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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. "
A Text-book of Geometry - Page 211
by George Albert Wentworth - 1888 - 386 pages
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...sides are in the 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...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...III. Regular polygons of the same number of sides are similar. Corollary. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles ; and their areas are to each other...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...given 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,...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...A'B' B'C' C'D'' '" Therefore, AE and A'-E' are similar. = = CD PROPOSITION V. THEOREM. (§ 252.) 349. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. D AFB D' Let P and P' denote their perimeters, R and R' their radii,...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...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...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 394 pages
...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...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...^Therefore the 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...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...are similar. AB OA Hence And A'B' AB O'A' OF §466 §150 §285 §274 §290 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...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...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...
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Elements of Geometry, Part 1

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...
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