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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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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...homologous sides? With the ratio of their radii? Of their apothems ? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D M a Data : Any two regular polygons of the same number of sides,...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular polygons of the same number of sides are to each other as the squares upon their radii and also as the squares upon their apothems. 386, 345 Ex. 645. The...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular polygons of the same number of sides are to each other as the squares upon their radii and also as the squares upon their apothems. 386, 345 Ex. 645. The...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...IV. Regular polygons of the same number of sides are similar. THEOREM V. 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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Plane and Solid Geometry

George Albert Wentworth - 1900 - 344 pages
...equivalent to the sum of the three given octagons. Let x be the side of the regular octagon required. Two regular polygons of the same number of sides are to each other as the squares of their sides. 446 .-. y? = O2 + 72 + 82. Ex. 381 .-. x = Ve2 + 72 + 82 = V36 + 49...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...circles; that is, as the radii of the polygons, or as the apothems of the polygons. 351. COROLLARY II. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. Let Si and 83 be the lengths of the sides in...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...OD: O'D'= AO: A'O'. (W h y?) But P: P' = AB: A'B' = AD: A'D'. (Why ?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...= AO: A'O'. But P:P' = AB:A'B' = AD:A'D'. (398) (Why?) (Why?) (Why?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'=OD: O'D' = AO : A'O'. QED 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...= OD : O'D' = AO: A'O'. (Why ?) But P:P' = AB:A'B' = AD:A'D'. (Why?) 407. COR. The areas of regular polygons of the same number of sides are to each other as the squares of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of...
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