 | 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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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. 
