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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. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 117
by Francis Joseph Grund - 1834 - 190 pages
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First lessons in Plane Geometry. Together with an application of them to the ...

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...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

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...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

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...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

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...
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A Treatise on Special Or Elementary Geometry

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...
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A Treatise on Special, Or Elementary Geometry

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...
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Elements of geometry, with ... trigonometry

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...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

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...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

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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Exercises in Arithmetic

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...
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