 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...angles, and bouud the spherical polygon, is less than the circumference of a great circle. 526. Cor. The sum of the three sides of a spherical triangle is less than the circumference of a great circle, since a triangle is a polygon of three sides. PROPOSITION V. — THEOREM. 527. The extremities of a... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...in the letters, we may deduce analogous formulae for } B and } C. 154. It is shown in geometry that the sum of the three sides of a spherical triangle is less than a circumference of a great circle. Calling S the difference, we shall have s= 180о — }j( s — a=... | |
 | Isaac Stone - Educational tests and measurements - 1869 - 272 pages
...is less if measured on the arc of a great circle than on the arc of a small circle. 193. Show that the sum of the three sides of a spherical triangle is less than the circumference of a great circle. 194. Make the diagram of any arc greater than 90 degrees, with its sine, cosine, &c., designating each... | |
 | William Thomas Read - Nautical astronomy - 1869 - 176 pages
...180 - d. therefore, A + B + C = 540° — (a' + V + d) And taking into consideration the truth, that the sum of the three sides of a spherical triangle is less than the circumference of a great circle (360°), therefore, A + B + C = 540° — a quantity less than 360° But 540° — 360° = 180° Therefore,... | |
 | Webster Wells - Trigonometry - 1883 - 234 pages
...base and the vertical angle, and divides it into two symmetrical right triangles. (e). The sum of the sides of a spherical triangle is less than the circumference of a great circle ; that is, less than 360°. (/). The sum of the angles of a spherical triangle is greater than two... | |
 | 1884 - 648 pages
...remaining parts may be found. If there is any "ambiguity" in the solution account for it. 5 marks. 7. The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Give the proof. 5 marks. 8. Given two sides of an oblique-angled spherical triangle, and the angle... | |
 | Canada - 1893 - 1092 pages
...sides and angles of the polar triangle lire the supplements of the primitive triangle. 2. Prove that the sum of (the three sides of a spherical triangle...is less than the circumference of a great circle. cos a — cos b cos c 3. Prove the following :— Cos A—— ^Tdsin c. 4. Give Napier's rules for... | |
 | Canada. Department of the Interior - 1893 - 1280 pages
...sides and angles of the polar triangle are the supplements of the primitive triangle. 2 Prove that the sum of the three sides of a spherical triangle is less than the circumference of n great circle. 34 cos a@cos b cos c Prove the following :@Cos A=@eip ^ Bin c @ Give Napier's rules... | |
 | Florian Cajori - Mathematics - 1893 - 476 pages
...properties in much the same way as Euclid treats plane triangles. In it are also found the theorems that the sum of the three sides of a spherical triangle is less than a great circle, and that the sum of the three angles exceeds two right angles. Celebrated are two theorems... | |
 | Florian Cajori - Mathematics - 1896 - 336 pages
...their properties in much the same way as Euclid treats plane triangles. He gives the theorems that the sum of the three sides of a. spherical triangle is less than a great circle, and that the sum of three angles exceeds two right angles. Celebrated are two theorems... | |
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The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D. 
