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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... "
An Elementary Treatise on Plane and Solid Geometry - Page 88
by Benjamin Peirce - 1871 - 150 pages
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'O?B' (fig. 136) are, by the same reasoning as in 97, the same...parts of their respective circles, which the angle O = 0' is of four right angles ; and, therefore, they are to each other as these circles, or, by 271,...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 182 pages
...sectors are to each other as the squares of their radii. Proof. The similar sectors JIOB, A' OB' (fig. 136) are, by the same reasoning as in 97, the same...segments are to each other as the squares of their radii. 1? find a Trianjle equivalent tu a given Hoi gou. Proof. Let ADB, ADB' (fig. 136) be the similar segments....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1865 - 186 pages
...their radii. Proof. The similar sectors AOB, A1 OB' (fig. 136) are, by the same reasoning as in fj 97, the same parts of their respective circles, which the angle O= 0' is of four right angles ; and, therefore, they are to each other as these circles, or, by 271,...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 150 pages
...sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'VB' (fig. 136) are, by the same reasoning as in 97, the same...right angles ; and, therefore, they are to each other ag these circles, or, by 271, as the squares of the radii 288. Theorem. Similar segments are to...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 266 pages
...are to each other as the squares of their radii. 224. Theorem. Sector of n = — X •* r\ 360 225. Theorem. Similar segments are to each other as the squares of their radii. PROBLEMS. 226. To inscribe a square in a given circle. 227. To inscribe a regular hexagon and an equilateral...
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Report

Rutgers University. College of Agriculture - 1887
...The area of a regular polygon is equal to one-half the product of its apothegm by its perimeter. 6. Similar segments are to each other as the squares of their radii. — Ix Algebra. (Time, two hours.) 2x — l 2. Given - + — - = 79. and 16 — -- = 44, to find the...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...circles, are to each other as the squares of their radii, PROPOSITION X. THEOREM. 428. The areas of two similar segments are to each other as the squares of their radii. p Let AC and A'C" be the radii of the two similar segments ABP and A'B'P. To prove ABP : A'B'F = AC*...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 270 pages
...sectors are to each other as the squares of their radii. 224. Theorem. Sector of n = — X Trr\ 225. Theorem. Similar segments are to each other as the squares of their radii. PROBLEMS. 226. To inscribe a square in a given circle. 227. To inscribe a regular hexagon and an equilateral...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...are to each other as the squares of their radii. 224. Theorem. Sector of n = — X TTI*. ooU 225. Theorem. Similar segments are to each other as the squares of their radii. PROBLEMS. 226. To inscribe a square in a given circle. 227. To inscribe a regular hexagon and an equilateral...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 393 pages
...is equal to half the product of its radius and arc. Proposition 1 0. Theorem. 441. The areas of two similar segments are to each other as the squares of their radii. Hyp. Let S and S' be the areas of the two similar sectors AOB, A'O'B', T and T' the areas of the two...
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