| Francis Joseph Grund - Geometry, Plane - 1834 - 204 pages
...each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas **of two regular polygons of the same number of sides, are to each other as the** areas of the squares constructed upon the radii of the inscribed or circumscribed circles. 36. The... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...Two regular polygons of the same number of sides are similar figures. 34. The sums of all the sides **of two regular polygons of the same number of sides, are to each other** in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...homologous sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. **The perimeters of two regular polygons of the same number of sides, are to each other as** their homologous sides, and their surfaces are to each other as the squares of those sidei (Book IV.... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. The homologous sides of regular **polygons of the same number of sides are to each other as the radii of** their circumscribed circles, -and also as the radii of their inscribed circles. Demonstration. Let... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...equal, and their homologous sides proportional ; therefore they are similar (162). 264. Corollary. **The perimeters of two regular polygons of the same number of sides are to each other as** their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...the apothem of the polygon. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, having **the same number of sides, are to each other as the radii of the circumscribed circles, and** also as the radii of the inscribed circles ; and their surfaces are to each other as the squares of... | |
| Nathan Scholfield - 1845 - 894 pages
...circle would be obtained. PROPOSITION XIII. THEOREM. The perimeters of two regular polygons, having **the same number of sides, are to each other as the radii of the circumscribed circles, and** also, as the inscribed circles ; and their areas are to each other as the squares of those radii. Let... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...circumscribed about a circle by means of §§ 212-221, and 228. 232. Theorem. The homologous sides of regular **polygons of the same number of sides are to each other as the radii of** their circumscribed circles, and also as the radii of their inscribed circles. Proof. Let ABCD, &c.,... | |
| Thomas Tate (mathematical master.) - 1848 - 284 pages
...polygon =nx AB X ^ FO ; but re x AB = the perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. **THEOREM. The perimeters of two regular polygons of...other as the radii of the circumscribed circles ; and** moreover their areas are to each other as the squares of the radii. Let i and s be the centres of the... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...equal, and their homologous sides proportional; consequently they are similar (Book IV. Def. 1.). . Cor. **The perimeters of two regular polygons of the same number of sides, are to each other as** their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV.... | |
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