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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 Geometry Upon the Inductive Method: To which is Added an ... - Page 65
by James Hayward - 1829 - 172 pages

## 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...

## 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...

## 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...

## 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...

## 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...

## Schultze and Sevenoak's Plane and Solid Geometry

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...

## Schultze and Sevenoak's Plane Geometry

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...

## Plane and Solid Geometry

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...