 | 1884 - 538 sider
...more than two equal lines to the circumference, that point is the centre of the circle. . 15. Similar polygons may be divided into the same number of similar...another that the polygons have, and the polygons are to one another in the duplicate ratio of their homologous sides. . / 16. "From the same point in a given... | |
 | George Albert Wentworth - 1881 - 266 sider
...areas of the two similar polygons ABC, etc., and A' B' C', etc., respectively. Then S : S' : : (similar polygons are to each other as the squares of their homologous sides). fö : у^ : : AB : A' B', § 268 or, AB : A' B' : : \ß : \¡S7. GEOMETRY. — BOOK IV. ON CONSTRUCTIONS.... | |
 | Franklin Ibach - 1882 - 208 sider
...EF; (237) BC X AD : FG X EH : A& : EF* (169) ELEMENTS OF PLANE GEOMETRY. THEOREM XXXI. 291. Similar polygons are to each other as the squares of their homologous sides. Let the polygons ABCDE and FGHKM be similar, and denote their surfaces by s and S. To prove that s : S... | |
 | Franklin Ibach - 1882 - 208 sider
...о : p; . ' . the square whose side is DE is the required one. QEF 314. SCHOLIUM. — Since similar polygons are to each other as the squares of their homologous sides, we can find, by means of the above problem, the homologous side of a polygon similar and having a given... | |
 | Euclid, Isaac Todhunter - 1883 - 428 sider
...first to a similar and similarly described triangle on the second. PROPOSITION 20. THEOREM. Similar polygons may be divided into the same number Of similar...another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides. Let ABODE, FGHKL be similar polygons,... | |
 | Euclides - 1884 - 434 sider
...be divided into the same number of similar and similarly situated triangles. 5. Prove that similar polygons may be divided into the same number of similar triangles having their vertices at points situated within the polygons. (Such points are called homologous points with... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 sider
...similar polygons are to each other as their homologous diagonals, or as any other homologous lines ; and the polygons are to each other as the squares of their homologous diagonals, or as the squares of any other homologous lines. Cor. 2. If the three sides of a right-angled... | |
 | Webster Wells - 1886 - 392 sider
...equations (1) and (2), we have ABC = AB x AC AB'C' 'AB'xAC'' PROPOSITION IX. THEOREM. 337. Two similar polygons are to each other as the squares of their homologous sides. A' B' Let K and K' denote the areas of the similar polygons AE and A'-E'. To prove that K_ _ Alf '... | |
 | Albert Taylor Bledsoe - 1886 - 253 sider
...of the same number of sides are inscribed in two circles of different sizes. Having established that the polygons are to each other as the squares of their homologous lines, they concluded, by the method of exhaustion, that the circles are to each other as the squares... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 sider
...Similar triangles are to each other as the squares of their homologous sides. PROPOSITION IX. Similar polygons are to each other as the squares of their homologous sides. PROPOSITION X. BOOK V. THEOREMS. PROPOSITION I. If the circumference of a circle be divided into any... | |
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Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. 
