 | Euclides - 1834 - 518 pages
...angle, and DAG less * than a right angle, DA is greater * than DG : but DA is equal t to DH ; therefore DH is greater than DG, the less than the greater ; which is impossible : theret 15 Def. • 5. I. fHyp. * 17. 1. • 12. 1. • 17. 1. • 19. 1. f 15 Def. ^ BOOK III. PROP.... | |
 | Robert Simson - Trigonometry - 1835 - 513 pages
...1. angle, and DAG lessb than a right angle; DA is greaterd than DG: But DA is equal to DH; therefore DH is greater than DG, the less than the greater,...point A between AE and the circumference, which does notcut the circle, or, which amounts to the same thing, however great an acute angle a straight line... | |
 | Euclid - Geometry - 1838 - 478 pages
...DA is greater (19. 1.) thanDG: but DA is equal to DH : therefore DH is greater than DG, the less E than the greater, which is impossible : therefore...at the point A, or however small an angle it makes B with AE, the circumference passes between that straight line and the perpendicular AE. ' And this... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...DA is greater (19. 1.) thanDG: but DA is equal to DH : therefore DH is greater than DG, the less E than the greater, which is impossible : therefore...at the point A, or however small an angle it makes B with AE, the circumference passes between that straight line and the perpendicular AE. ' And this... | |
 | Euclides - 1838 - 264 pages
...DH is greater than DG, a part than the whole, which is impossible. Therefore no straight line 1i ( can be drawn from the point A, between AE and the circumference, which doen not cut the circle. COR. From this it is manifest, that the straight line which is drawn at right... | |
 | Euclides - 1841 - 378 pages
...less* than a right angle; therefore DA is * 19-1. greater* than DG: but DA is equal to DH; therefore DH is greater than DG, the less than the greater,...small an angle it makes with AE, the circumference must pass between that straight is to be understood, when, in the Greek text and translations from... | |
 | Euclides - 1842 - 320 pages
...less (17. 1.) than a right angle, DA is greater (19. 1.) than DG : but DA is equal to DH : therefore DH is greater than DG, the less than the greater,...does not cut the circle ; or, which amounts to the game thing, however great an acute angle a straight line makes with the diameter at the point A, or... | |
 | Euclides - 1845 - 544 pages
...(i. 17.) therefore DA is greater than DG: (i. 19.) but DA is equal to DH ; (i. def. 15.) therefore DH is greater than DG, the less than the greater,...small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE. " And this is all that is to be understood,... | |
 | Euclides - 1846 - 292 pages
...than a right angle, therefore DA is greater than DG (1. 19) : But DA is equal to DH ; therefore also DH is greater than DG, the less than the greater — which is absurd : Therefore no straight line can be drawn from the point A between AE and the circumference,... | |
 | Euclides - 1853 - 146 pages
...than a right angle, (1. 19.) , -; .-. 1. DA is greater than DG: but DA is equal to DH; therefore 2. DH is greater than DG, the less than the greater, which is impossible : therefore 3. No straight line can be drawn from the point A, between AEand the circumference, which does not... | |
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DH; (I. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same... 
