| 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 - 544 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 - 470 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 - Geometry - 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 - 316 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 - 546 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... | |
| |