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 170by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...when 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 - 228 pages
...proved to be similar, and so on in every pair of corresponding triangles ; hence, similar polygons may **be divided into the same number of triangles, similar each to each, and similarly** situated. Conversely. Let the polygons be composed of the Same number of similar triangles similarly... | |
| 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
...squares 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 - 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 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. A 0 .' D? ; т d I Oi¡ Let ABODE, FG IJ I К be two ^^f\ . H similar polygons ; they may... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...proportion (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
...PROPOSITION XXX. — THEOREM. LLEMfcNTS OF UEOMETRY. 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, F I. The two polygons... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...PROPOSITION 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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