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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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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...circumscribed about a circle by means of 212-221, and 228. 232. Theorem. The homologous sides of 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. Proof....
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Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848 - 284 pages
...X ^ FO ; but re x AB = the perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. THEOREM. The perimeters of two regular polygons of the same number of sides are to each other as the radii of the circumscribed circles ; and moreover their areas are to each other as the squares...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...radius of the inscribed circle. Therefore, the area of a regular polygon, &c. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons of the same number of sides, are as the radii of the inscribed or circumscribed circles, and their surfaces are as the squares of the...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...consequently they are similar, (B. IV, Def. 3.) Cor. The perimeters of two regular polygons having 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, (B. IV, Prop.-xvi.) (92.) It has been shown,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same...surfaces are to each other as the squares of those sides (B. iv., P. 27). Cor. 2, The angle of a regular polygon, like the angle of an equiangular polygon,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same...surfaces are to each other as the squares of those sides (B. 1v., P. 27). 136 GEOMETRY. Cor. 2. The angle of a regular polygon, like the angle of an equiangular...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...triangle OGA, OG = >/OA2-AG2; that is, r = ^W^^tf. We also have p=na; consequently, na THEOREM vI. The perimeters of two regular polygons of the same number of sides are proportional to the radii of their inscribed circles, or of their circumscribed circles ; and their...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...sides taken in the same order proportional ; consequently, they are similar (B. rv., D. 1). Cor. 1. The perimeters of two regular polygons of the same...homologous sides, and their surfaces are to each other aa tho squares of those sides (B. IV., p. 27). Cor. 2. The angle of a regular polygon, like the angle...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same ..lumber of sides, are to each other as their homologous sides. and their areas are us the squares of those sides (Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 252 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same Climber of sides, are to each other as their homologous sides. and their areas are us the squares of those sides ^Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon...
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