The geomteric postulates formed the basis for all of Euclid's theorems. The propositions in the Elements arose from these postulates, definitions, axioms and assumptions.The first to sixth volumes were dedicated to plane geometry. Volume five is said to be the finest discovery of Greek mathematics. It explained geometry as dependent on the use of proportion. The seventh to ninth volumes are dedicated to number theory. Volume ten is dedicated to the theory of irrational numbers. The eleventh to thirteenth volumes are dedicated to three-dimensional geometry.

The content of the Elements is very much geometrically based, however the word ‘geometry’ does not appear. This is largely due to the notion that Euclid did not want people to think his theorems were for practical use. Euclid, like Pythagoras disliked applying his mathematics to practical use and the meaning of geometry is ‘earth measurement’, geo for earth and metria for measurement. 

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