THE CAYLEY-VERONESE CLASS OF CONFIGURATIONS.

CAYLEY, ARTHUR & GIUSEPPE VERONESE.

Sur quelques théorèmes de la géométrie de position (Cayley) (+) Behandlung der projectivischen Verhältnisse der Räume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens. 2 vols.

Berlin, G. Reimer, 1846. - Leipzig, B.G. Teubner, 1881. 4to and 8vo. Cayley's paper in "Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, Bd. 31: Drittes Heft.1846". Pp. (179-)268,(2) and 1 plate. The whole issue (Drittes Heft) present with titlepage, stitched without wrappers. Cayley's paper pp. 213-226. - Veronese's paper in "Mathematische Annalen. In Verbindung mit C. Neumann...hrsg. von Felix Klein und Adolph Meyer. XIX. Band. 2 Heft. 1881." Pp. (161-)234. The whole issue (2. Heft) present with orig. printed wrappers. No backstrip. Veronese's paper pp. (161-)234.

Both papers first edition and first apperance in print of these two main papers in the history of projective geometry.
"Cayley, in his paper "Sur quelques théorèmes de la géométrie de position", (the paper offered) first calls attention to the figures obtained by taking the section, by a plane or 3-dimensional space, of the complete n-point (viz., n points, and the (n/2) lines, (n/3) plans etc. dtermined by them) in a flat spaceof v dimensions. Later Veronese discusses more fully the nature of this class of configurations thus obtained in r dimensions (the second paper offered). Both Cayley and Veronese state that these same configurations can also be obtained as projections of higher-dimensional figures." (Walter B. Carver). Veronese "in particular may be considered the main founder of the projective geometry of hyperspaces with n dimensions, which had previously been linear algebra presented geometrically, rather than geometry."(DSB). - An: Veronese-paper see Sommerville Bibliography of Non-Euclidean Geometry, 1881:3.
This issue of "Crelle's Journal" contains one more paper of Cayley: "Problème de géometrie analytique.", pp. 227-230.

Order-nr.: 41240