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TWo like Segments of a Circle described on the same Line, are equal.
I call like Segments of a Circle, those which contain equal Angles; and I say that if they be described on the same Line AB; they shall fall one on the other, and shall not surpass each other in any part. For if they did surpass each other, as doth the Segment ACB, the Segment ADB; they would not be like. And to demonstrate it,
draw the Lines ADC, DB, and BC.
Demonstration. The Angle ADB is exteriour in respect of the Triangle BDC: Thence (by the 21th. of the 1st.) it is greater than the Angle ACB, and by consequence, the Segments ADB, ACB, containeth unequal Angles, which I call unlike.