 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...A'D' = OD : O'D' = 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 pentagon... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...A'O ' . (303) But 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 pentagon... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 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 apofhems. D r AMB A' M.' B' Given the regular polygons with perimeters... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 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. D' AMB A'~ M' B' Given the regular polygons with perimeters... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...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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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. 
