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Book III   Proposition 13
Then, since
    the point G is the center of the circle ABDC,
    BG is equal to GD;
therefore
    BG is greater than HD;
therefore
BH is much greater than HD.
Again, since
    the point H is the center of the circle EBFD,
BH is equal to HD;
but it was also proved much greater than it: which is impossible.

Therefore
    a circle does not touch a circle internally at more points than one.
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