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So I look for a book that has geometric approaches to (quote unquote) everything there is to know about Euclidian geometry.

I am not a bookworm so I am basically wondering blindly in a dark room but the books I checked thus far did not satisfy me because they seem either to just be partially euclidean partially everything else (analytical/calculus/algebra/ other types of geometries etc)

Basically I would like a book like the elements but better written/written as a textbook (because the books I found on Elements are more focused on translating the ancient script rather than mentioning the concepts in a modern and easy to understand way and with an order that makes sense in nowadays geometric applications they also luck examples/conclusions/exercises)

After reading and understanding this book I would like to be able to know everything there is about e.g how to measure lines using circles and tangents in order to construct a shape or what not how to compare circles how to construct vertices using circles how to cut shapes or distances in equal parts etc etc etc

Actually what I described above is somehow misleading but it's hard for me to articulate what I am looking for.... think of Euclidea the game, I want to be able to solve everything there (<-- this is not my target but I think it gives a good idea of what I am looking for)

The purpose of wanting this is that in many math problems I encounter there is an intuitive geometrical approach that I miss because my geometry knowledge is limited but my teacher or fellow students point out.

I thank you in advance for your time.

P.S No children's books with basic stuff, I need it to be as comprehensive as it can get.

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    $\begingroup$ Hey, there's an old English print of Euclid's 'Elements' in Google Books... $\endgroup$ Commented Aug 22, 2020 at 3:47
  • $\begingroup$ Check on Google Books... you'll get what you want there. $\endgroup$ Commented Aug 22, 2020 at 3:49
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    $\begingroup$ @Spectre OP said they don't want Euclid's 'Elements'. $\endgroup$ Commented Aug 22, 2020 at 3:51
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    $\begingroup$ Check The book by Evan Chen on Euclidean geometry. It's a wonderful book! It's covers almost everything along with olympiad problems. The exact name is Euclidean geometry in mathematical olympiads. It has $328$ pages. $\endgroup$ Commented Aug 22, 2020 at 3:53
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    $\begingroup$ @Spectre OP means "original poster", in other words papajo. $\endgroup$ Commented Aug 22, 2020 at 3:54

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I find The Bones to be really helpful. It includes all the definitions and diagrams from the Elements without the proofs.

Here is the publisher's page for it at the Green Lion Press. You can also look the book here on Google Books.

The text of the Elements which is present comes from Heath's translation, which is not so modern, but with so much pruned out, that for me at least, it is much, much more accessible than the elements itself.

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  1. Hilbert, David :Foundations Of Geometry.

  2. Coxeter, Donald : Introduction To Geometry.

  3. Coxeter, Donald : Geometry Re-Visited.

I also recommend the geometric problems in "101 Great Problems In Elementary Mathematics" by Heinrich Dorrie.

BTW Archimedes invented a device for trisecting angles. It is so simple that I can never remember it.

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