 | Thomas Keith - 1810 - 478 σελίδες
...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. Since... | |
 | Charles Hutton - 1811 - 404 σελίδες
...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 - 1812 - 624 σελίδες
...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 - 1824 - 572 σελίδες
...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 D. . Then... | |
 | Thomas Keith - 1826 - 504 σελίδες
...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 than... | |
 | Dionysius Lardner - 1828 - 434 σελίδες
...'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 three... | |
 | Alexander Ingram - 1830 - 458 σελίδες
...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 any two... | |
 | Pierce Morton - 1830 - 584 σελίδες
...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... | |
 | Robert Simson - 1835 - 544 σελίδες
...(4. 1.) and consequently the sides AC, BC of the spherical triangle are equal. QED PROP. VI. FIG. 4. Any two sides of a spherical triangle are together greater than the third. Let ABC be a spherical triangle, any two sides AB, BC are greater than the third side AC. Let D be... | |
 | 1835 - 684 σελίδες
...such relations exist as would render the expressions of any of the remaining parts impossible. (A.) Any two 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)... | |
| |
Any two sides of a spherical triangle are together greater than the third side. 
