 | Adrien Marie Legendre - 1822 - 394 pàgines
...similar, when they have two angles in each respectivety equal. Second. Two polygons are similar, when both may be divided into the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, ftie number... | |
 | John Radford Young - 1827 - 246 pàgines
...equal to those of the triangle DEF (Prop. X.), that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the...of triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each... | |
 | Adrien Marie Legendre - 1830 - 344 pàgines
...two angles in each respectively equal. Second. Two polygons are similar when both may be divided info the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, the number... | |
 | Charles Davies - 1850 - 218 pàgines
...ratio ; hence, ABC : DEF : : AL : DN. THEOREM XX. Two similar polygons may be divided into an equal number of triangles, similar each to each, and similarly...placed. Let ABCDE and FGHIK be two similar polygons. From the angle A draw the diagonals AC, AD ; and from the homologous angle F, draw FH, FL Now, since... | |
 | Charles Davies - 1850 - 238 pàgines
...: AL : DX. FH : DEF ABK DE; DME, N D THEOREM XX. Two similar polygons may be divided into an equal number of triangles, similar each to each, and similarly...placed. Let ABCDE and FGHIK be two similar polygons From the angle A draw the diagonals AC, AD: and from the homologous angle F, draw FH, FI. Now, since... | |
 | Charles Davies - 1886 - 340 pàgines
...ABC : DEF : : AL : DN Two similar polygons may be divided into an equal number of triangles, s1milar each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons. From the angle A draw the diagonals AC, AD : •1ngle, Jf, draw FH, r/, . .'Now, since die polygons... | |
 | Adrien Marie Legendre - 1852 - 436 pàgines
...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided ,into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two. polygons are... | |
 | Charles Davies - 1854 - 436 pàgines
...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two polygons are... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 pàgines
...remaining triangles are similar, whatever be the number of sides in the polygons proposed: therefore, two similar polygons may be divided into the same number of triangles, similar, and similarly placed. Scholium. The converse of the proposition is equally true: If two polygons are... | |
 | Benjamin Greenleaf - 1862 - 532 pàgines
...the same manner, it may be shown that the corresponding triangles ADE, FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 276. Cor. Conversely, if two polygons are composed of the same number of similar triangles,... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
