| 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... | |
| Elias Loomis - Conic sections - 1857 - 226 pages
...&c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the fame numoet of trianglet, **similar each to each, and similarly situated. Let...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 polygon FGHIK,... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 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... | |
| Elias Loomis - Conic sections - 1858 - 234 pages
...similar triangles, &c. PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numoet **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,... | |
| Elias Loomis - Conic sections - 1861 - 244 pages
...divided into the same numbei of triangles, similar each to each, and similarly situated. Let ABODE, **FGHIK be two similar 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 polygon FGHIK,... | |
| Benjamin Greenleaf - Geometry - 1862 - 514 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...triangles similar each to each, and similarly situated.** 276. Cor. Conversely, if two polygons are composed of the same number of similar triangles, -and similarly... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 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...triangles similar each to each, and similarly situated.** of the same number of similar triangles, and similarly situated, the two polygons are similar. For... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...the same manner, it may be shown that the corresponding triangles AD E, FIK are similar ; hence the **similar polygons may be divided into the same number...triangles similar each to each, and similarly situated.** of the same number of similar triangles, and similarly situated, the two polygons are similar. For... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...with the first proportion (B. II, P. IV.), we have, ABC : DEF : : AC2 : DF\ PROPOSITION XXVI. THEOREM. **Similar polygons may be divided into the same number...of triangles, similar, each to each, and similarly** placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to Gr,... | |
| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...AC, DF, or as the squares described on any other two homologous sides. PROPOSITION XXX.—THEOREM. **similar polygons; they may be divided into the same number of triangles similar each to each,** and similarly situated. From the homologous angles A and P, draw the diagonals AC, AD and FH, F I.... | |
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