 | George Albert Wentworth - Geometry - 1899 - 498 pages
...O'A' = OM : O'M'. § 445 §364 §431 § 436 Also, §357 § 351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles. § 413 PROPOSITION... | |
 | William James Milne - Geometry - 1899 - 404 pages
...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular polygons of the same number of sides are to each other as the squares upon their radii and also as the squares upon their apothems. §§ 386, 345 Ex. 645. The sides... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...proportional. Therefore the two polygons are similar. § 351 QBD 446. COR. The areas of two regular polygon* of the same number of sides are to each other as the squares of any two homologous sides. § 412 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447.... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...homologous sides? With the ratio of their radii? Of their apothems? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D MG Data : Any two regular polygons of the same number of... | |
 | William James Milne - Geometry - 1899 - 398 pages
...homologous sides? With the ratio of their radii? Of their apothems ? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D M a Data : Any two regular polygons of the same number of... | |
 | George Albert Wentworth - 1900 - 344 pages
...equivalent to the sum of the three given octagons. Let x be the side of the regular octagon required. Two regular polygons of the same number of sides are to each other as the squares of their sides. § 446 .-. y? = O2 + 72 + 82. Ex. 381 .-. x = Ve2 + 72 + 82 = V36 + 49 + 64... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...circles; that is, as the radii of the polygons, or as the apothems of the polygons. 351. COROLLARY II. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. Let Si and 83 be the lengths of the sides in... | |
 | Arthur Schultze - 1901 - 260 pages
...OD: O'D'= AO: A'O'. (W h y?) But P: P' = AB: A'B' = AD: A'D'. (Why ?) 407. 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. 948. The lines joining the midpoints of the radii of a regular... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'=OD: O'D' = AO : A'O'. QED 407. 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. 948. The lines joining the midpoints of the radii of a regular... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...= OD : O'D' = AO: A'O'. (Why ?) But P:P' = AB:A'B' = AD:A'D'. (Why?) 407. 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. 948. The lines joining the midpoints of the radii of a regular... | |
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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. 
