A First Course in Projective Geometry (Classic Reprint)

Excerpt from A First Course in Projective Geometry

This work is intended for the use of students who have read the substance of Euclid, Books I.-XI., and who desire some introduction to the. Properties of the conic before proceeding to the study of the more advanced works on modern pure geometry. The subject of Geometrical Conics, through the medium of which such an introduction is usually acquired, often proves repulsive to the average student. In my Opinion this is due to two causes first, the demands which it makes upon the memory owing to its lack of coher ence as commonly treated; and, secondly, to the very slight extension of outlook as regards method which it affords. In the presentation here adopted, which, I venture to think, is in some respects original, I have endeavoured to overcome as far as possible these defects, while at the same time giving a slight sketch of the method of projection, and of the great principles of homography and duality upon which the further development of pure geometry so greatly depends. No systematic treatment of imaginary elements or of the theory of involution is attempted, as these subjects are, in my judgment, unsuitable for a first course.