 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...homologous sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are to each other as the squares of those sidei (Book IV. Prop. XXVII.). Scholium. The angle of a regular... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. The homologous sides of 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. Demonstration.... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...sides proportional ; therefore they are similar. THEOREM. 22 J. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. Demonstration. 1. By the nature of similar figures, we have Ffe. 129. AB:FG::BC:GH::CD:HI, &c. (fig.... | |
 | Charles Waterhouse - Arithmetic - 1842 - 180 pages
...which are similar to each other, and similarly disposed. 23. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. 24. The product of three sides of a triangle is equal to the surface multiplied by double the diameter... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...area of a circle is equal to its circumference multiplied by half its radius.* PROP. VII. THEOREM. The perimeters of two regular polygons of the same number of sides, are to each other as the radii of the circumscribed circles : and their areas are to each other, as the squares of those... | |
 | Charles WATERHOUSE - Arithmetic - 1844 - 228 pages
...perimeter, multiplied by half the radius of the inscribed circle. 13. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. 14. The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...; consequently they are similar (B. FV, Def. 3). Cor. The perimeters of two regular polygons having 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 (B. IV, Prop. xvi). (84.) It has been shown (... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...circumscribed about a circle by means of §§ 212-221, and 228. 232. Theorem. The homologous sides of 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. Proof.... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 pages
...X ^ FO ; but re x AB = the perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. THEOREM. The perimeters of two regular polygons of the same number of sides are to each other as the radii of the circumscribed circles ; and moreover their areas are to each other as the squares... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...equal, and their homologous sides proportional; consequently they are similar (Book IV. Def. 1.). . Cor. The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV. Prop. XXVII.). PROPOSITION II. THEOREM. Any regular... | |
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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. 
