| 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 their... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...^Therefore the triangles are similar. § 285 AB OA Hence '='- §274 AB OF QED 482. COR. I. The per1meters **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 polygons... | |
| Webster Wells - Geometry - 1898 - 250 pages
...similar. D AD ZX (The 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. B Given P and P' the perimeters, R and R' the radii, and ;- and... | |
| 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. *~~«^1 350. The... | |
| Webster Wells - Geometry - 1898 - 264 pages
...Cor. Let .K" denote the area of polygon .4(7, and K' of (§ 322 ) That is, tte areas o/ <wo 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. <• c PROP. VI. THEOREM. "^ ^ 350. The,... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, The perimeters of regular **polygons of the same number of sides are to each other as** any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular polygon is... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...sides proportional. Therefore the two polygons are similar. §351 QED 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. B M' B' Let P and P'... | |
| 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 are to each other as the squares of these... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...= HK, etc. (?) AB BC CD ,,, .-. = = .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... | |
| Webster Wells - Geometry - 1899 - 424 pages
...D D' AB (The 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' FB F' B' Given P and P' the perimeters, R and R' the radii,... | |
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