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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. "
Elements of Plane Geometry: For the Use of Schools - Page 87
by Nicholas Tillinghast - 1844 - 96 pages
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...their circumscribed circles, and also as the radii of their inscribed circles. 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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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...^Therefore the triangles are similar. 285 AB OA Hence '='- 274 AB OF QED 482. COR. I. The per1meters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply 308. 483. COR. II. The areas of two regular polygons...
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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 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' Let P and P'...
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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 are to each other as the squares of these...
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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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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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