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the angle ACB is equal to the angle ADB,
Therefore
on the same straight line AB the cannot be constructed two similar and unequal segments segments of circles ACB, ADB, on the same side.
Being what it was required to prove.
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T H E E L E M E N T S |
Book III Proposition 23 | |
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Then, since the segment ACB is similar to the segment ADB, and similar segments of circles are those which admit equal angles, [III.Def.11] the angle ACB is equal to the angle ADB, Therefore on the same straight line AB the cannot be constructed two similar and unequal segments segments of circles ACB, ADB, on the same side. Being what it was required to prove. |
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