This book claims to contain the substance of the plane and solid analytical geometry (except straight line and circle) required for Pass and Engineering students at Universities, and for the more advanced pupils of Secondary Schools. It is refreshing to find plane and solid geometry in one volume, but the plan possesses the inherent objection that not very much ground in either can be covered in one book. Furthermore, "any portions of the subject which are difficult or of algebraic interest only" have been avoided. The book therefore consists in the main of what may be called numerical analytical geometry of the conics and conicoids. There are also chapters on the General Conic, Poles and Polars, Confocal Conics and Conicoids, and a final chapter on Curvature; but the great method of abridged notation, which is the very essence of the subject, is only hinted at in one chapter. The book is thus very limited in its outlook, and professes to be so.

An elementary knowledge of Calculus is assumed; but alternative methods are given, usually in the examples at the end of a chapter. No mention is made, however, of Burnside's beautiful method for writing down secants. Perhaps the author regards this as artificial and "difficult". In any case it might have found a place among the examples, which on the whole are a very good collection. There is a short historical note at the beginning, and an admirable plate showing photographs of models of conicoids. The book is beautifully printed and the diagrams are clear.