| 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 number... | |
| John Radford Young - Euclid's Elements - 1827 - 246 pages
...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 - Geometry - 1830 - 344 pages
...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 - Geometry - 1850 - 218 pages
...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 - Geometry - 1850 - 238 pages
...: 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 - Geometry - 1886 - 340 pages
...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 - 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... | |
| Charles Davies - Geometry - 1854 - 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...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,... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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. of the same number of similar triangles, and similarly situated, the two polygons are similar.... | |
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