| George Washington Hull - Geometry - 1897 - 408 pages
.../.A = Z G, ZJ3= Ztf, etc. Therefore ABCDEF and GHKLMN are similar. § 217 324. COR.— The perimeters **of regular polygons of the same number of sides are to each other as the** radii of the circumscribed circles, or as the radii of the inscribed circles; and their areas are to... | |
| 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, area... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...+ 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 - 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... | |
| George Albert Wentworth - Geometry - 1899 - 498 pages
...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...squares of the radii of the circumscribed circles, and** of the inscribed circles. § 413 PROPOSITION VI. THEOREM. 449. If the number of sides of a regular... | |
| Harvard University - Geometry - 1899 - 39 pages
...formed. THEOREM IV. Regular polygons of the same number of sides are similar. THEOREM V. The perimeters **of regular polygons of the same number of sides are to each other as the** radii of the circumscribed circles, or as the radii of the inscribed circles ; and their areas are... | |
| William James Milne - Geometry - 1899 - 398 pages
...any two homologous sides? With the ratio of their radii? Of their apothems ? Theorem. The perimeters **of regular polygons of the same number of sides are to each other as** their radii and also as their apothems. D M a Data : Any two regular polygons of the same number of... | |
| William James Milne - Geometry, Modern - 1899 - 258 pages
...any two homologous sides? With the ratio of their radii? Of their apothems? Theorem. The perimeters **of regular polygons of the same number of sides are to each other as** their radii and also as their apothems. D MG Data : Any two regular polygons of the same number of... | |
| William James Milne - Geometry - 1899 - 404 pages
...regular polygon is equal to one half the product of its perimeter by its apothem. 390. Cor. II. Regular **polygons of the same number of sides are to each other as the squares** upon their radii and also as the squares upon their apothems. §§ 386, 345 Ex. 645. The sides of a... | |
| George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...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' M'... | |
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