| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...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.... | |
| Edward Butler (A.M.) - 1862 - 154 pages
...360°. 2n The area of the polygon and its perimeter will be nr'tan— 360o, amj 2srtan ^- 360°. 82. The **areas of regular polygons of the same number of sides are to** one another as the squares of their sides, or of their radii; and the perimeters are as the sides,... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...(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 example,... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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.... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...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... | |
| Eli Todd Tappan - Geometry - 1868 - 444 pages
...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... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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.... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...etc. 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... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...circumferences of the circles, and we shall have C : c : : R : r. Again, the areas of the polygons are **to each other as the squares of the radii of the circumscribed circles** (Prop. VIII.). But when the number of sides of the polygons is indefinitely increased, the areas of... | |
| Edward Olney - 1872 - 270 pages
...each other as the corresponding diagonals (35O), p : P :: r : S. QED 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). 371,... | |
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