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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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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...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 under the...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...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 of B. In...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...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 of B. '...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 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 + B + С> 180 whence, A > 180 - (B + C) But if B + C> 180, we have, in the polar...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 359 pages
...the sum of the other two. III. The sum of the angles is greater than 180. IV. Each angle is greater than the difference between 180 and the sum of the other two. V. Of any two sides, that is the greater which is opposite the greater angle. VI. Of any two sides,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...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 angle....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 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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Catalogue - Harvard University

Harvard University - 1874
...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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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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