 | Edward Olney - Geometry - 1883 - 344 pages
...homologous sides are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons (382)417. COROLLARY 2.—The circumferences of circles are to each other as... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...PROPOSITION V. THEOREM. 373. Tlie homologous sides of similar regular polygons have the same ratio as ihe radii of their circumscribed circles, and, also as the radii of their inscribed circles. Let 0 and 0' be the centres of the two similar regular polygons ABC, etc., and A'B'C', etc. From 0... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...(Def. 3, Sec. VII, Book I). Therefore, the perimeters, etc. THEOREM XVII. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABCDE, abcde, be two regular polygons of the same number of sides; for... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...etc. Therefore the polygons fulfil the two conditions of similarity. 11. COROLLARY. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles; and their areas are to each other... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...the same ratio as their bases). .-.P:P'=OA: O'A' = OM: OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the . radii of their... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...the same number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides are to each other as the squares of any two homologous* sides. (379) Proposition 4. Theorem. 417. Tlie perimeters of any two... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...homologous* sides proportional. . •. the polygons are similar. (307) QED 415. COR. 1. The perimeters of regular polygons of the same number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides... | |
 | George Albert Wentworth - Geometry - 1890 - 296 pages
...THEOREM. 413. The perimeters of two regular polygons cf the same number of sides are to each other as tlie radii of their circumscribed circles, and also as the radii of their inscribed circles. D D' AMBA! M' Let P and P' denote the perimeters, 0 and O ' the centres, of the two regular polygons.... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...THEOREM. 413. The perimeters of two regular polygons of the same number of sides are to each oilier as the radii of their circumscribed circles, and also as the radii of their inscribed circles. D' AMBA! M' Let P and F" denote the perimeters, 0 and Cf the centres, of the two regular polygons.... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...the two polygons are similar. § 319 QED PROPOSITION V. THEOREM. 413. The perimeters of two regular polygons of the same number of sides are to each other as the radii of tlieir circumscribed circles, and also as the radii of their inscribed circles. AMD A. M, B, Let P... | |
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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. 
