 | John Macnie - Geometry - 1895 - 390 pages
...similarly, all the sides about the equal A are proportional ; ... P is similar to p'. QED (284) 384 COR. The perimeters of regular polygons of the same number of sides are as their radii, or apothems; and their areas are as the squares of these lines. For the radii and apothems... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...m2 r2 s2 — =- — —='; -'. by substitution — = — ^ = -75 = —^ ' mrs P" a' m'2 r'2 s 2 2. The perimeters of regular polygons of the same number of sides are proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. 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 V. THEOREM 484. The circumference... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...411. Two regular polygons of the same number of sides are similar. 412. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of any two homologous sides. 413. The perimeters of two regular polygons of the same number... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...sides are to each other as their radii or as their apothems. 483. COR. II. 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 V. THEOREM 484, The circumference... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...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... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...A'B' + B'C' + C'D' + etc. ~~ A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular polygon is... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...Cor. Let .K" denote the area of polygon .4(7, and K' of (§ 322 ) That is, tte areas o/ <wo 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. <• c PROP. VI. THEOREM. "^ ^ 350. The,... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...the conditions of similarity given in § 252.) PROP. V. THEOREM. 348. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. p D' FD Given P and P' the perimeters, R and R' the radii,- and... | |
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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. 
