| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896
...are to each other 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... | |
| Webster Wells - Geometry - 1898 - 250 pages
...polygon AC, and K' of A'C ' . But -Br. whence K_K>_r> *' A'B' ~R'~r" ' K' -R»-^ That is, 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. PROP. VI. THEOREM. 350. The area of... | |
| Webster Wells - Geometry - 1898 - 282 pages
...polygon AC, and K' of Aff. T7~ A Tt* (§ 322) ^ = ^=-^-. 777 73(2 «f2 -M Jl y-- That is, <fte areas q/~ **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. A '\ PROP. VI. THEOREM. *~~«^1 350.... | |
| Webster Wells - 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.... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...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... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...= HK, etc. (?) AB BC CD ,,, .-. = = .etc. (?) FG GH HK .: .Pand Q are similar polygons. QED COB. I. **The perimeters of two regular polygons of the same number of sides are to each other as** any two homologous sides. 206 Proposition 199. Theorem. 236. The perimeters of two regular polygons... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 278 pages
...squares of any two homologous sides. § 412 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. **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 oftheir inscribed circles. D' MB A'... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...sides proportional. Therefore the two polygons are similar. §351 QED PROPOSITION V. THEOREM. 447. **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. B M' B'... | |
| George Albert Wentworth - Geometry - 1899 - 500 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... | |
| Webster Wells - Geometry - 1899 - 424 pages
...polygon AC, and K' of A'C'. -wr- A -r^ r (§ 322) ^^ J?2 . ~' A. Jt ™ ^' = !Br2 = ^' That is, 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. PROP. VI. THEOREM. 350. Tlie area... | |
| |