 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...of the 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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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.... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...and a 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 of... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...a 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 of... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...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... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...a 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 of... | |
 | André Darré - 1872 - 226 pages
...i!, + *, : : T : t : : AB2 : a6' . . . . ; that is, S : s : : AB2 : <z62 : : BD3 : 6d2, &c. Cor. i. The areas of two regular polygons of the same number of sides are related to each other as the squares of their right and oblique radii (96). Cor. ii. If E and r be... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...the corresponding diagonals (35O), p : P : : r : HQED , .g,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). 3TÍ... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...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 to... | |
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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. 
