 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...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 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... | |
 | 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... | |
 | Yale University - 1898 - 212 pages
...triangle is a, and the angle at the vertex is 30°; show that the length of the base equals a\2 — -/3 7. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the radii of the inscribed or circumscribed circles. JUNE, 1900. SOLID AND SPHERICAL. 1.... | |
 | Mathematics - 1898 - 228 pages
...triangle is a, and the angle at the vertex is 30°; show that the length of the base equals \2 — i/3 7. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the radii of the inscribed or circumscribed circles. V JUNE, 1900. SOLID AND SPHERICAL.... | |
 | 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.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...of polygon AC, and K' of A'C'. -wr- A -r^ r (§ 322) ^^ J?2 . ~' A. Jt ™ ^' = !Br2 = ^' 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.... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...denote the area of polygon AC, and K' oiA'C'. (§322) ^B_^_r.wh JBT_^_r2. 3^~^"P! ^ ' ^~l5~^ 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.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...and CDF are similar. Then consult Prop. 198, Cor. I., and Prop. 140. Proposition 2OO. Theorem. 237. 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. Use a method of proof... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...P:P' = OA: O'A' = OM : O'M'. § 445 §364 §431 § 436 Also, §357 § 351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles.... | |
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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. 
