 | William James Milne - Geometry, Modern - 1899 - 258 pages
...with the ratio of any two 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
...the ratio of any two 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 - Geometry - 1899 - 496 pages
...§ 412 216 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. A' it' B' Let P and... | |
 | 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 - 1899 - 498 pages
...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... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...the conditions of similarity given in § 252.) PROP. V. THEOREM. 348. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. D D' FB F' B' Given P and P' the perimeters, R and R' the radii,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...2 —,- -, = -, = —,; s'sby substitution — = -;-= = -.-, = -= s m' r' s' 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. 442. The... | |
 | 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.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
....-. = = .etc. (?) FG GH HK .: .Pand Q are similar polygons. QED COB. I. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides. 206 Proposition 199. Theorem. 236. The perimeters of two regular polygons... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...Hence AD: A'D' = OD: O'D' = AO: A'O'. (Why?) But P:P' = AB:A'B' = AD: A'D'. (WRy?) 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... | |
| |
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. 
