 | 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... | |
 | 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.... | |
 | 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, 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... | |
 | William Chauvenet - 1893 - 340 pages
...PROPOSITION III. Regular polygons of the same number of sides are similar. 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... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...A'-E' are similar. __ A'B' B'C' '' (§ 252.) PROPOSITION V. THEOREM. 349. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. I" B' Let AE and A'-E' be two regular polygons of the same number... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...difference in the meaning of the word equal here and in question 2. 6. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Define regular polygons, their radii, their apothems. CORNELL UNIVERSITY,... | |
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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. 
