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" Any angle is greater than the difference between 180° and the sum of the other two angles. "
A Treatise on Trigonometry by Profs. Oliver, Wait and Jones - Pągina 68
per Cornell University. Department of Mathematics - 1881
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 92 pągines
...89°, B = 5°, С = 88° ; to solve the triangle. (822) 71. Theorem. Each angle of a spherical triangle is greater than the difference between 180° and the sum of the other two angles. Demonstration. Since sin. B and sin. C are posi(823) tive, the denominator of the fraction...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 84 pągines
...Ans. a = 53° 10', b= 4°, с = 53° 8'. / Л . (822) 71. Theorem. Each angle of a spherical triangle is greater than the difference between 180° and the sum of the other two angles. Demonstration. Since sin. В and sin. С are posi(823) tive, the denominator of the fraction...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 498 pągines
...Each side is less than the sum of the other two. III. The sum of the sides is less than 360°. IV. Each angle is greater than the difference between 180°, and the sum of the other two angles. There are, however, cases in which these conditions are all satisfied by each of the values...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 498 pągines
...Each side is less than the sum of the other two. III. The sum of the sides is less than 360°. IV. Each angle is greater than the difference between 180°, and the sum of the other two angles. There are, however, cases in which these conditions are all satisfied by each of the values...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pągines
...two. III. The sum of the 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 + B + С> 180° whence, A > 180° - (B + C) But if B + C> 180°, we have, in...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 518 pągines
...is greater than 180°. IV. Ttie 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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 638 pągines
...angles is greater than 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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 504 pągines
...angles is greater than 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...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1864 - 512 pągines
...the sides is less than 360°. 5. The sum of the angles is greater than ISO°, and less than 540°. 6. Each angle is greater than the difference between 180° and the sum of the other angles. For, A + B + C > 180°. Principle 5. . • . A > 180°- (B + CO. The last formula is always...
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Catalogue - Harvard University

Harvard University - 1874 - 668 pągines
...sides, and what term is applied to the triangle* ? 11. Prove that eiioh angle of a spherical triangle is greater than the difference between 180° and the sum of the other two. 12. The height ot'a right cylinder is equal to the diameter of the base. What is the ratio of its entire...
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