| George Roberts Perkins - Geometry - 1860 - 468 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 - 1862 - 520 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. **Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their** areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. **Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their** areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Benjamin Greenleaf - Geometry - 1863 - 506 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. **Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their** areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| 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,... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...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 - Geometry - 1868 - 338 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. **Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their** areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Eli Todd Tappan - Geometry - 1868 - 436 pages
...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 - 1869 - 516 pages
...their angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. **Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their** areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...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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