 | Elias Loomis - Conic sections - 1849 - 252 pages
...the 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... | |
 | 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 number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (B. iv.,... | |
 | 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 number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (B. 1v.,... | |
 | 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... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...right-angled triangle OGA, OG = VOA'-AG2; that is, r = We also have j> = na; consequently, "" - a 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... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...inscribed circle. PROPOSITION IX. — THEOREM. 369. The perimeters of two regular polygons, havingthe same number of sides, are to each other as the radii of the circumscribed circles, and, also, as the radii of the inscribed circles ; and their areas are to each other as the squares of those... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI.... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...two polygons (Def. 3, Sec. VII, BI) Therefore, the perimeters, etc. BOOK II. 67 THEOREM XI. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABODE, abede, be two regular polygons of the same number of sides, for... | |
| |
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. 
