How is Euclid's 4th and 5th common notion represented? i dont undersatnd it?

Question

please help me, i dont undersatnd it!

Answer 1

C.N.4 requires interpretation. On the face of it, it seems to say that if two things are identical (that is, they are the same one), then they are equal, in other words, anything equals itself. But the way it traditionally is interpreted is as a justification of a principle of superposition.. Using this principle, if one thing can be moved to coincide with another, then they are equal.

C.N.5, the whole is greater than the part, could be interpreted as a definition of "greater than." To say one magnitude B is a part of another A could be taken as saying that A is the sum of B and C for some third magnitude C, the remainder. Symbolically, A > B means that there is some C such that A = B + C. At any rate, Euclid frequently treats these two conditions as being equivalent.

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