 | Robert Simson - Trigonometry - 1835 - 544 pages
...the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, Book vI. DEF are not unequal, that is, they are equal ; and the angle v•— v™-' at A is equal to the angle at D ; wherefore the remaining angle at C is equal to the... | |
 | Euclid - 1835 - 540 pages
...the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, Book VI. DEF are not unequal, that is, they are equal ; and the angle v"»v™-' at A is equal to the angle at D ; wherefore the remaining angle at C is equal to the remaining... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...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 ; wnerefore the remaining angle at C is equal to the remaining angle at F : Therefore the triangle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...: and the angle at A is half of the angle BGC, and the angle at D half of the angle EHF : therefore the angle at A is equal to the angle at D. Wherefore, in equal circles, &c. QED PROP. XIX. THEOR. In equal circles, equal straight lines cut off equal circumferences,... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...equal to DE. Then, if GC were drawn, the sides AG, AC would be respectively equal to the sides DE, DF; and the angle at A is equal to the angle at D. Therefore, on this supposition, the angle GCA would be equal to EFD by ART. Ji; and consequently to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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...therefore the triangle ABC is equiangular to the triangle DEP. Next, let each of the angles at O, F, be not less than a right angle ; the triangle ABC is also... | |
 | Euclides - 1838 - 264 pages
...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 is, they are equal: and the tH angle at A is equalt to the angle at D : wheretssPi. fore the remaining angle at C is equalt to... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...: and the angle at A is half of the angle BGC, and the angle at D half of the angle EHF : therefore the angle at A is equal to the angle at D. Wherefore, in equal circles, &c. QED PROP. XXVIII. THEOR. IN equal circles, equal straight lines cut off equal... | |
 | Euclides - Geometry - 1841 - 378 pages
...greater than a right angle: but this is absurd, because, by hypothesis, F is less than a right angle: therefore the angles ABC, DEF are not unequal, that is, they are equal: and the angle at A is * Hyp. equal* to the angle at D; wherefore the remaining angle * 32.1. at C is equal* to the remaining... | |
 | Euclides - 1842 - 316 pages
...the angle at A (20. 3.) is half of the angle BGC, and the angle at D half of the angle EHF: therefore the angle at A is equal to the angle at D. Wherefore, in equal circles, &c. QED PROP. XXVIII. THEOR. IN equal circles, equal straight lines cut off equal... | |
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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... 
