| 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 sides, as ABCDE... | |
| 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... | |
| William James Milne - Geometry, Modern - 1899 - 258 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... | |
| Harvard University - Geometry - 1899 - 39 pages
...IV. Regular polygons of the same number of sides are similar. THEOREM V. 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... | |
| 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... | |
| 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, 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... | |
| 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... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...= AO: A'O'. But P:P' = AB:A'B' = AD:A'D'. (398) (Why?) (Why?) (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... | |
| 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... | |
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