III.10 Proposition III.10
A circle does not cut a circle at more points than two.
Proof
Suppose two circles meet at three points A, B, C. By III.9,
the centre of each circle is the unique point equidistant from any
three points on its circumference — so both circles have the same
centre. Then by III.5 they coincide, contradicting their being two
distinct circles.
lines 74–74 in main.tex