| 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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