 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...parallelogram. State the difference in the meaning of the word equal here and in question 2. 6. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Define regular polygons, their radii, their apothems. CORNELL... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...triangles are similar. § 285 AB OA AB OF And - = -- §2QO A'B' O'F' QED 482. COR. I. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. 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. PROPOSITION V. THEOREM 484. The... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...their circumscribed circles, and also as the radii of their inscribed circles. 414. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the radii of... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...polygons fulfil 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' Given P and P' the perimeters, R and R' the radii, and r... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...polygon AC, and K' of Aff. T7~ A Tt* (§ 322) ^ = ^=-^-. 777 73(2 «f2 -M Jl y-- That is, <fte areas q/~ 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. A '\ PROP. VI. THEOREM. *~~«^1... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...homologous sides, § 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'... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...polygon AC, and K' of A'C'. -wr- A -r^ r (§ 322) ^^ J?2 . ~' A. Jt ™ ^' = !Br2 = ^' That is, 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. PROP. VI. THEOREM. 350. Tlie area... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...are similar. Then consult Prop. 198, Cor. I., and Prop. 140. Proposition 2OO. Theorem. 237. 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. Use a method of proof similar to... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...homologous sides. § 412 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 oftheir inscribed circles. D' MB... | |
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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. 
