Synopsis
CHAPTER 1. SYSTB:IS OF COORDIXATBS. 1. Ix the analyticn.1 treatment by Des Cartos of the Geometry of Spa.ce, the point is the ~p:lce-clcment; the researches of PODcclct and other geometers, and in pnrticular the Priociplc of Duality, IC:ld llaturally to the plane' as a space-clemellt; finally to PlUcker- 1S du(; the conception of a geometry in which t.hc line serve~ as the clement of space. Just as the point ~l-lld phtne arc defineu by coordinates and the in"cstigation of loci of points and envelopes of plalles is conducted by :Igebl'r.ical lllethod~ ill the older gcometry, so in that with which this work is cOlleerned, line-coordinates are employed. a.nd loci of lines nrc by their means discussed. The object of the present treatise is then, mainly, the illvestigation of the propeltics of the assemblage of lines which satisfy olle Or more given conditions, i.e. of lines whose coordinates satisfy olle 01' more equatiolJs of given form. If only one condition is
Table of Contents
ART; II, III; i,', ~; ,i-x; xi-xiv; XY, xyi; xvii; 2-9; 10-1:J; 14; 15-1G; 17; 18; 19-21; 22; 2:3; 24; ~2:i-27; 28; 20; CONTEN'l'S,; INTRODUCTION,; Double ratio; Cnl'I'CSI'OldellCe of poillts on the samc li1lf~; Im'olntion; COn'csponciences 011 difrCruut lin~; Collillc,tion; Involutions OJ! D curve; (2, 2) C01TC8}londcnce~; CHAPTER 1; SY~TE~lS OF COORDlKATE~,; Definition of complex and congruence; Systcms of COOrdillllte::;; Pencil, sheaf
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
CHAPTER 1. SYSTB:IS OF COORDIXATBS. 1. Ix the analyticn.1 treatment by Des Cartos of the Geometry of Spa.ce, the point is the ~p:lce-clcment; the researches of PODcclct and other geometers, and in pnrticular the Priociplc of Duality, IC:ld llaturally to the plane' as a space-clemellt; finally to PlUcker- 1S du(; the conception of a geometry in which t.hc line serve~ as the clement of space. Just as the point ~l-lld phtne arc defineu by coordinates and the in"cstigation of loci of points and envelopes of plalles is conducted by :Igebl'r.ical lllethod~ ill the older gcometry, so in that with which this work is cOlleerned, line-coordinates are employed. a.nd loci of lines nrc by their means discussed. The object of the present treatise is then, mainly, the illvestigation of the propeltics of the assemblage of lines which satisfy olle Or more given conditions, i.e. of lines whose coordinates satisfy olle 01' more equatiolJs of given form. If only one condition is
Table of Contents
ART; II, III; i,', ~; ,i-x; xi-xiv; XY, xyi; xvii; 2-9; 10-1:J; 14; 15-1G; 17; 18; 19-21; 22; 2:3; 24; ~2:i-27; 28; 20; CONTEN'l'S,; INTRODUCTION,; Double ratio; Cnl'I'CSI'OldellCe of poillts on the samc li1lf~; Im'olntion; COn'csponciences 011 difrCruut lin~; Collillc,tion; Involutions OJ! D curve; (2, 2) C01TC8}londcnce~; CHAPTER 1; SY~TE~lS OF COORDlKATE~,; Definition of complex and congruence; Systcms of COOrdillllte::;; Pencil, sheaf
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A Treatise on the Line Complex (Classic Reprint)
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Paperback. Etat : New. Print on Demand. This book presents a comprehensive guide to line geometry, a branch of geometry that analyzes figures in three-dimensional space by defining straight lines as fundamental elements rather than points or planes. Historically significant for its influence on the development of geometry and other fields like sphere geometry, this book provides an introduction to line geometry's foundational principles, including complex systems, congruence, the intersection of lines, and more. The author employs Klein coordinates to provide elegant analytical solutions and geometrical methods, inviting readers to explore the rich tapestry of line geometry and its applications in understanding the world around us. Through its insights and detailed explanations, this book will benefit students, researchers, and anyone fascinated by the intricate world of geometry. 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 9781440047909_0
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