 | 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 - 1816 - 618 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...proposition Is a necessary consequence of the truth, lhat the shortest distance between any two points, measured on the surface of the sphere, is the arc... | |
 | Charles Hutton - Arithmetic - 1818 - 652 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...truth, that the shortest distance between any two point«, measured on the surface of the sphere, is the arc of a great circle passing through these... | |
 | Charles Hutton - Mathematics - 1822 - 680 pages
...Gfreater than the Third. '' " ' ''. ' . .' " . " . " ' ' ' 5 • ' . ; ' : ('*.,.'• . '••!•. ' ' This proposition is a necessary consequence of the...shortest distance between any two points, measured on ttie surface of the sphere, is the arc of a great circle passing through these points. THEOREM IL The... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Charles Hutton - Mathematics - 1831 - 656 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 n necessary consequence of the truth, that the shortest distance between any two points, measured on... | |
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Any Two Sides of a Spherical Triangle are together Greater than the Third. 
