|Book III Proposition 13|
Then, since on the circumference of each of the circles ABDC, ACK two points A, C
have been taken at random,
the straight line joining the points will fall within each circle; [III.2]
it fell within the circle ABDC and outside ACK [III.Def.3]: which is absurd.
a circle does not touch a circle externally at more points than one.
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