 | Benjamin Greenleaf - 1863 - 504 σελίδες
...FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PROBLEM XXXVI. 341. Two similar polygons being given, to construct... | |
 | Adrien Marie Legendre - 1863 - 464 σελίδες
...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, C to H, and... | |
 | Benjamin Greenleaf - 1868 - 340 σελίδες
...FIK similar to AD E. The polygon FGHIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Prop. XXX. Cor., Bk. IV.). PBOBLEM XXXVI. 341. Two similar polygons being given, to construct... | |
 | William Chauvenet - 1871 - 380 σελίδες
...through O. In the same 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 ABCD, etc., be composed of the triangles ABC, ACD, etc.;... | |
 | William Chauvenet - 1872 - 382 σελίδες
...through O. In the same 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.;... | |
 | William Chauvenet - 1872 - 382 σελίδες
...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... | |
 | Charles Davies - 1872 - 464 σελίδες
...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,... | |
 | Benjamin Greenleaf - 1873 - 202 σελίδες
...FIK similar to AD E. The polygon FG HIK will be similar to ABCDE, as required. For these two polygons are composed of the same number of triangles, similar each to each, and similarly situated (Theo. XX. Cor., Bk. IV.). PROBLEM VII. To inscribe a square in a given circle. Draw two diameters,... | |
 | L J V. Gerard - 1874 - 428 σελίδες
...each, to the 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... | |
 | Adrien Marie Legendre - 1874 - 500 σελίδες
...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,... | |
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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. 
