| Charles Butler - Mathematics - 1814 - 528 pages
...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 - 352 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 - 588 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 - 454 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 - 800 pages
...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 - 354 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 - 446 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,... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...oiher, have their sides about the equal angles reciprocally proportional : And parallelograms which **have one angle of the one equal to one angle of the other, and** their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...parallelogram BC. Therefore equal ograms, Лес. Q. E, D. PROP. XV. THEOR. Equal triangles nhich have **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional : And triangles nhich have one angle... | |
| George Lees - 1826 - 266 pages
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which **have one angle of the one equal to- one angle of the other, and** their sides about the equal angles reciprocally proportional, are equivalent. Let the triangles be... | |
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