| Education - 1844 - 688 pages
...line makes with the touching line, shall be equal to the angles in the alternate segments. 12. If two **triangles have one angle of the one equal to one angle...proportionals, the triangles shall be equiangular.** MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON, TRINITY COLLEGE. Pint Division... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two **triangles have one angle of the one equal to one angle...the sides about the equal angles proportionals; the** remaining angles are equal, each to each, viz. those which are opposite to the homologous sides. Let... | |
| Euclides - 1845 - 546 pages
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. Equal parallelograms, which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional : and conversely, parallelograms... | |
| Euclid - Geometry - 1845 - 218 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two **triangles have one angle of the one equal to one angle of the** oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
| Scottish school-book assoc - 1845 - 444 pages
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which **have one angle of the one equal to one angle of the other,** have the sides about these angles reciprocally proportional ; and if two triangles have one angle of... | |
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...(c)p. 8, 1; (c)p. 4, 6; (/)ax. 1, 1. 6 Th. If two triangles have one angle of the one equal to one **of the other, and the sides about the equal angles...and shall have those angles equal which are opposite** homologous sides. Given two triangles ABC, DEF, having the angles A and D equal, and BA to AC as ED... | |
| Euclides - 1846 - 292 pages
...parallelogram BC. Wherefore, Equal parallelograms *rc. QED PROP. XV. THEOR. Equal triangles, which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional : and triangles, which have one angle... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which **have one angle of the one equal to one angle of the other** have their sides about the equal angles reciprocally proportional ; And triangles which have one angle... | |
| Euclides - 1846 - 272 pages
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which **have one angle of the one equal to one angle of the other,** are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... | |
| Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 136 pages
...than the sum of the two sides by the diameter of the inscribed circle. 23. If two triangles have an **angle of the one equal to one angle of the other, and** also another angle of the one equal to the supplement of another angle of the other, the sides about... | |
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