| John Playfair - Euclid's Elements - 1806 - 311 pages
...Wherefore, if two triangles, &c. QED PROP. VII. THEOR. Book vi. IF two triangles have one angle of **one equal to one angle of the other, and the sides about** two other angles proportional ; and if each of the remaining angles be either less, or not less, than... | |
| John Mason Good - 1813
...a mean proportional between two given straight lines. Prop. XIV. Theor. Equal parallelograms which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proport ional : and parallelograms that have one... | |
| Euclides - 1814
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. **THEOR. IF two triangles have one angle of the one...equal to one angle of the other, and the sides about** two other angles proportionals, then, if each of the remaining angles be either less, or not less,... | |
| Charles Butler - Mathematics - 1814
...a •••• b : ai=the square of the product, wherefore ^/afc=the 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;... | |
| Daniel Cresswell - Geometry - 1816 - 294 pages
...(Art. 97.) BA 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 each,... | |
| Euclides - 1816 - 528 pages
...parallelogram BO. Therefore equal parallelograms, gtc. QED, PROP. XV. TIIEOR. EQU AL 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.... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...two given circles, and also touch the chord on the same side as the less circle touches it. (XI 1 1.) **If two triangles have one angle of the one, equal to one angle of the other, and** also another angle of the one, together with another angle of the other, equal to two right angles,... | |
| John Mason Good - 1819
...the trijiigles shall be equiangular, and have their Cjuil 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,** arid 'be tides about the equal angles proportionals, the »angles shall be equiangular, and shall have... | |
| John Playfair - 1819 - 317 pages
...D. Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. Q, ED **PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the** oiker, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...having its base DH in BC, and terminated by the given point D, is a rhombus. PROP. XI. 17. THEOREM. **If two triangles have one angle of the one, equal to one angle of the other, and** also another angle of the one, together with another angle of the other, equal to two right angles,... | |
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