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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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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...334), and two regular polygons of the same number of sides are similar. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. D' AMU A' W B' Given the regular polygons with perimeters...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apothems. D' AMB A'~ M' B' Given the regular polygons with perimeters...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...'sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters of two regular polygons of the same number of sides are to each other as their radii, and also as their apofhems. D r AMB A' M.' B' Given the regular polygons with perimeters...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...AO : A'O'. Hence, But .'. P: P' = OD : ' = AO:A'0'. (303) (Why?) QBD 417. 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.- 1315. The lines joining the mid-points of the radii of a regular...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P: P'= OD : O'D'= AO:A'O'. QED 417. 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. 1315. The lines joining the mid-points of the radii of a regular...
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...polygon, and the sum of the areas of the triangles is the area of the polygon, 479. Theorem. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, and also as the squares of their apothems. EXERCISES 1. Prove that the area...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...number of sides are to each other as the squares of their sides. The proof is left to the student. 253. Theorem. — The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. Hypothesis. AB and CD are sides, and M and N the centers, respectively,...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides ; and the areas of two regular polygons of the same number of sides are to...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...-— . = -— -^ = etc. Ax. V MN NO 9. .-. ABCD MNOP -. Def. sim. poly. 252. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. 253. Theorem. — The perimeters of two regular polygons of the same number...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...similar. Suggestion. The student can prove this by showing a close connection with Art. 226. Corollary 1. The perimeters of two regular polygons of the same number of sides are proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular...
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