 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.  Elements of Geometry - Page 215by Andrew Wheeler Phillips, Irving Fisher - 1896Full view - About this book
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...a corresponding side of the second. Therefore, the polygons are similar (433). 450. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary — The ratio of the radius to the side of a regular... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351). 3TÍ... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. 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... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...the corresponding diagonals (35O), p : P : : r : R q. ED 370. COR. 1. — 77(6 perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351). 371.... | |
 | André Darré - 1872 - 226 pages
...i!, + *, : : T : t : : AB2 : a6' . . . . ; that is, S : s : : AB2 : <z62 : : BD3 : 6d2, &c. Cor. i. The areas of two regular polygons of the same number of sides are related to each other as the squares of their right and oblique radii (96). Cor. ii. If E and r be... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. 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 (Theo. XXI.).... | |
 | David Munn - 1873 - 160 pages
...It follows, therefore, that the lateral surfaces, or the total surfaces of similar cylinders, are to each other as the squares of their radii, or as the squares of their heights. Cor. 2. — If h = r, that is, if the height be equal to the radius of the base, the lateral... | |
 | Harvard University - 1873 - 732 pages
...construct a polygon similar to a given polygon^ upon a given line. 6. The homologous sides of 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. Prove ; and... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. 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 (Theo. XXI.).... | |
 | L J V. Gerard - 1874 - 428 pages
...other, as any one side of the first is to any one side of the second, WWTBD COROLLARY I. The perimeters of two regular polygons of the same number of sides, are to each other as their radii. THEOREM 61. A regular polygon is symmetric to each radius produced lieyond the centre.... | |
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