical implications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781330303634_0
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An Introduction to Projective Geometry Classic Reprint
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330303634
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An Introduction to Projective Geometry Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781330303634
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