| 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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