(1) Principles of Geometry (2) Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry (3) Elements of Projective Geometry

Abstract

(1) CHRISTIAN VON STAUDT'S “Beiträge zur Geometrie der Lage” was published so long ago as 1857; about the year 1871 Felix Klein wrote a series of papers emphasising the fact that it is possible to build up, on von Staudt's lines, the whole of projective geometry, independently not only of axioms of parallelism but also of the notions of distance and congruence. Yet it is astonishing how little effect this discovery has had upon English treatises on projective geometry, which still, with very few exceptions, base their subject upon metrical geometry, and are content to prove purely projective properties of conies by “projecting into a circle.” There are. it is true, Whitehead's two tracts on the “Axioms of Projective Geometry” and “Axioms of Descriptive Geometry,” but these, as their titles imply, deal only with the logical preliminaries. There is also G. B. Mathews' “Projective Geometry,” which suffers rather from undue compression and somewhat confuses the issue by talking about infinity so early as Chapter II.; and there is the important two-volume treatise by Veblen and Young, which is certainly not for the ordinary man.

(1) Principles of Geometry.

By Prof. H. F. Baker. Vol. 2: Plane Geometry, Conics, Circles, Non-Euclidean Geometry. Pp. xv + 243. (Cambridge: At the University Press, 1922.) 15s. net.

(2) Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry.

By Prof. F. S. Woods. Pp. x + 423. (Boston and London: Ginn and Co., 1922.) 22s. 6d. net.

(3) Elements of Projective Geometry.

By G. H. Ling G. Wentworth D. E. Smith. (Wentworth-Smith Mathematical Series.) Pp. vi + 186. (Boston and London: Ginn and Co., 1922.) 12s. 6d. net.