 | Thomas Keith - Navigation - 1810 - 478 pages
...distant from the angular point, for CB, and not IH, is the measure of the angle BAC, PROPOSITION IV. (S) Any two sides of a spherical triangle are together greater than the third side. DEMONSTRATION. Let ABC be the spherical triangle, AJ| and EC together, are greater than, AC.... | |
 | Charles Hutton - Mathematics - 1811 - 404 pages
...premised and comprehended, the student may pass to the consideration of the following theorems. THEOREM r. Any Two Sides of a Spherical Triangle are together Greater than the Third. This proposition is a necessary consequence of the truth, that the shortest distance between any two... | |
 | Charles Hutton - Mathematics - 1812 - 624 pages
...premised and comprehended, the student may pass to the consideration of the following theorems. THEOREM I. Any Two Sides of a Spherical Triangle are together Greater than the Third. This proposition is a necessary consequence of the truth, that the shortest distance between any two... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...angles are equal, the angle EDB is equal to the angle EDC, therefore AC is equal to A B. PROPOSITION V. Any two sides of a spherical triangle are together greater than the third side. Let AB С be a spherical triangle, and letD be the centre of the sphere, join AD, BD, and С... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...187-), and DE is the hypothenuse, being the supplement of the angle в (S. 136.) PROPOSITION v. (Y) Any two sides of a spherical triangle are together greater than the third side. DEMONSTRATION. Let ABC be a spherical triangle, any two sides AC and вс, are together greater... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...'SECTION II. Of spherical triangles . • • • • 73 (126.) Definition of a spherical triangle. (127.) Any two sides of a spherical triangle are together greater than the third side. (128.) Cor. The difference of any two sides is less than the third side. (129.) The sum of the... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...same point, the sum of all the angles about that point will be equal to four right angles. PROP. 9. Any two sides of a spherical triangle are together greater than the third fide ; and any side of a spherical triangle ig greater than the difference of the other two. Let А... | |
 | Alexander Ingram - Mathematics - 1830 - 458 pages
...spherical triangle be equal to one another, the sides opposite to them are also equal. PROP. VIII. Any two sides of a spherical triangle are together greater than the third side, and the difference of any two sides is less than the third. Cor. The arc which passes through... | |
 | Richard Wilson - Logarithms - 1831 - 372 pages
...from the preceding article, 180° (a + ß + у) is less than 2. 180°, ora+/3+y . . . . 2ir; that is, the sum of the three sides is less than the circumference of a great circle, rad = 1. ч 31. COк. If a', ß', у, be arcs to rad = r, then o= °,/3==£ty = JL, У У У hence... | |
 | Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...relations exist as would render the expressions of any of the remaining parts impossible. (A.) Any tivo sides of a spherical triangle are together greater than the third, and all three sides together are less than a whole circle. In this proposition we must remember (5) that... | |
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Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle. 
