| 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...and also as the radii of their inscribed circles. A' it' B' Let P and P' denote the perimeters, O and O' the centres, of the two regular polygons. From... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Q. £. D. REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same number of sides are to each other...and also as the radii of their inscribed circles. D' A' M' B' Let P and F~ denote the perimeters, 0 and 0' the centres, of the two regular polygons.... | |
| Harvard University - Geometry - 1899 - 39 pages
...formed. THEOREM 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... | |
| William James Milne - Geometry, Modern - 1899 - 258 pages
...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
...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 - 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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.... | |
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