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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 71
by Euclid - 1826 - 180 pages
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...17) ; therefore 1. DA is greater than DG (I. 19) ; but DA is equal to DH (I. Def. 15) ; 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 AE and the circumference, which does not...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 446 pages
...is greater than DG: (i. 19.) but DA is equal to DH; (i. def. 15.) therefore DH1s greater than Dff, the less than the greater, which is impossible : therefore...small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE. QEp COR. From this it is manifest, that...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...[I. 17. therefore DA is greaterthanZ>Gf. [I.19. But DA is equal to DH; [I. Definition 15. therefore DH is greater than DG, the less than the greater ;...from the point A between AE and the circumference, so as not to cut the circle. FE / Wherefore, the straight line &c. QED COROLLARY. From this it is manifest,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...[I. 17. therefore DA is greaterthan_D6r. [1.19. But DA is equal to DH; [I. Definition 15. therefore DH is greater than DG, the less than the greater ; which is impossible. FE Wherefore, the straight line &c. QBB COROLLARY. From this it is manifest, that the straight line...
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Books 3-9

Euclid - Mathematics, Greek - 1908 - 456 pages
...angle DAG is less than a right angle, AD is greater than DG. [i. 19] But DA is equal to DH ; therefore DH is greater than DG, the less than the greater : which is impossible. Therefore another straight line cannot be interposed into the space between the straight line and the circumference....
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - History - 2001 - 516 pages
...and the angle DAG is less than a right angle, AD is greater than DG. But DA is equal to DH; therefore DH is greater than DG, the less than the greater: which is impossible. Therefore another straight line cannot be interposed into the space between the straight line and the circumference."...
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The Thirteen Books of Euclid's Elements

Euclid - 452 pages
...angle DAG is less than a right angle, AD is greater than DG. [i. 19] But DA is equal to DH; therefore DH is greater than DG, the less than the greater : which is impossible. Therefore another straight line cannot be interposed into the space between the straight line and the circumference....
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