Theorem 5.9: The length of the arc of the unit circle above the points a and c on the x-axis is given by
The proof of this theorem requires a Lemma
Lemma: Let P0, P1, . . . , Pn be points on the upper half of the unit circle where
Then P0, P1, . . . , Pn is a partition of the arc on the upper half of the unit circle if and only if x0 < x1 < . . . < xn.
Proof of the Lemma
Proof of Theorem 5.9
next theorem (5.10)