 | 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. 351. The area... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...parallelogram. State the difference in the meaning of the word equal here and in question 2. 6. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Define regular polygons, their radii, their apothems. CORNELL UNIVERSITY,... | |
 | 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. 351. The... | |
 | George Albert Wentworth - 1894 - 318 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...sides are to each other as their radii or as their apothems. Hint. — Apply § 308. 483. COR. II. 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 V. THEOREM 4:84:. The circumference... | |
 | George Albert Wentworth - Mathematics - 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 the radii of their... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...triangles are similar. § 285 AB OA AB OF And - = -- §2QO A'B' O'F' QED 482. COR. I. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular polygons... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...^Therefore the triangles are similar. § 285 AB OA Hence '='- §274 AB OF QED 482. COR. I. The per1meters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular polygons... | |
 | George Albert Wentworth, George Anthony Hill - Arithmetic - 1897 - 476 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 - 1898 - 250 pages
...the area of polygon AC, and K' of A'C ' . But -Br. whence K_K>_r> *' A'B' ~R'~r" ' K' -R»-^ 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. PROP. VI. THEOREM. 350. The area of a... | |
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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. 
