 | George Albert Wentworth - 1900 - 344 pages
...equivalent to the sum of the three given octagons. Let x be the side of the regular octagon required. Two regular polygons of the same number of sides are to each other as the squares of their sides. § 446 .-. y? = O2 + 72 + 82. Ex. 381 .-. x = Ve2 + 72 + 82 = V36 +... | |
 | 1902 - 762 pages
...points and from a given straight line. When is it impossible to do so ? Q. Prove that the perimeters of two regular polygons of the same number of sides are to one another as the radii of their circumscribing circles. Prove that in a given circle the perimeter... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...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. § 413 PROPOSITION... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...are similar. Art. 321. QED 268 BOOK V. PLANE GEOMETRY PROPOSITION VI. THEOREM 434. I. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...proportional. Hence K and K' are similar. Art. 321. QED PROPOSITION VI. THEOKEM 434. I. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their... | |
 | Yale University. Sheffield Scientific School - 1905 - 1074 pages
...a given line. 6. In two regular polygons of the same number of sides, two corresponding sides have the same ratio as the radii of the inscribed or circumscribed circles. 7. When is a straight line said to be the locus of all points satisfying a given condition? Given two... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...number of sides will be inscribed. PLANE GEOMETRY — BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. B' HYPOTHESIS. P and P' are the perimeters, O and 0' the centers,... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...number of sides will be inscribed. PLANE GEOMETRY— BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. HYPOTHESIS. P and P' are the perimeters, O and O' the centers,... | |
 | Education - 1907 - 656 pages
...reading we would find ourselves doing the impossible. As for example take the theorem, " The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles and also as the radii of their inscribed circles." The... | |
 | 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... | |
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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. 
