 | Euclides - 1855 - 230 σελίδες
...in the same manner it may be shown that the angle at E is not greater than the angle ABC; therefore they are equal, and the angle at A is equal to the...remaining angle at C is equal to the remaining angle at F ; and the triangles ABC and DEF are equiangular, and therefore have the sides about the equal angles... | |
 | Euclides - 1855 - 270 σελίδες
...equal to the angle D EF (I. Ax. 1). For the same reason, the angle A С B is equal to the angle D FE, and the angle at A is equal to the angle at D. Therefore the triangle AB С is equiangular to the triangle DE F. Wherefore, if the sides, &e. QED... | |
 | John Playfair - 1856 - 346 σελίδες
...greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that...the remaining angle at C is equal to the remaining anglo at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles... | |
 | Robert Potts - 1860 - 380 σελίδες
...by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF me not unequal, that is, they are equal : and the angle at A is equal to the angle at D : (hyp.) wherefore the remaining angle at C is equal to the remaining angle at F: (I. 32.) therefore... | |
 | Eucleides - 1860 - 396 σελίδες
...in the same manner it may be shown that the angle at E is not greater than the angle ABC ; therefore they are equal, and the angle at A is equal to the angle at D, wherefore toe remaining angle at C is equal to the remaining angle at F ; and the. triangles ABC and DEF are... | |
 | Euclides - 1864 - 448 σελίδες
...greater than a right angle; but, by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that...equal : and the angle at A is equal to the angle at D : (hyp.) wherefore the remaining angle at C is equal to the remaining angle at F: (I. 32.) therefore... | |
 | Euclides - 1865 - 402 σελίδες
...right angle. But, by the hypothesis, it is less than a right angle; which is absurd ; therefore thc angles ABC, DEF, are not unequal, that is, they are...equal ; and the angle at A is equal to the angle at D ; (hyp.) wherefore the remaining angle at C is equal to the remaining angle at F; (L 32.) therefore... | |
 | Robert Potts - 1865 - 528 σελίδες
...the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF ax& not unequal, that is, they are equal : and the angle at A is equal to the angle at D : (hyp.) wherefore the remaining angle at C is equal to the remaining angle at F: (i. 32.) therefore... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...by hypothesis; therefore the angle BGC is acute. But BGC was shewn to be obtuse j which ia absurd. Therefore the angles ABC DEF are not unequal ; that is, they are equal. Therefore the triangles A BC, DEF are equal in all respects, by I. 4. ° Next, suppose the angles at... | |
 | Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...acute, by hypothesis; therefore the angle BGC is acute. But BGC was shewn to be obtuse; which is absurd. Therefore the angles ABC, DEF are not unequal ; that is, they are equal. Therefore the triangles A BC, DEF are equal in all respects, by I. 4. Next, suppose the angles at C... | |
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But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore... 
