| Benjamin Peirce - Geometry - 1847 - 150 pages
...circumscribed about a circle by means of §§ 212-221, and 228. 232. Theorem. 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. Proof.... | |
| Thomas Tate (mathematical master.) - 1848 - 284 pages
...X ^ FO ; but re x AB = the perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. THEOREM. **The perimeters of two regular polygons of the same number of sides are to each other as** the radii of the circumscribed circles ; and moreover their areas are to each other as the squares... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...radius of the inscribed circle. Therefore, the area of a regular polygon, &c. PROPOSITION VIII. THEOREM. **The perimeters of two regular polygons of the same number of sides, are** as the radii of the inscribed or circumscribed circles, and their surfaces are as the squares of the... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...consequently they are similar, (B. IV, Def. 3.) Cor. The perimeters of two regular polygons having **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, (B. IV, Prop.-xvi.) (92.) It has been shown,... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. **The perimeters of two regular polygons of the same...surfaces are to each other as the squares of those sides** (B. iv., P. 27). Cor. 2, The angle of a regular polygon, like the angle of an equiangular polygon,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. **The perimeters of two regular polygons of the same...surfaces are to each other as the squares of those sides** (B. 1v., P. 27). 136 GEOMETRY. Cor. 2. The angle of a regular polygon, like the angle of an equiangular... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...triangle OGA, OG = >/OA2-AG2; that is, r = ^W^^tf. We also have p=na; consequently, na THEOREM vI. **The perimeters of two regular polygons of the same number of sides are** proportional to the radii of their inscribed circles, or of their circumscribed circles ; and their... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...sides taken in the same order proportional ; consequently, they are similar (B. rv., D. 1). Cor. 1. **The perimeters of two regular polygons of the same...homologous sides, and their surfaces are to each other** aa tho squares of those sides (B. IV., p. 27). Cor. 2. The angle of a regular polygon, like the angle... | |
| Elias Loomis - Conic sections - 1857 - 242 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same ..lumber **of sides, are to each other as their homologous sides. and their** areas are us the squares of those sides (Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon... | |
| Elias Loomis - Conic sections - 1858 - 252 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same Climber **of sides, are to each other as their homologous sides. and their** areas are us the squares of those sides ^Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon... | |
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