 | 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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The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. 
