| Euclides - 1841 - 351 Seiten
...the parallelogram BC. Therefore equal parallelograms, &c. 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 triangle* which have one angle... | |
| John Playfair - 1842 - 317 Seiten
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • 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 parallelograms which have one... | |
| Euclides - 1842
...parallelogram в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT 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... | |
| 1843
...angle, and one of the other sides of a triangle are given ; construct it. 4. 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... | |
| 1844
...this 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...proportionals, the triangles shall be equiangular.** MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON, TRINITY COLLEGE. Pint Division... | |
| Euclides - 1845 - 382 Seiten
...to DFE, and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. **PROP. VI. THEOR. — If two triangles have 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... | |
| Euclid - 1845 - 199 Seiten
...ABC is 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
...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... | |
| Euclides - 1845
...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... | |
| Euclides - 1846
...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.... | |
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