 | Charles Butler - 1814 - 528 σελίδες
...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 - 294 σελίδες
...(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 σελίδες
...For the same reason, the angle ACB is equal to the angle DFE, and tbe angle at A, to the angle at D. Therefore the triangle ABC is 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... | |
 | Daniel Cresswell - 1817 - 454 σελίδες
...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,... | |
 | Daniel Cresswell - 1819 - 410 σελίδες
...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 Mason Good - 1819 - 740 σελίδες
...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... | |
 | Euclid, John Playfair - 1819 - 348 σελίδες
...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... | |
 | John Playfair - 1819 - 317 σελίδες
...For the same reason, the angle ACB is equal to the angle DFE, and the angle at A to the angle at 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... | |
 | Peter Nicholson - 1825 - 372 σελίδες
...the tame rearon, the angle ACB ii equal to tiie angle DFE, ада the angle at A, to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, ice. QED 1'R.OB. VI. THF.OR. /"iwo triangles have one angle of the ont equal to ont angle... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...the angle BAG is equal to the angle EDF (Hyp.) ; wherefore also the remaining angle at B is equal to the remaining angle at E. Therefore the triangle ABC...to the triangle DEF. Wherefore, if two triangles, &e. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other,... | |
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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. 
