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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

## First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...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 under...

## 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...

## 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. '...

## 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...

## An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 394 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,...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 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....

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 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....

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 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....