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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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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...^ = ^.. Prove AAOE~A A'OE 1 (535 and 428). Then AE = OA = OF A'E' O'A' O'f ( 435). 539. Cor. 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. Ex. 998. Two regular...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...r:r'. p:p' = AB:A'B'. ...p:p'=R:R', p:p' : :r: r'. 382 Why ? Why? 391 452 Ax. 1 455. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii and also as the squares of their apothems. 452 PROPOSITION...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 360 pages
...two regular polygons of the same number of sides are to each other as any two homologous sides; and the areas of two regular polygons of the same number of sides are to each other as the squares of any two homologous sides. 415, 416 453. COROLLARY 2. In a given...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...441, .^ = .4^r> Prove AE (535 and 428). Then A' . OA _ OF A'E' O'A' O'f (435). 539. Cor. Tlie areas of two regular polygons of the same number of sides are to each other as tJie squares of their radii or as the squares of their apothems. "Ex.. 998. Two regular...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...corresponding angles equal. Therefore the two polygons are similar, by 282. QED 374. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters...
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Plane Geometry

Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...OM AM 2 AM AB Sec. 311 2. 0'M'~A'M'~2A'M'~A'B' 429. COR. 1. The radii of two circumscribed circles of two regular polygons of the same number of sides, are in the same ratio as the corresponding sides of the polygons. 430. COR. 2. The perimeters of two regular polygons of the same...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...same number of sides are proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, to the squares of their apothems, to the squares of their...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...p:p' = AB:A'B'. .:p:p' = R:R't p :p' \ : r : r'. 382 Why? Why? 391 452 Ax. 1 455. COROLLARY. The areas of two regular polygons of the same number of sides are to each, other as the squares of their radii and also as the squares of their apothems. 462 456....
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...etc. Def. reg. poly. ,, AB BC . -rr 9. .-. ABCD ---- MNOP .... Def. aim. poly. 252. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. The proof is left to the student. 253. Theorem. — The...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...same number of sides are proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, to the squares of their apothems, to the squares of their...
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