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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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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...their angles equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. 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 (Theo. XXI.)....
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...their angles equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. 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 (Theo. XXI.)....
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 pages
...perimeter of the other, as any one side of the first is to any one side of the second, WWTBD COROLLARY I. The perimeters of two regular polygons of the same number of sides, are to each other as their radii. THEOREM 61. A regular polygon is symmetric to each radius produced lieyond the centre....
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...a straight line, to draw a circle through the point! and touching the line. 11. Prove that regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed or of their inscribed circles. Extend the theorem to the...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...XCII. Two circumferences are to one another as their radii. This proposition follows from the fact that the perimeters of two regular polygons of the same number of sides are as the radii of the circumscribed or the radii of the inscribed circles. Let GH be a circumference...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...proportional ; they are consequently similar (B. IV., Def. 4). Therefore, regular polygons, etc. Cor. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their areas are as the squares of those sides (B. IV., Pr. 27). Scholium....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...V. PROPOSITION V. THEOREM. 373. The homologous sides of similar regular polygons have the same ratio as the radii of their circumscribed circles, and, also as the radii of their inscribed circles. 1) Let 0 and 0' be the centres of the two similar regular polygons ABС, etc., and A' B'С', etc. From...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...angle be if the chord passes through the centre of the circle ? 5. Prove that the perimeters of regular polygons, of the same number of sides, are to each other as the radii of the circumscribed circles. State, without proving, what the ratio of the areas of the polygons is....
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...PROPOSITION V. THEOREM. .373. The homologous sides of similar regular polygons have the same ratio as the radii of their circumscribed circles, and, also as the radii of their inscribed circles. E Let 0 and 0' be the centres of the two similar regular polygons ABC, etc., and A'B'C', etc. From...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1881 - 332 pages
...similar polygons with their perimeters (see 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, ('.) as the squares of their sides; ('.) as the squares of their perimeters. 3. If in two hexagonal parks a side...
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