 If two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed,...  Solid Geometry - Page 394by George C. Shutts - 1913Full view - About this book
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...they have two angles in each respectivety equal. Second. Two polygons are similar, when both may be divided into the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, ftie number... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...DEF (Prop. X.), that is, the triangles are similar. PROPOSITION XIX. THEOREM. Similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated ; and, conversely, polygons which are composed of the same number of triangles, similar each... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...two angles in each respectively equal. Second. Two polygons are similar when both may be divided info the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, the number... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...described on any other two homologous sides. PROPOSITION XXVI. THEOEEM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From any angle A, in the polygon AEDCB, draw diagonals,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...described on any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons may be div1ded into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From the vertex of any angle A, in the poly• C gon AEDCB,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...situated. A 0 .' D? ; т d I Oi¡ Let ABODE, FG IJ I К be two ^^f\ . H 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, FI. The two polygons... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...described on any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. ELEMENTS OF GEOMETRY. Let ABCDE, FGHIK be two similar polygons ; they may be divided into... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...(B. II, P. 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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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
...XXX. • — THEOREM. ELEMENTS OP GEOMETRY. H 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, FI. The two polygons... | |
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