A Treatise on the Line Complex (Classic Reprint)

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