 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...— •— st. 2£s (§ 193), and are, therefore, equal. .-. ABCDEF ~ GHIKLM. §363 QED 471. COK. 1. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The area of a regular... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...r:r' = a: a', by Ax. 8. §373 §291 §364 Ax. 8 §288 §282 §286 §282 OED 376. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on the radii of the circumscribed circles, and also as the squares on the radii of the... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...= w~ st. 2£s (§ 193), n and are, therefore, equal. .-. ABCDEF ~ GHIKLM. § 363 0. ED 471. COR. 1. The perimeters of two regular polygons of the same number of sides are to each oiher as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The... | |
 | 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 hexagons are inscribed... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...inches and 72 inches, respectively ; what is the ratio of their areas ? PROPOSITION VIII. THEOREM 538. The perimeters of two regular polygons of the same number of sides are to each otlIer as their radii or as tlIeir apothems. E' Given regular polygons ABCDE and A'B'C'D'S' having... | |
 | Geometry, Plane - 1911 - 192 pages
...sides are proportional. and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons of the same number of sides are in.the same ratio as the radii of the inscribed or circumscribed circles. 5. To construct a circle... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...tangents drawn at the points of division form a regular polygon circumscribed about the circle. 538. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. 541. I. The perimeter and area of a regular polygon inscribed in a circle... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of 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... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. The perimeters of 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... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
....^ = .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 hexagons are... | |
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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 surfaces are to each other as the squares of those sides (Book IV. 
