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S		 Book VI   Proposition 21
For, since A is similar to C,
    it is equiangular with it and has the sides about the equal angles proportional. [VI.Def.1]

Again, since B is similar to C,
    it is equiangular with it and has the sides about the equal angles proportional.

Therefore,
    each of the figures A, C is equiangular with C and with C has the sides about the equal angles proportional;
therefore
    A is similar to B.
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