 | George Roberts Perkins - 1856 - 460 pagina’s
...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 - 1860 - 472 pagina’s
...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 - 1862 - 518 pagina’s
...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. Bk.... | |
 | Benjamin Greenleaf - 1861 - 638 pagina’s
...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. Bk.... | |
 | Benjamin Greenleaf - 1863 - 504 pagina’s
...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. Bk.... | |
 | Evan Wilhelm Evans - 1862 - 116 pagina’s
...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,... | |
 | Eli Todd Tappan - 1864 - 288 pagina’s
...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... | |
 | Benjamin Greenleaf - 1868 - 340 pagina’s
...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. Bk.... | |
 | Eli Todd Tappan - 1868 - 444 pagina’s
...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... | |
 | Elias Loomis - 1871 - 302 pagina’s
...radius of the inscribed circle. Therefore *he 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 cir cles, and their surfaces are as the squares of the... | |
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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. 
