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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. "
A Text-book of Geometry - Page 215
by George Albert Wentworth - 1888 - 386 pages
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...called the apothem of the polygon. PROPOSITION X. THEOREM. The perimeters of regular polygons having the same number of sides are to each other as the radii of the circumscribed circles, and, also, as the radii of the inscribed circles ; their surfaces are to...
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Catalogue - Harvard University

Harvard University - 1882 - 336 pages
...have the same value in whatever direction the secant be drawn. 4. Prove that 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 hence show that the ratio...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons 1382). 417. COROLLARY 2.—The circumferences of circles are to each other...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...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 number of sides; for...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1884 - 422 pages
...PROPOSITION V. THEOREM. 373. Tlie homologous sides of similar regular polygons have the same ratio as ihe radii of their circumscribed circles, and, also as the radii of their inscribed circles. Let 0 and 0' be the centres of the two similar regular polygons ABC, etc., and A'B'C', etc. From 0...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...III. Regular polygons of the same number of sides are similar. 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 each other...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...275. Two regular polygons of the same number of sides are similar. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles....
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...a regular pentedecagon in a given circle. Proposition X. A Theorem. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles....
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides are to each other as the squares of any two homologous* sides. (379) * Since the polygons are regular, any side of one may be...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...sides proportional. . • . the polygons are similar. (307) QED 415. COR. I. The perimeters of regular polygons of the same number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides...
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