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Books Books 1 - 10 of 43 on But it was proved that the angle AGB is equal to the angle at F ; therefore the angle....
" But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Page 248
by Euclides, David Gregory - 1765 - 464 pages
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Euclid's Elements of geometry: from the Latin translation of Commandine. To ...

John Keill - Logarithms - 1723 - 364 pages
...Right Angle; and confequently, AGBis greater than a Right Angle. But the Angle AGB has been proved equal to the Angle at F ; therefore the Angle at F, is greater than a ... Right Angle: But (by the Hyp.) it is not greater, lince C is not greater than a Right Angle, which is abfurd. Wherefore...
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Euclid's Elements of geometry: from the Latin translation of Commandine. To ...

John Keill - Trigonometry - 1733 - 397 pages
...confequently, AGB is greater than a Right Angle. But the Angle AGB has been proved equal to the Angla at F ; therefore the Angle at F, is greater than a Right Angle: But (by the Hyp.) it is not greater, fince G is riot greater than a Right Angle, which is abfurd. Wherefore...
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...right angle, and the adjacent angle AGB muft be greater t- f3- «• than a right angle g. But it was proved that the angle AGB is equal to the angle at...the angle at F is greater than a right angle. but, by the Hypothefis, it is lefs than a right angle ; which is abfurd. Therefore the angles ABC, DEF are...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...lefs than a right angle, and the adjacent angle AGB muft be greater than a right angle 3. But it was proved that the angle AGB is equal to the angle at...the angle at F is greater than a right angle : But, by the hypothefis, it is Iefs than a right angle i which is abfurd. Therefore fore the angles ABC,...
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The elements of Euclid: with dissertations intended to assist and ..., Volume 1

James Williamson - Mathematics - 1781
...adjacent to it viz. AGB is (by 13. i.) greater than a right angle ; and it has been demonftrated to be equal to the angle at F ; therefore the angle at F...fuppofed to be lefs than a right angle; which is abfurd: wherefore the angle ABC is not unequal to the angle DEF, therefore it is equal : and alfo (by fupp.)...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...a right angle, and the 8 i3. r. adjacent angle AGB muft be greater than a right angle*. But it was proved that the angle AGB is equal to the angle at F j therefore the angle at F is greater than a right angle : But, by the hypothefis, itislels than a...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 400 pages
...3 and Book VI. an<i the adjacent angle AGB muft be greater than a right 'g ' r angle g. But it was proved that the angle AGB is equal to the angle at...the angle at F is greater than a right angle : But, by the hypothefis, it is lefs than a right angle ; which is abfurd. . Therefore the angles ABC, DEF...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...right angle, and the adjacent angle AGB muft be greater than a right j. 13. i. angle s. But it was proved that the angle AGB is equal to the angle at...the angle at F is greater than a right angle» but, by the Hypothefis, it is lefs tlun a right angle^ which is ab» furd. Therefore the angles ABC, DEF...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1804 - 440 pages
...the adjacent angle AGB irmft ' /~~~' be greater than a right angle g. But it was proved that the B ' angle AGB is equal to the angle at F ; therefore the angle 2.1 F is greater than a right angle : But, by the hypothefis, " it is lefs than a right angle; which...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...therefore the adjacent angle AGB v^*v"w must be greater than a right angled But it was proved that g 13. 1. the angle AGB is equal to the angle at F ; therefore...the angle at F is greater than a right angle. But, by hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not...
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