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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 surfaces are to each other as the squares of those sides (Book IV. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 105
by Charles Davies - 1849 - 359 pages
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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...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1881 - 338 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...
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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;...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - 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...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...the two polygons are similar. 319 QED REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 413. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. D BA M....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 260 pages
...altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the radii of their...
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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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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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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...the squares of any two homologous* sides. (379) Proposition 4. Theorem. 417. Tlie perimeters of any two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles. Hyp. Let P and...
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