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" Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD. "
Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry - Page 113
by John Playfair - 1829 - 186 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...angle AEC is therefore equal to the angle ACE h : But the * ^ *• angle AEC is equal to the outward And opposite angle BAD ; and the angle ACE is equal to the alternate angle CAD bi, Wherefore also the angle BAD is equal to the angle CAD; Therefore the angle BAC is cut into two...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...1.) to DA, and let BA produced meet CE in E. Because the straight line AC meets the parallels AD, EC, the angle ACE is equal to the alternate angle CAD (29. 1.) : But CAD, by the hypothesis, is equal to the angle BAD ; wherefore BAD is equal to the angle ACE....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...equal to AE (9. 5.), and the angle AEC is therefore equal to the angle ACE (5. 1.). But the angle AEC is equal to the exterior and opposite angle BAD ; and the angle f . , ACE is equal to the alternate an- g DC gle CAD (29. 1.) : Wherefore also the angle BAD i9 equal...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...1.) to DA, and let BA produced meet CE in E. Because the straight line AC meets the parallels AD, EC, the angle ACE is equal to the alternate angle CAD (29. 1.); but CAD, by the hypothesis is equal to the angle BAD; wherefore BAD is equal to the angle ACE. Again,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...to the outward and opposite angle BAD; and the angle ACE equal to the alternate angle CAD: (99. 1.) Wherefore also the angle BAD is equal to the angle CAD: Therefore the angle ВАС is cut into two equal angles by the straight line AD. Therefore, if the angle, &c. QED equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...equal to AE (9. 0.), and the angle AEC is therefore equal to the angle ACE (5. 1.). But the angle AEC is equal to the exterior and opposite angle BAD; and...angle ACE is equal to the alternate angle CAD (29. l.): Wherefore also the angle BAD is equal totheangle CAD ; Therefore the angle BAG is eut into two...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...to the exterior and opposite angle BAThand theangleACE isequal to the alternate angle CAD (29. BDC . 1.): Wherefore also the angle BAD is equal to the angle CAD: Therefore the angle BAG is cut into two equal angles by the straight line AD. Therefore, if the angle, &c. QED PROP. A....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 346 pages
...equal to AE ' (9. 5.), and the angle AEC is therefore equal to the angle ACE (5. 1.) But the angle AEC is equal to the exterior and opposite angle BAD ; and the angle ACE is equal to the alternate an- JJ DC 'gle CAD (29. 1.) : Wherefore also the angle BAD is equal to the an. gle CAD : Therefore...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...equal to AE (9. 5.), and the angle AEC is therefore equal to the angle ACE (3. 1.). But the angle AEC is equal to the exterior and opposite angle BAD; and...the angle ACE is equal to the alternate angle CAD (21. 1.): Wherefore also the B angle BAD is equal to the angle D C ge s eqa CAD-. Therefore the angle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...AEC is therefore equal to the angle ACE": But the g •?• *• angle AEC is equal to the outward and opposite angle BAD ; and the angle ACE is equal to the alternate angle CAD:* Wherefore also, the angle BAD is equal to the angle CAD: Therefore, the angle BAG is cut into two equal...
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