 | 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 of triangles similar each to each, and similarly situated. of the same number of similar triangles, and similarly situated, the two polygons are 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 of triangles similar each to each, and similarly situated. of the same number of similar triangles, and similarly situated, the two polygons are similar.... | |
 | 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...of 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... | |
 | 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... | |
 | 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 A', let diagonals... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...way, Dd is shown to pass through O. PROPOSITION X.— THEOREM. 38. If two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon AB CD, etc., be composed of the triangles ABC, A CD, etc.;... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...AC* : DF*; combining this, with the first proportion (B. II., P. IV.), we have, ABC : DEF : : AC* : DF\ PROPOSITION XXVI. THEOREM. Similar polygons may...similarly placed. Let ABCDE and FGHIK be two similar poly gone, the angle A being equal to the angle F, B to (?, C to If, and so on : then can they be divided... | |
 | 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 A', let diagonals... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...way, Dd is shown to pass through O. PROPOSITION X.— THEOREM. 38. Ij two polygons are composed of the same number of triangles similar each to each and similarly placed, the polygons are similar. Let the polygon ABCD, etc., be composed of the triangles ABC, ACD, etc.;... | |
 | 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 of triangles similar each to each, and similarly situated. 217. Cor. Conversely, if two polygons are composed of the same number of similar triangles,... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
