Higly axiomatic geometry book recomendation

Question

Recently I have started dipping my toes in mathematical waters besides calculus,and with varying success I have started learning bit of something about "everything".

But I have one issue,namely I can not find a satisfactory book regarding geometry. My problem with book choice is two-fold and it will be laid out in few points below.

First issue is that I know almost no geometry. Besides calculating areas of basic shapes,and a few very very basic theorems about chords and circles,I am a blank slate.

Second issue I have is that I can not handle non-axiomatic arguments,which are laid out in many good books.It is not that I find them bad or anything,I just like precision.

So now I will list few points which a book should satisfy,and then I will list a few examples of books which do not satisfy,and why.

Firstly book or book series should contain both plane a 3D geometry(or however it is called).

Exercises should be abundant(not essential)

The more theorems proved in the text,the better.

It should start from scratch.Namely from basic axioms, be it Euclidean or Hilbert or any other axiomatization.Then it should proceed from these axioms,and using strictly them,prove theorems.For reference think of Enderton's Set Theory book,first it lays out the axioms and then proceeds to results, given book should proceed in similar manner.

Any terms used used should be previously or timely defined

It should start from very basic concepts,like lines,circles,angles and etc. and proceed up to higher concepts,whatever they may be.

Now for books which do not satisfy and why. First example is Kiselev's Planimetry and Stereometry. These two books are great, but lack of rigor is very frustrating.

Hartshorne's Geometry book is great according to reviews but my problem with it is that it assumes knowledge which I do not posses. Same goes for Coxeter.

I thank you for your generous help,in advance.

Answer 1

I learned plane & solid Geometry from these old but super nice books, they are what you want. They Start from scratch with axiomatic presentation. You can download them free of charge from archive.org

George Albert Wentworth Plane Geometry

Beman,_David_Eugene_Smith New_Plane Geometry

Wentworth & Smith Solid Geometry

Beman & Smith Solid Geometry

Answer 2

if you want a very axiomatic treatment of elementary geometry, go back to the real source: Euclid. There are many books on this. My favourite is the Byrne book where colour is used instead of names.

http://www.amazon.com/Oliver-Byrne-First-Elements-Euclid/dp/3836544717/

Answer 3

Yes, Euclid did leave quite a bit to unspoken assumptions. A great more rigorous geometry source that I believe is your level is Foundations of Geometry by Venema.

http://www.amazon.com/gp/aw/d/0136020585/ref=mp_s_a_1_2?qid=1423436640&sr=8-2&keywords=foundation+geometry&pi=AC_SY200_QL40&dpPl=1&dpID=51wVLMhYlTL&ref=plSrch

Answer 4

The only book I have found that treats 3d geometry axiomatically (ie, based on set theory) is "Elementary geometry from an advanced standpoint" by Edwin Moise.