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Deductive Geometry

E. A. Maxwell
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Ittay Weiss
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“The aim of this book is to give, in concise form, the whole of the geometry of the straight line, circle, plane and sphere…” is the opening line of the preface. The author means business, there is no doubt about that, as he immediately confesses that “this is a subject which, at the moment of writing, is less popular than it deserves, but I hope that the treatment may help to stimulate interest as well as to satisfy an existing need.” The book under review is a 2015 unabridged republication of the original work, published in 1962. Unfortunately, the original did not succeed in stimulating sufficient interest; it is rather safe to say that the popularity of the subject matter today is not substantially greater, if it is greater at all, than it was at the time of the first publication.

The subject matter is elementary Euclidean geometry, a topic that was once a standard part of the high school education programme in many countries. Its pedagogical enthusiasts celebrated the accessibility of its notions and the pathway to formal proofs and logical thinking that it forges. As is often the case, fame tends to dilute, and so textbooks emerged (such as the ones I was exposed to in my school days) spanning hundreds of pages of endless exercises (all designed to prepare me for the exams) in which the heart of the subject matter was not beating. E. A. Maxwell’s passion for education, coupled with his deep understanding of the subject matter, resulted half a century ago in a book which is as relevant today as ever.

There is something quite exhilarating in holding a pocket-size book containing the whole of geometry on the straight line, circle, plane and sphere. For one, it subdues all of those years of grappling with an infinite stream of mundane school-imposed exercises into a very short and manageable source of proper mathematical exposition. This lovely little book, with its concise and unique form of presentation, is a valuable addition to the bookshelf of students (high school students included) who wish to find a coherent treatment of the fundamentals. Undergraduate students may find that reaching, once in a while, to their copy of the book and spending several minutes coming to terms with yet another fundamental notion of Euclidean geometry is a pleasantly enriching activity. High school students, finding themselves feeling suffocated by a hoard of pointy triangles, may find solace and sanity in the orderly manner in which the book organises everything. Finally, if you simply wish to allow Euclidean truths to become permanent citizens in your neural network, then this book will concisely serve as your guide.

Ittay Weiss is a Teaching Fellow at the University of Portsmouth, UK.

The table of contents is not available.