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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... "
Elements of Geometry, Containing the First Six Books of Euclid - Page 73
by Euclid - 1826 - 180 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

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....
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

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...
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The Elements of Euclid

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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

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,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

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,...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

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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