 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...triangles is equal to the ratio of the squares of the homologous sides. But, two similar polygons may be decomposed into the same number of triangles similar each to each, and having the same ratio of similarity ; therefore, as the ratio of the surfaces of two homologous triangles... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...triangles is equal to the ratio of the squares of the homologous sides. But, two similar polygons may be decomposed into the same number of triangles similar each to each, and having the same ratio of similarity ; therefore, as the ratio of the surfaces of two homologous triangles... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...conditions 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 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
...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 (?, C to If,... | |
 | 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
...squares described on any other two homologous sides. THEOREM XX. 216. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. Let ABCDE, FGHIK be two similar polygons ; they may be divided into the same number of triangles... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...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 G, C to II,... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...that the corresponding triangles AD E, F IK 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,... | |
 | L J V. Gerard - 1874 - 428 pages
...remaining triangles of the polygon A' B' C' D' E' F' G' H' ; that is, the two polygons are composed of the same number of triangles similar each to each and similarly placed : therefore they are similar to each other [42], WWTBD THEOREM 44. Two parallelograms about the same... | |
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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. 
