 | Edward Olney - Geometry - 1886 - 348 pages
...Also, as the homologous sides are to each other as the corresponding diagonals (387), pr 416. COROLLARY 1. — The perimeters of regular polygons of the same...are to each other as the apothems of the polygons (382)417. COROLLARY 2. — The circumferences of circles are to each other as their radii, and as their... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...inscribed in it. 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... | |
 | 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 - 418 pages
...equiangular and have their 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... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...have their homologous* sides proportional. . • . the polygons are similar. (307) QED 415. COR. I. 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... | |
 | William Chauvenet - 1893 - 340 pages
...B'C', or CD : C'D', 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... | |
 | 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,... | |
 | John Macnie - Geometry - 1895 - 390 pages
...similarly, all the sides about the equal A are proportional ; ... P is similar to p'. QED (284) 384 COR. The perimeters of regular polygons of the same number of sides are as their radii, or apothems; and their areas are as the squares of these lines. For the radii and apothems... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...m2 r2 s2 — =- — —='; -'. by substitution — = — ^ = -75 = —^ ' mrs P" a' m'2 r'2 s 2 2. The perimeters of regular polygons of the same number of sides are proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The... | |
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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. 
