| 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,... | |
| 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.... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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*... | |
| 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... | |
| 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... | |
| 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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