 | Charles Butler - 1814 - Liczba stron: 528
...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 - 1816 - Liczba stron: 352
...(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 - Liczba stron: 588
...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 - 1819 - Liczba stron: 446
...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 - 1819 - Liczba stron: 486
...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... | |
 | John Playfair - 1819 - Liczba stron: 350
...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 - Liczba stron: 800
...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 - Liczba stron: 354
...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 - 1825 - Liczba stron: 1046
...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 - Liczba stron: 276
...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,... | |
| |
If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
