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from
Brown Corpus
On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.
As S increases we consider the two free corner points of the square, Af and Af, adjacent to P and Q respectively.
As S approaches T the square will be outside C and therefore both Af and Af must cross C an odd number of times as S varies from zero to T.
The points may also touch C without crossing.
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