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" Any angle is greater than the difference between 180 and the sum of the other two angles. "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 30
by Benjamin Peirce - 1836 - 71 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...180. IV. The greater side is opposite the greater angle, and conversely. .V. Any angle is greater than the difference between 180 and the sum of the other two angles. VI. A side which differs more from 90 than another side, is of the same species as its opposite angle....
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A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

Cornell University. Department of Mathematics - 1881 - 122 pages
...lies between 180 aud 540. Each side is less than the sum of the other two. Each angle is greater than the difference between 180 and the sum of the other two. Of any two unequal sides, the greater lies opposite the greater angle ; and conversely. Each side or...
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A Treatise on Trigonometry

James Edward Oliver - Trigonometry - 1881 - 120 pages
...lies between 180 and 540. Each side is less than the sum of the other two. Each angle is greater than the difference between 180 and the sum of the other two. Of any two unequal sides, the greater lies opposite the greater angle ; and conversely. Each side or...
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1883 - 234 pages
...-с1, А'=Ш-а, Б'=180-Ь, С"=180-с. (г) . Either angle of a spherical triangle is greater than the difference between 180 and the sum of the other two angles. 187. A spherical triangle is called right, bi-rectangular, or tri-rectangular, according as it has...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...one, two, or three obtuse angles. 671. COROLLARY II. Either angle of a spherical triangle is greater than the difference between 180 and the sum of the other two angles. For since A + B + C > 180 ( 668) , we have A>180-(B+C); which proves the theorem when B+C< 180....
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - Trigonometry - 1892 - 202 pages
...between 0 and 360. The sum of the three angles lies between 180 and 540. Each angle is greater than the difference between 180 and the sum of the other two. If two sides are equal, the angles opposite them are equal ; and conversely. If two sides are unequal,...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...between 0 and 360. The sum of the three angles lies between 180 and 540. Each angle is greater than the difference between 180 and the sum of the other two. If two sides are equal, the angles opposite them are equal ; and conversely. If two sides are unequal,...
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Plane and Spherical Trigonometry

Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...lies between 180 and 540. Each side is less than the sum of the other two. Each angle is greater than the difference between 180 and the sum of the other two. Of any two unequal sides, the greater lies opposite the greater angle ; and conversely. Each side or...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1896 - 274 pages
...sides is less than 360. IV. The sum of the angles is greater than 180. V. Each angle is greater than the difference between 180 and the sum of the other two angles. For, by IV., A + В + C> 180 whence, A > 180 — (B + 0) But if В + C> 180, we have, in the...
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Documents of the Senate of the State of New York, Volume 11

New York (State). Legislature. Senate - Government publications - 1897 - 1304 pages
...quadrantal triangle, Napier's circular parts. 2 Prove that each angle of a spheric triangle is greater than the difference between 180 and the sum of the other two angles. 3 Prove that the hypotenuse of a right spheric triangle is less than 90 only when both the other...
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