Fishback W.T. Projective and Euclidean Geometry

New York: John Wiley & Sons, 1969. — 328 p.This is an interesting book which will recall the breadth and sweep of geometry to all who have been privileged to study the subject. Those who wish to abolish the topic should at least read it to see what a range of study is actually involved; the outline is all the clearer for a fairly vigorous pruning of the material.
The book starts with a chapter, ‘‘Euclid Reexamined,” in which the founder is put through his paces and failed with first class honours. Hilbert’s axioms follow, in reasonable detail. The way is now clear to trace the development up to Projective Geometry, with a chapter on Fundamentals.
The argument next switches to Natural Homogeneous Coordinates, followed by chapters on ‘‘Vectors and Matrices” and ‘‘Fundamentals of Analytic Projective Geometry.” The next chapter deals with conics, and the book concludes with chapters on ‘‘Axiomatic Projective Geometry” and ‘‘Descendents of Real Projective Geometry’’—the latter giving various genealogies, and also some account of groups and subgroups of transformations.
The book may not fit readily into any course here, and may, indeed, be thought somewhat expensive. But it will be found well worthy of study by anyone who wishes to have a clear overall picture of essentials unclouded by excess of detail.