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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 211
by George Albert Wentworth - 1888 - 386 pages
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 250 pages
...similar. D AD ZX (The polygons fulfil the conditions of similarity given in 252.) PROP. V. THEOREM. 348. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. B Given P and P' the perimeters, R and R' the radii, and ;- and...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 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. The...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 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. The,...
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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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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...two polygons are similar. 351 Q. . D. REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same...and also as the radii of their inscribed circles. D' A' M' B' Let P and F~ denote the perimeters, 0 and 0' the centres, of the two regular polygons. From...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...sides proportional. Therefore the two polygons are similar. 351 QED PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same...and also as the radii of their inscribed circles. A' M Let P and P' denote the perimeters, 0 and 0' the centres, of the two regular polygons. From 0,...
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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...and also as the radii of their inscribed circles. B M' B' Let P and P' denote the perimeters, 0 and 0' the centres, of the two regular polygons. From...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...D D' AB (The polygons fulfil the conditions of similarity given in 252.) PROP. V. THEOREM. 348. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. D D' FB F' B' Given P and P' the perimeters, R and R' the radii,...
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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 and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 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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