 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...sides, are to each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares, constructed upon the radii of the inscribed or circumscribed... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Edward Olney - 1872 - 270 pages
...proportional ; 'Aat is, they are similar, QED 350. COR. 1.—The corresponding diagonals of regular polygons of the same number of sides are in the same ratio as the sides of the polygons. Let the student draw a figure and demonstrate the fact. 351. COR. 2.—The radii... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...are similar. QED ELEMENTARY PLANE GEOMETRY. 350, COR. 1. — The corresponding diagonals of regular polygons of the same number of sides are in the same ratio as the sides of the polygons. Let the student draw a figure and demonstrate the fact. 351. COR. 2. — The... | |
 | 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... | |
 | 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... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...PROPOSITION X. 382. Theorem.—The radii of the circumscribed, and also of the inscribed circles, of regular polygons of the same number of sides, are in the same ratio as the sides of the polygons. DEMONSTRATION. Fig 189. Let ABCDEF and abcdefbe two regular polygons of the... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...perimeters of the two polygons (Def. 3, Sec. VII, Book I). Therefore, the perimeters, etc. THEOREM XVII. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABCDE, abcde, be two regular polygons of the same... | |
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The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. 
