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I want to know if there's a good book or any other type of guide to study Euclidean geometry by only the 5 axioms in plane geometry and prove every other theorems from them?

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Of course, Euclid's Elements were written starting from those axioms. But we know now that Euclid did not use only those axioms. More precisely, he used other axioms implicitely. I suggest that you take a look at Robin Hartshone's Geometry: Euclid and Beyond or at David Hilbert's Foundations of Geometry.

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    $\begingroup$ The chapter Ordered Geometry in the book Introduction To Geometry, by Coxeter, is axiom-based. Euclid makes implicit assumptions about "betweenness"..... In elliptic geometry you can have three points on a line, all equidistant from each other, and it doesn't mean much to say whether any one of them is between the other two.......+1 $\endgroup$ – DanielWainfleet Nov 3 '18 at 20:02
  • $\begingroup$ Who is the author of Euclid's Elements? $\endgroup$ – Masked Man Nov 4 '18 at 9:31
  • $\begingroup$ I think that it's a safe bet to say that Euclid wrote Euclid's Elements. $\endgroup$ – José Carlos Santos Nov 4 '18 at 9:39
  • $\begingroup$ The other two book you offered match my criteria? $\endgroup$ – Masked Man Nov 4 '18 at 14:08
  • $\begingroup$ No, since the authors of both books know that other axioms are needed. $\endgroup$ – José Carlos Santos Nov 4 '18 at 14:09

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