| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...DF, or as the squares described on any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. **Similar polygons may be divided into the same number...similar each to each, and similarly situated. Let** ABODE, FGHIKbetwo ^^f\ H similar polygons ; they may be divided into the same number of triangles similar... | |
| Benjamin Greenleaf - 1868 - 338 pages
...the same manner, it may be shown that the corresponding triangles ADE, FIK are similar ; hence the **similar polygons may be divided into the same number...triangles similar each to each, and similarly situated.** of the same number of similar triangles, and similarly situated, the two polygons are similar. For... | |
| Edward Brooks - Geometry - 1868 - 294 pages
...X AF : :AB * :IS\ Comparing this with the first proportion, we have, ABC:ADE::AB*:AD\ THEOREM XVII. **Similar polygons may be divided into the same number...triangles, similar each to each, and similarly situated.** ~LetABCDE and FGHIK\}& two similar polygons, having the angle A equal to the angle F, B to G, CtoH,... | |
| Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION XXX. — THEOREM. ELEMENTS OF GEOMETRY. K 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 being similar,... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...PROPOSITION XXV. THEOREM. Two similar polygons may be divided into the same numtiei of triangles, simila: **each to each, and similarly situated. Let ABCDE, FGHIK...polygons ; they may be divided into the same number of** similar triangles. Join AC, AD, FH, FI. Because the polygon ABCDE is similar to the K polygon FGHIK,... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...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 ABCD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and... | |
| Charles Davies - Geometry - 1872 - 464 pages
...the first proportion (B. II., P. 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...of 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... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...the same manner, it may be shown that the corresponding triangles AD E, FIK are similar ; hence the **similar polygons may be divided into the same number...triangles similar each to each, and similarly situated.** 217. Cor. Conversely, if two polygons are composed of the same number of similar triangles, and similarly... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 pages
...other as the squares of AB and DE, or of 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... | |
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