 | 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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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. 
