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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. "
Plane Geometry: With Problems and Applications - Side 182
av Herbert Ellsworth Slaught, Nels Johann Lennes - 1910 - 280 sider
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - 1830 - 274 sider
...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...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 204 sider
...sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. The areas of two regular polygons of the same number of sides, are in the same ratio as the squares constructed upon the radii of the inscribed or circumscribed circles. Thus the area of the regular...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 212 sider
...are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular polygons of the same number of sides, are in the same ratio as the squares constructed upon the radii of the inscribed or circumscribed circles. Thus the area of the regular...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Del 1

Francis Joseph Grund - 1834 - 202 sider
...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...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - 1862 - 116 sider
...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...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1864 - 288 sider
...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...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 438 sider
...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...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 sider
...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...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 472 sider
...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...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 sider
...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...
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