 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...perpendicular CD, D being in the largest semicircle. A PLANE GEOMETRY PROPOSITION XVII. THEOREM 426. Similar segments are to each other as the squares of their radii. Hyp. S and »S" are two similar segments, having the radii R and R' respectively. To prove ' = R2:... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...diameter is the perpendicular CD, D being in the largest semicircle. A PROPOSITION XVIL THEOREM 426. Similar segments are to each other as the squares of their radii. Hyp. S and S' are two similar segments, having the radii R and R' respectively. To prove S : S' = R.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...diameter is the perpendicular CD, D being in the largest semicircle. A PROPOSITION XVII. THEOREM 426. Similar segments are to each other as the squares of their radii. Hyp. S and S' are two similar segments, having the radii R and R' respectively. To prove S : S' = R2... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...Similar sectors are to each other as the squares of their radii. [§§ 776 and 788.] 790. COROLLARY V. Similar segments are to each other as the squares of their radii. 791. EXERCISE. The circumferences of two circles are 942.48 -t. and 157.08 ft. respectively. The diameter... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...smaller wheel make while the larger wheel revolves once f PROPOSITION XIV. THEOREM 455. The areas of tivo similar segments are to each other as the squares of their radii. Given the similar segments ABC and AfBfCf in ciralet whose radii are R and R' . To prove segment ABC... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...larger wheel revolves once ? BOOK V. PLANE GEOMETRY PROPOSITION XIV. THEOREM 455. The areas of two similar segments are to each other as the squares of their radii. X O' A A' a Given the similar segments ABC and A'B'C' in cirales •whose radii are R and R'. To prove... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...sectors are to each other as the squares of their radii. PROPOSITION XII. THEOREM. 466. The areas of two similar segments are to each other as the squares of their radii. Let AC and A'C' be the radii of the two similar sectors ACB and A'C'B', and let ABP and A'B'P' be the... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...Prove : T : T' = R2 : R'2. .-. JL = -— (?). .-. T: T' = R* : 7?'2. (Explain.) QED TTR TTR * 456. THEOREM. Similar segments are to each other as the squares of their radii. Given: (?). To Prove: (?). o Proof: &AOB and A'O'B' are similar (?) (317). &AOB R2 ,9 ' and sector... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...and B'. To Prove : T : T' = B2 : B'2. T Z. ... _ZL = ^(?). ... T: T'=B2:B'2. (Explain.) QED 2 '2 456. THEOREM. Similar segments are to each other as the squares of their radii. Given : (?). To Prove : (?). o Proof: AA OB and A'O'B' are similar (?) (317). AAOB B2 /9^ ^QQQN •77... | |
 | Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...to each other as their radii. 3. Similar sectors are to each other as the squares of their radii. 4. Similar segments are to each other as the squares of their radii. 5. The areas of two circles are in the ratio 1 : 5|. If the radius of the larger is 4 feet 1 inch,... | |
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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... 
