 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...Prove AAOE~A A'OE 1 (§535 and §428). Then AE = OA = OF A'E' O'A' O'f (§ 435). 539. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. Ex. 998. Two regular hexagons are inscribed... | |
 | Geometry, Plane - 1911 - 192 pages
...sides are proportional. and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons of the same number of sides are in.the same ratio as the radii of the inscribed or circumscribed circles. 5. To construct a circle... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...tangents drawn at the points of division form a regular polygon circumscribed about the circle. 538. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. 541. I. The perimeter and area of a regular polygon inscribed in a circle... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides ; and the areas of two regular polygons of the same number of sides are to... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides; and the areas of two regular polygons of the same number of sides are to... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
....^ = .4^r> Prove AE (§535 and §428). Then A' . OA _ OF A'E' O'A' O'f (§435). 539. Cor. Tlie areas of two regular polygons of the same number of sides are to each other as tJie squares of their radii or as the squares of their apothems. "Ex.. 998. Two regular hexagons are... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...'sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apofhems. D r AMB A' M.' B' Given the regular polygons with perimeters p and... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...334), and two regular polygons of the same number of sides are similar. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. D' AMU A' W B' Given the regular polygons with perimeters p and... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...§286 §282 QED .'. r : r = a : a. .-.p : p' = r : r' = a : a', by Ax. 8. 376. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on the radii of the circumscribed circles, and alto as the squares on the radii of the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P: P'= OD : O'D'= AO:A'O'. QED 417. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 1315. The lines joining the mid-points of the radii of... | |
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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. 
