 | Adrien Marie Legendre - 1822 - 394 sider
...triangles similar and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
 | John Radford Young - 1827 - 246 sider
...number of triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each to each, and similarly situated, are themselves similar. ELEMENTS OP GEOMETRY. while the sides containing these angles are... | |
 | John Playfair - 1835 - 336 sider
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
 | Adrien Marie Legendre - 1836 - 394 sider
...die squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons tire composed of the same number of triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in ' the polygon ABCDE, draw... | |
 | Adrien Marie Legendre - 1837 - 376 sider
...triangles, similar, and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
 | Adrien Marie Legendre - 1838 - 372 sider
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, ^- „... | |
 | John Playfair - 1842 - 332 sider
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
 | Nathan Scholfield - 1845 - 894 sider
...triangles, similar and similarly situated. Scholium. 1. The converse of the proposition is equally true : If two polygons are composed of the same number of triangles similar and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
 | Euclid, John Playfair - 1846 - 334 sider
...upon the first, to a similar, and similarly described rectilineal figure upon the second. SCHOLIUM. If two polygons are composed of the same number of triangles similar, and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
 | Charles Davies - 1849 - 372 sider
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated.' From any angle A, in c Let ABCDE, FGHIK. be two similar polygons. the polygon ABCDE, B^--^\... | |
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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. 
