| 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... | |
| 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... | |
| 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. '... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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.... | |
| 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.... | |
| Harvard University - 1874 - 668 pages
...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... | |
| Henry Nathan Wheeler - Trigonometry - 1876 - 202 pages
...the sides is less than 360°. L The sum of the angles is greater than 180°. m. Each angle is greater **than the difference between 180° and the sum of the other two angles.** n. A side which differs more from 90° than another side is in the same quadrant as its opposite angle.... | |
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