| 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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