Book recommendations for Euclidean/Non-Euclidean Geometry
Not only do I agree with brainjam's suggestion re archive.org, but that suggestion dovetail's into mine. I think that is often challenging to find "just the right book" for you re a specific math topic (e.g. Geometry).
I offer generic suggestions:
- Look for a book that has a lot of exercises. In every math topic that I have explored with a book (e.g. calculus, number theory, complex analysis) I have always learned much more from the exercises. As far as I am concerned, the more exercises the better.
This is especially true given the existence of the MathSE forum. For an exercise that you deem valuable that you just can not solve, all you have to do is provide context (i.e. the theorems leading up to the problem) and show your work. Then you will generally get very helpful responses from this site. Given such a crutch, this adds value to a book that has a lot of exercises.
Review queries on this site that are tagged [book-recommendation] and [geometry].
Try to find impartial reviews of a book that you are considering. Personally, I have found Amazon book reviews to be very reliable.
Try to obtain a free copy of the book, either through archive.org (as brainjam suggested) or by googling for a specific title, including the "pdf" suffix. For example, you might google : coxeter geometry pdf. Surprisingly, I have often found (and downloaded) totally free pdf copies of math books that were very highly recommended.
The point here is not to save the cost of one book. Instead, the point is that you may have to try 10 different books before you find the one that best fits your needs. After you find such a book, you might then consider buying the book (even if you already have a free pdf copy). I have found that having a physical copy of the book (either hardback or paperback) is often helpful.
- Ironically, you will have to take the recommendations of others (e.g. from this site or from Amazon reviews) with a large grain of salt. A math book needs to be customized to your intelligence, math-background, math-goals (re what you are trying to accomplish via the book) and level of committment. It isn't reasonable to expect a book customized for someone else to necessarily be the right book for you.
It looks like you've looked around for books and found a lot that are not to your taste, or are at the wrong level of difficulty.
Have you browsed through archive.org? If you type the search term "Geometry" into the Internet Archive search box you get hundreds, maybe thousands of books on geometry. Browse away until you find the right level and mix of exercises.
Geometry as a subject was a much bigger part of the math curriculum during the 19th century than it was in the 20th century. Archive.org has a wealth of 19th century texts, and I've found that many of them are full of exercises. So I'd recommend that you look through some of those. The great thing about math is that it doesn't become obsolete, and everything you're likely to learn about Euclidean geometry at this stage was well known in the 19th century.
You can of course narrow down your search terms to focus on euclidean, solid, or projective geometry.