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. Elements of Geometry - Page 80by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| 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.... | |
| 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'... | |
| George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...squares of any two 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 A'... | |
| 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... | |
| 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... | |
| 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... | |
| 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 sides,... | |
| 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... | |
| William James Milne - Geometry, Modern - 1899 - 258 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... | |
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