...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...

...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...

...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...

...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...

...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...

...'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...

...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 points...

...the 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...

...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...

...(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...