If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Plane Geometry - Page 179by John Wesley Young, Albert John Schwartz - 1915 - 223 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...triangles similar and similarly situated. Scholium. The converse of the proposition is equally true : **If two polygons are composed of the same number of triangles similar** and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
| John Radford Young - 1827
...number of triangles, similar each to each, and similarly situated ; and, conversely, polygons which **are composed of the same number of triangles, similar each to each, and similarly** situated, are themselves similar. ELEMENTS OP GEOMETRY. while the sides containing these angles are... | |
| John Playfair, James Ryan - Euclid's Elements - 1835 - 316 pages
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. **If two polygons are composed of the same number of triangles similar,** and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...die squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons tire **composed of the same number of triangles, similar each to each, and similarly** situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in ' the polygon ABCDE, draw... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...triangles, similar, and similarly situated. Scholium. The converse of the proposition is equally true : **If two polygons are composed of the same number of triangles similar** and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
| Adrien Marie Legendre - Geometry - 1838 - 359 pages
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar **polygons are composed of the same number of triangles, similar each to each, and similarly** situated. Let ABCDE, FGHIK, be two similar polygons. From any angle A, in the polygon ABCDE, ^- „... | |
| John Playfair - Mathematics - 1842 - 317 pages
...similar rectilineal figures are to one another as the squares of their homologous sides. SCHOLIUM. **If two polygons are composed of the same number of triangles similar,** and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
| Nathan Scholfield - 1845
...triangles, similar and similarly situated. Scholium. 1. The converse of the proposition is equally true : **If two polygons are composed of the same number of triangles similar** and similarly situated, those two polygons will be similar. For, the similarity of the respective triangles... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...upon the first, to a similar, and similarly described rectilineal figure upon the second. SCHOLIUM. **If two polygons are composed of the same number of triangles similar,** and similarly situated, those two polygons will be similar. For the similarity of the two triangles... | |
| Charles Davies, Sir David Brewster, Adrien Marie Legendre - Trigonometry - 1849 - 359 pages
...AC, DF, or as the squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar **polygons are composed of the same number of triangles, similar each to each, and similarly** situated.' From any angle A, in c Let ABCDE, FGHIK. be two similar polygons. the polygon ABCDE, B^--^\... | |
| |