| 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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