Geometry Book Recommendation?

Can someone recommend a good basic book on Geometry? Let me be more specific on what I am looking for. I'd like a book that starts with Euclid's definitions and postulates and goes on from there to prove thereoms about triangles, circles and other plane shapes. I'm not interested (at this time) in a book that ties geometry in with linear algebra or explains non-euclidean geometry. All the books I've seen seem to be of two types 1) Let us use linear algebra and other techniques to put geometry on a firm footing. Let us assume you already know Eucliean geometry and move on to more interesting stuff. These are probably too advanced for me. 2) Let us skip all that complicated postulates/proofs and make geometry fun. Too easy.

When I was in 9th grade Honors Geometry way back in 1981/82 we had a textbook that, as I recall through my foggy memory, was very good and did systematically build up geometry from the propositions (5 of them?). And it certainly didn't attempt to address Hilbert's contributions to geometry or explain non-Euclidean geometry. Unfortunately, I don't recall the title or author. I suspect the book was used nationally though and for quite a number of years, so perhaps someone with a better memory than me can provide a title/author. I do recall it had all the postulates and most major thereoms listed at the end of the book.

My motivation is two fold... 1. Review the material myself in preparation for my advanced texts. 2. Help my children in a few years when they take geometry.

Books I could get for the iPad/Kindle or free books (Google?) would be most appreciatied, but I'm not opposed to killing a tree either :) Thanks for all the help. Dave

Solution 1:

• Introduction to Geometry by Coxeter.
• Elementary Geometry From An Advanced Viewpoint by Moise.
• Geometry: Euclid and Beyond by Hartshorne.

Solution 2:

Searching for Geometry textbooks between about 1970 & 1982 in one possible database (probably not very complete), I found:

• Jurgensen 1975
• Jacobs 1974
• Moise & Downs 1971
• Coxford & Usiskin 1971

Could one of these or the "related" books be the one you used?

A free possibility, alas without figures, might be Geometry Unbound (Kedlaya 1996).

Solution 3:

My recommendations from the earlier thread : Book recommendation on plane Euclidean geometry - are still to me as good a set of recommendations as there are.

I'll also throw my support behind Robin Hartshorne's Geometry: Euclid and Beyond as a great book for showing the connections between abstract algebra and classical geometry,but it's considerably more difficult then the other books on my list. You really need to be very comfortable with basic group and ring theory to be able to read it without a struggle.

Elmer Rees' classic Notes On Geometry is still the classic textbook on plane geometry from an advanced standpoint and should be in every mathematician's library. Again,to be able to read it,one needs to be very comfortable with both linear algebra and group theory and a certain comfort with basic real and complex analysis will help. But it's well worth the effort as there's probably no better single source on this material at this level.

Those 2 lists should get you started. Good luck!