 | John Playfair - 1844 - 338 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 triangle ABC is equiangular to the triangle DEF. wherefore (4. 6.), AB : BG :: DE : EF; but, by hypothesis, DE : EF :: AB : BC, therefore, AB : BC :... | |
 | Euclides - 1845 - 546 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... | |
 | Euclid - 1845 - 218 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 is, they are equal : and the angle at A is t Hyp. equal t to the angle at D; wherefore the remaining angle at C is equal to the remaining angle... | |
 | Euclides - 1846 - 292 σελίδες
...the angle at A is half of the angle BGC, aad the angle at D half of the angle EHF ; therefore also the angle at A is equal to the angle at D. Wherefore, In equal circles §c. QED PROP. XXVIII. In equal circles, equal straight lines cut off equal circumferences,... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...it: 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... | |
 | Royal Military Academy, Woolwich - 1853 - 400 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 is, they are equal : and the angle at A is equal (Hyp.) to the angle at D ; wherefore the reEUCLID S ELEMENTS. maining angle at C is equal to the remaining... | |
 | Euclides - 1853 - 334 σελίδες
...DFE is greater than a right angle. But by hyp* it is less than a right angle : which is impossible. Therefore the angles ABC, DEF are not unequal, that is, they are equal, and the angle BAC is equal to the angle EDF. Hence the two triangles ABC, DEF have the two angles CBA, BAC respectively... | |
 | Euclides - 1853 - 176 σελίδες
...it. And the angle at a is half of the angle bgС, 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 PROPOSITION XXVIII. — THEOREM., In equal circles, equal straight lines... | |
 | Euclides - 1853 - 146 σελίδες
...angle at A is half of the angle BGC, and the angle at D half of the angle EHF; therefore (Ax. 7.) 4. The angle at A is equal to the angle at D. Wherefore, in equal circles, &c. QED PROP. XXVIII. THEOREM. In equal circles, equal straight lines cut off equal... | |
 | John Playfair - 1855 - 334 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...remaining angle at C is equal to the remaining angle atF; Therefore the triangle ABC is equiangular to the triangle DEF. wherefore (4. 6.), AB : BG :: DE... | |
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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... 
