Projective Geometry

Extract

Projective geometry derives both interest and importance from the fact that it assumes only the simplest and most fundamental axioms. The following sketch of the first principles, and proof of the fundamental theorem, is taken from Prof. Federigo Enriques' Projektive Geometrie (B. G. Teubner, Leipzig, 1903, 8vo, pp. xiv, 374). This work is specially adapted for school teaching. The first (Italian) edition appeared in 1898, and the axioms on which it is founded were explained, four years earlier in the Rendiconti R. 1st. Lombardo, Vol. 27, pp. 550-567.

Projective geometry is the geometry originated by von Staudt in the Geometrie der Zage, of which an excellent account by Prof. C A. Scott has already been given in the Mathematical Gazette, Vol. I., Nos. 19, 20, 22, pp. 307, 323, 363. Russell's very original Foundations of Geometry is the only English work which treats the subject from a strictly logical standpoint, but is unfortunately very unreliable as far as the mathematics is concerned.