 | Adrien Marie Legendre - 1819 - 574 σελίδες
...proportion AC : DF : : AC : DF, we shall hare AB X AC; DE X DF : : AC : DF. Hence ABC : DEF : : AC : DF. Therefore two similar triangles ABC, DEF, are to each...polygons are composed of the same number of triangles, which are similar to each other and similarly disposed. Demonstration. In the polygon ABCDE (Jig. 129)... | |
 | Adrien Marie Legendre - 1825 - 570 σελίδες
...identical proportion. AC:DF::AC:DF, we shall have AB x AC : DE x DF : : AC : DF. Hence ABC:DEF::TC:DF. Therefore two similar triangles ABC, DEF, are to each...squares of any other two homologous sides. THEOREM. 21 9. Two similar polygons are composed of the same number of triangles, which are similar to each... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...proportion. AC : DF : : AC : DF, we shall have AB x AC : DE x DF : : AC : DF. Hence ABC: DEF:: AC: DF. Therefore two similar triangles ABC, DEF, are to each...squares of any other two homologous sides. THEOREM. 21 9. Two similar polygons are composed of the same number of triangles, which are similar to each... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...identical proportion. AC:DF::AC: DF, we shall have Hence AB x AC : DE x DF : : AC : DF. ABC : DEF ::AC: DF. Therefore two similar triangles ABC, DEF, are to each...squares of any other two homologous sides. THEOREM. 21 9. Two similar polygons are composed of the same number of triangles, which are similar to each... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...identical proportion. AC:DF::AC:DF, we shaft have AB X AC : DE X DF : : AC : DF. Hence ABC : DEF ::AC: DF. Therefore two similar triangles ABC, DEF, are to each other as the squares of the homologous sides AC, OF, or as the squares of any other two homologous sides THEOREM. "/(. 219. Two similar polygons are... | |
 | George Lees - 1826 - 276 σελίδες
...lines be cut by parallel lines, they are cut in the same ratio. 2. If, on two bases, there be placed the same number of triangles, similar each to each, and similarly situated, the polygons formed by joining the vertices of the triangles will be similar. 3. A straight line, drawn... | |
 | John Radford Young - 1827 - 246 σελίδες
...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 proportional... | |
 | John Radford Young - 1827 - 228 σελίδες
...that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the same 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,... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...remaining triangles are similar, whatever be the number of sides in the polygons proposed : . therefore two similar polygons are composed of the same number of triangles, similar, and similarly situated. Scholium. The converse of the proposition is equally true : If two polygons... | |
 | Adrien Marie Legendre - 1837 - 376 σελίδες
...: : AC : DF, there will result AB.AC : DE.DF : : AC2 : DP. Consequently, " ABC : DEF : : AC2 : DF. Therefore, two similar triangles ABC, DEF, are to each other as the squares described on their homologous sides AC, DF, or as the squares of any other two homologous sides. PROPOSITION... | |
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Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated. 
