 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...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 radii. Let ABCDEF,... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...the apothem of the polygon. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, having the same number of sides, are to each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their surfaces are... | |
 | Nathan Scholfield - 1845 - 894 pages
...circle would be obtained. PROPOSITION XIII. THEOREM. The perimeters of two regular polygons, having the same number of sides, are to each other as the radii of the circumscribed circles, and also, as the inscribed circles ; and their areas are to each other as... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...of sides with ABC &c. 231. Corollary. A regular polygon of 4, 8, 16, &c.; 3, 6, 12, &c. ; 5, 10, 20, &c. ; 15, 30, 60, &c. sides ; or, one similar to any...regular polygons of the same number of sides, and let O, 0* be their centres ; OA, O'A' are the radii of their circumscribed circles, and the perpendiculars... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 pages
...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 of the radii.... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...consequently similar (Def. 3, B. IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are as the squares of those sides (Prop. XXVI., B. IV.). Scholium.... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...proportional; consequently they are similar (Book IV. Def. 1.). . Cor. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV.... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (B. iv.,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (B. 1v.,... | |
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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. 
