| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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... | |
| George Lees - 1826 - 276 pages
...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 - 246 pages
...those of the triangle DEF (Prop. X.), that is, the triangles are similar. PROPOSITION XIX. THEOREM. **Similar polygons may be divided into the same number...triangles, similar each to each, and similarly situated** ; and, conversely, polygons which are composed of the same number of triangles, similar each to each,... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...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. Let the polygons in the margin be similar, the angle A being equal to the angle... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons tire composed of **the same number of triangles, similar each to each,...situated. Let ABCDE, FGHIK, be two similar polygons.** From any angle A, in ' the polygon ABCDE, draw diagonals AC, AD to the other angles. From the homologous... | |
| Adrien Marie Legendre - Geometry - 1838 - 382 pages
...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.** 92 GEOMETRY. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, draw... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...similar triangles, &c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numba **of triangles, similar each to each, and similarly...polygons; they may be divided into the same number of** similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the E polygon FGHIK,... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...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^--^\ ., ^-A... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...two-thirds of this line from the vertex. PROPOSITION XIX. THEOREM. Two similar polygons are composed of **the same number of triangles similar each to each, and similarly situated. Let** ABCDF, GHKLM be two similar polygons. From any angle A in the polygon ABCDF, draw the diagonals AC,... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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... | |
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