| Thomas Keith - 1810 - 420 sider
...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 - 1816
...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 - 1818
...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... | |
| Edward Riddle - 1824
...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 - 1826 - 442 sider
...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 - 1828 - 317 sider
...'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 - 1830
...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 - 1830 - 272 sider
...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 - 1831
...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... | |
| 1835
...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)... | |
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