| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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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