write all the euclid's definition
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Answer:
Euclid seems to define a point twice (definitions 1 and 3) and a line twice (definitions 2 and 4). This is rather strange.
Euclid never makes use of the definitions and never refers to them in the rest of the text.
Some concepts are never defined. For example there is no notion of ordering the points on a line, so the idea that one point is between two others is never defined, but of course it is used.
As we noted in The real numbers: Pythagoras to Stevin, Book V of The Elements considers magnitudes and the theory of proportion of magnitudes. However Euclid leaves the concept of magnitude undefined and this appears to modern readers as though Euclid has failed to set up magnitudes with the rigour for which he is famed.
When Euclid introduces magnitudes and numbers he gives some definitions but no postulates or common notions. For example one might expect Euclid to postulate a + b = b + a, (a + b) + c = a + (b + c)a+b=b+a,(a+b)+c=a+(b+c), etc., but he does not.
When Euclid introduces numbers in Book VII he does make a definition rather similar to the basic ones at the beginning of Book I:
A unit is that by virtue of which each of the things that exist are called one
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