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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. "
An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in ... - Page 117
by Francis Joseph Grund - 1834 - 190 pages
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Elements of Geometry

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...
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Elements of Geometry, Volume 1

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...
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Exercises in Arithmetic

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...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

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....
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

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....
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Essentials of Geometry (plane).

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....
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The Essentials of Geometry

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....
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The Essentials of Geometry

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....
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The Elements of Plane Geometry

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...
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Plane and Solid Geometry

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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