...arcs AB, AC, BC, which measure these angles, is less than the sum of the two others. PROPOSITION vm. 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, AC, to meet inD. Then, since two great circles...

...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...

...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=...

...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...

...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,...

...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...

...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...

...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...

...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...

...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...