 | George Albert Wentworth - Geometry - 1888 - 264 pages
...homologous altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...Let 2 R represent the diameter ; the circumference will be 2irR. Proposition XIII. A Theorem. 278. The areas of two regular polygons of the same number of sides are to each other : I As the squares of their sides. ; { \tl; As the squares of the radii of circumscribed... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...II. Let 2 J? represent the diameter ; the circumference will be 2 Proposition XIII. A Theorem. 278. The areas of two regular polygons of the same number of sides are to each other : I. As the squares of their sides. Proposition XIV. A Theorem. 279. The areas of circles... | |
 | George Irving Hopkins - 1891 - 208 pages
...in the same ratio as the squares of any two homologous sides. Sug. Consult 431. 494. The perimeters of two regular polygons of the same number of sides are in the same ratio as the radii of their circumscribed circles. Sug. Consult 359 and 492. 495. The perimeters of two regular... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...same ratio as the radii of their circumscribed circles. Sug. Consult 359 and 492. 495. The perimeters of two regular polygons of the same number of sides are in the same ratio as their apothegms. 496. The areas of two regular polygons of the same number of sides are in the same... | |
 | George Albert Wentworth - Algebra - 1892 - 312 pages
...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their... | |
 | George Albert Wentworth - 1894 - 320 pages
...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...Then, But, Whence, AB* AW*' K' AB ^R_ A'B' ~ R' K ^ R2 _ Iff 7? '2 ~ .A. Ji (§ 320.) ,.'2 That is, 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. PROPOSITION VI. THEOREM.... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...K' denote the areas of the polygons AE and A'-E'. Then, 7 JF = §-?. Whence, ^-_^^rj. That is, ŁAe areas of two regular polygons of the same number of sides are to each other ax the squares of their radii, or as the squares of their apothems. PROPOSITION VI. THEOREM.... | |
 | George Albert Wentworth - Geometry - 1896 - 68 pages
...the radii of their circumscribed circles, and also as the radii of their inscribed circles. 414. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of... | |
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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. 
