 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...of similar sectors are to each other as the squares of their radii. M' M 499. COK. 6. The areas of similar segments are to each other as the squares of their radii or as the squares of their chords. For let S and S' denote the areas of the similar As AOB and A'O'B',... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...their radii. Ex. 1015. Similar sectors are to each other as t'.Ie squares of their radii. • Ex. 1016. Similar segments are to each other as the squares of their radii. 0 A HINT. Prove / \ sector AOB _ &AOB sector CPD A CPD' apply §§ 396 and 399. Then \ PROPOSITION... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...and T1, radii S and R1 . To Prove : T : T' = B2 : B'J. T ^TTB2 _B2 QED PROPOSITION XI. THEOREM 439. Similar segments are to each other as the squares of their radii. Given : Similar segments ABC and A'B'C'. To Prove : Segment ABC : seg. Proof : A AOB and A'O'B' are... | |
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Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'&B ' (ng. 136) are, by the same reasoning as in § 97, the same parts of their respective circles, which the angle O= O... 
