 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...IV.), we have, ABC : DEF : : ^C* : DF2. 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 G, C to H,... | |
 | George Anthony Hill - 1886 - 368 pages
...II.); also the triangles ANO, AOD; and the triangles A OP, ADE. Hence the two polygons ABCDE, AMNOP are composed of the same number of triangles, similar each to each and similarly placed. Now the two polygons have the same number of sides; A Jf IT Q and it is very easy to prove that they... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...equal to Abe, by I., Proposition IX., and is consequently similar to ABC. PROPOSITION VI.— THEOREM. 22. If two polygons are composed of the same number...the polygon ABCD, etc., be composed of the triangles ABC,A CD, etc.; and let the polygon A'B'C'D', etc., be composed of the triangles A'B'C', A'C'D', etc.,... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...Abe, by I., Proposition IX., and is consequently similar to ABC. PROPOSITION VI.— THEOREM. 22. Tf two polygons are composed of the same number of triangles...the polygon ABCD, etc., be composed of the triangles ABC,ACD, etc. ; and let the polygon A'B'C'D', etc., be composed of the triangles A'B'C', A'C'D', etc.,... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...PROPOSITION V. Two triangles are similar when their homologous sides are proportional. PROPOSITION VI. If two polygons are composed of the same number of...each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of triangles, similar... | |
 | William Chauvenet - Geometry - 1888 - 346 pages
...equal to Abe, by I., Proposition IX., and is consequently similar to ABC. PROPOSITION VI.—THEOREM. 22. If two polygons are composed of the same number...the polygon A'B'C'D', ^^ etc., be composed of the respectively, and similarly placed; then the polygons are similar. 1st. The polygons are mutually equiangular.... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...Bb passes 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...the polygon ABCD, etc., be composed of the triangles AB C, ACD, etc.; and let the polygon A'B'C'D', etc., be composed of the triangles A'B'C', A'C'D', etc.,... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...coincides with F. :. EF prolonged passes through O. SIMILAR POLYGONS. PROPOSITION XII. THEOREM. 331. If two polygons are composed of the same number of...each, and similarly placed, the polygons are similar. E BCW l!* In the two polygons ABCDK and A'B ' <yD>E', let the triangles AEB, EEC, CED be similar respectively... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar each to each, and similarly placed, the two polygons are similar. Proposition VII. A Problem. 212. A polygon being given, on a line corresponding... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar each to each, and similarly placed, the two polygons are similar. Proposition VII. A Problem. 212. A polygon being given, on a line corresponding... | |
| |
If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
