| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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 - 574 pages
...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 - Geometry - 1825 - 280 pages
...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 - Geometry - 1825 - 224 pages
...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 - Geometry - 1825 - 224 pages
...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
...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 - Euclid's Elements - 1827 - 208 pages
...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 - Euclid's Elements - 1827 - 208 pages
...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 - Geometry - 1836 - 359 pages
...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 - Geometry - 1837 - 359 pages
...: : 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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