| 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 - 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 - 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...about the two remaining angles shall be proportionals.** Let the two ^ ABC, DEF, have the L BAC = L EDF, and another L , as ACB, of the one A, together with... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...point D, is a rhombus. PROP. XI. 17. THEOREM. If two triangles have one angle of the one, equal to ons **angle of the other, and also another angle of the...about the two remaining angles shall be proportionals.** » c B equal to two right angles : Then AB : BC : : DF : FE. From F draw (S. 25. 1.) FG making with... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. 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... | |
| John Mason Good - 1819 - 740 pages
...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
...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... | |
| Peter Nicholson - Mathematics - 1825 - 372 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
...triangles, &c. QED Book IV. a Sup. « 2. 1. b 112. Alg. o 11. Alg. d 2- 4e11 1• PROP. VII. THEOREM. **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,... | |
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