The Foundations of Euclidean Geometry

At the time ?The Foundations of Euclidian Geometry? was published in 1927, critics noted two trends in teaching and higher studies of geometry. The first was that Euclid, often considered the founder of the field, told everything even elementary students needed to know if they wanted to learn the basics of geometry. The other trend, which started around the turn of the century, was of exactly the opposite opinion. Euclid, it held, made too many mistakes and too many assumptions to be taught uncritically. ?The Foundations? author Henry George Forder roundly proclaimed himself to be in that second camp. Reviewers of his book said he made his case with this book?perhaps too much so. ?Let it be said at once that Mr. Forder?s book is one of very high value. It should find a place in every mathematical and teachers? library,? wrote H.E. Piggot in 1927. ?As indicated by this analysis this book is of great importance and interest to all interested in the development of mathematical logic.? Two years later, F.W. Owens wrote: ?Mr. Forder has written an interesting book and one which should be welcomed by those interested in seeing the rigor of modern analysis achieved in geometrical studies.? But? How useful might it actually be to contemporary math teachers? It was a question they both, and other critics, asked. What Forder mainly did was examine every theorem, every axiom, every definition very closely, taking nothing for granted in an effort to teach the logic of geometry at its most rigorous. His idea was not only to teach students geometry in and of itself, but logical thinking. His critics thought that a fine idea, but do most geometry teachers have the time, or even the ability, to do the same? And can their students follow them? It?s an interesting question, made even more intriguing by what may otherwise be considered a flaw in this copy. The previous owner underlined a section from Forder?s preface, quoted by Piggot, that began, ?This book is clearly not intended for beginners.? and ended with ?At this stage the utmost rigour and abstractness are desirable: and this stage can be reached by some in the later years of school life.? That previous owner was Roland A. Hueston, Jr., math and physics teacher and later principal of the prestigious Chauncey Hall School in Boston, and the Chapel Hill-Chauncy Hall School after its merger and relocation. Our copy is a first edition, first printing, with Hueston?s name written on the front pastedown and the Chauncy Hall School name stamped on the top and bottom edges of the textblock, though the book came from his personal collection, not the school library. There is a small ink scribble on the bottom of the front pastedown. Besides the aforementioned pencil underlining, there is one small line where Hueston appears to have worked on a proof himself on page 51. Otherwise, there are no marks within the book. The hinges pull at a few places but are intact. The table of contents page has separated from the text block but is whole and otherwise untorn. There is a narrow insert of bound-in paper that appears to be part of the ?hooking? or ?guarding? method of adding a single page to a signature of a book by the binder that appears in pictures of other copies of this edition; it may be related to the loose table of contents page. Otherwise the dark blue binding is in good order, excepting for normal aging. Light shelfwear appears around all the edges of the boards. The shelfwear is heavier on the spine, and the corners are bumped, but there are no tears or chips and the gold stamped lettering on the spine and the coat of arms for the publisher, Cambridge University, are still quite bright. The pages show the usual age tanning for a book this old, and there is a very small brown stain on the last few pages of the fore edge that has carried over slightly to the inside margins of the pages and the back pastedown. Photos are forthcoming or available upon request.…