| 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 - 292 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 - 436 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 - 222 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 - 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... | |
| George Albert Wentworth, George Anthony Hill - Arithmetic - 1887 - 448 pages
...the same number of sides are proportional to their sides ; and the same is true of their apothems. **The areas of two regular polygons of the same number of sides are** proportional to the squares of their sides, or the squares of their radii, or the squares of their... | |
| |