 | Euclid - Euclid's Elements - 1789 - 296 pages
...with the triangle AGH (I. 7.) or ABC, as was to be fhewn. PROP. VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF... | |
 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...triangle DEF. Wherefore, if two triangles, &c. Q^ E. D f PROF. PROP. VII. THEO R. IF two triangles have one angle of the one equal to one angle of the other, and the fides about two other angles proportionals, then, if each of the remaining angles be either... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...other, have their fides about the equal angles reciprocally proportional : And parallelograms that have one angle of the one equal to one angle of the other, and their fides about the equal angles reciprocally proportional, are equal to one another. Let AB,... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...Wherefore if two triangles, &c. Q^ ED b. 32. i. c. 4. 6. f' *• i. PROP. VII. THEOR. IF two triangles have one angle of the one equal to one angle of the other, and the fides about two o. ther angles proportionals ; then if each of the remaining angles be either... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...Therefore, equal parallelograms, &c. Q. E« D. • Book VI. 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 in the one equal to one angle in the... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...DB is found. Which was to be done. PROP. XIV. THEOR. EQUAL parallelograms, which have one angle of one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms which have one angle of one equal to one angle of the... | |
 | John Mason Good - 1813 - 714 pages
...and have their equal angles opposite to the homologous sides. Prop. VI. Theor. If two triangles have one angle of the one equal to one angle of the other, and tbe sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | Charles Butler - 1814 - 582 pages
...a6=the square of the product, wherefore ^ai^zthe product. 234. Prop. 23. Hence, if two triangles have one angle of the one equal to one angle of the other, they will have to each other the ratio compounded of the ratios of the sides about their equal angles;... | |
 | Euclides - 1816 - 588 pages
...equiangular to the triangle DEF. Wherefore, if the sides, Ike. QED PROP. VI. THEOR. IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...is equal to FE, and the angle ABC to EFG. PROP. XIX. (114.) Theorem. If two spherical triangles have one angle of the one equal to one angle of the other, and have also the two sides about another angle in each severally equal, and if the third angle, in... | |
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IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 
