 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...DF, or as the squares described on any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number...similar each to each, and similarly situated. Let ABODE, FGHIKbetwo ^^f\ H similar polygons ; they may be divided into the same number of triangles similar... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 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... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...X AF : :AB * :IS\ Comparing this with the first proportion, we have, ABC:ADE::AB*:AD\ THEOREM XVII. Similar polygons may be divided into the same number...triangles, similar each to each, and similarly situated. ~LetABCDE and FGHIK\}& two similar polygons, having the angle A equal to the angle F, B to G, CtoH,... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION XXX. — THEOREM. ELEMENTS OF GEOMETRY. K Let ABCDE, FGHIK be two 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 F, draw the diagonals AC, AD and FH, F I. The two polygons being similar,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numtiei of triangles, simila: each to each, and similarly situated. Let ABCDE, FGHIK...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 K polygon FGHIK,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...similarity (24). PROPOSITION XI.— THEOREM. 39. Conversely, two similar polygons may be decomposed into the same number of triangles similar each to each and similarly placed. Let ABCD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...the first proportion (B. II., P. IV.), we have, ABC : DEF : : AC* : 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 poly gone, the angle A being equal to the angle F, B to... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...of similarity (24). PROPOSITION XI—THEOREM. 39. Conversely, two similar polygons may be decomposed into the same number of triangles similar each to each and similarly placed. Let AB CD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 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. 217. Cor. Conversely, if two polygons are composed of the same number of similar triangles, and similarly... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...other as the squares of AB and DE, or of BC and EF ; which was to be proved. PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number...of triangles, similar, each to each, and similarly placed. let ABODE and FGIIIK be two similar polygons, the angle A being equal to the angle F, B to... | |
| |
FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. 
