 | 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 - 242 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, Charles Davies - Geometry - 1857 - 442 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 - 256 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 - 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...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 - 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...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 - 504 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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FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
