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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. "
An Elementary Treatise on Plane and Solid Geometry - Page 70
by Benjamin Peirce - 1837 - 159 pages
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Pennsylvania School Journal, Volume 56

Education - 1907 - 652 pages
...find ourselves doing the impossible. As for example take the theorem, " The perimeters of two regular polygons of the same number of sides are to each other...and also as the radii of their inscribed circles." The phrase " Of the same number of sides " might be omitted and the untrained pupil would scarcely...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...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. AMB A' M' B' Given the regular polygons with perimeters p...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...and are, therefore, equal. .-. ABCDEF ~ GHIKLM. §363 QED 471. COK. 1. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The area of...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...and 441, ^ = -j^. Prove AAOE~&A' O'E' AE A'E' O'A' O'F' (§ 435). 539. Cor. 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. Ex. 998. Two regular hexagons are inscribed...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...tangency, prove that they are divided proportionally by the smaller circle. 6. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or their apothems. 6. Prove that if one acute angle of a triangle is double...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...of their perimeters ? of their areas ? PROPOSITION VIII. THEOREM 638. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. E A' F' E' Given regular polygons ABCDE and A'B'C'D'E' having the...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...division form a regular polygon circumscribed about the circle. 538. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. 541. I. The perimeter and area of a regular polygon inscribed in...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...AE (§535 and §428). Then A' . OA _ OF A'E' O'A' O'f (§435). 539. Cor. Tlie areas of two regular polygons of the same number of sides are to each other as tJie squares of their radii or as the squares of their apothems. "Ex.. 998. Two regular hexagons are...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...equal to 3.1416 linear units, nearly. It has been shown (§ 454) that the perimeters of two regular polygons of the same number of sides are to each other as their radii, and hence also as the diameters of their circumscribed circles. Then it may be assumed...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...equal to 3.1416 linear units, nearly. It has been shown (§ 454) that the perimeters of two regular polygons of the same number of sides are to each other as their radii, and hence also as the diameters of their circumscribed circles. Then it may be assumed...
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