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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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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896
...are to each other as their radii or as their apothems. Hint.— Apply 308. 483. COR. II. 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. PROPOSITION V. THEOREM 484. The circumference...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 250 pages
...polygon AC, and K' of A'C ' . But -Br. whence K_K>_r> *' A'B' ~R'~r" ' K' -R-^ That is, 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. PROP. VI. THEOREM. 350. The area of...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 282 pages
...polygon AC, and K' of Aff. T7~ A Tt* ( 322) ^ = ^=-^-. 777 73(2 f2 -M Jl y-- That is, <fte areas q/~ 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. A '\ PROP. VI. THEOREM. *~~^1 350....
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The Essentials of Geometry (plane)

Webster Wells - 1898 - 264 pages
...Cor. Let .K" denote the area of polygon .4(7, and K' of ( 322 ) That is, tte areas o/ <wo 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. <• c PROP. VI. THEOREM. "^ ^ 350....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular polygon is...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...= HK, etc. (?) AB BC CD ,,, .-. = = .etc. (?) FG GH HK .: .Pand Q are similar polygons. QED COB. I. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides. 206 Proposition 199. Theorem. 236. The perimeters of two regular polygons...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 278 pages
...squares of any two homologous sides. 412 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. 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 oftheir inscribed circles. D' MB A'...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...sides proportional. Therefore the two polygons are similar. 351 QED PROPOSITION V. THEOREM. 447. 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. B M' B'...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...O'A' = OM : O'M'. 445 364 431 436 Also, 357 351 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles. 413 PROPOSITION...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...polygon AC, and K' of A'C'. -wr- A -r^ r ( 322) ^^ J?2 . ~' A. Jt ™ ^' = !Br2 = ^' That is, 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. PROP. VI. THEOREM. 350. Tlie area...
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