...finished goods respectively. HIGHER MATHEMATICS. (OPTIONAL.) Time allowed, 3£ hours. 1. Prove that the area of a spherical triangle is proportional to the excess of the sum of the angles over two right angles. 2. State Napier's rules for the solution of right-angled spherical...

...extent. "2. In elliptic space there are still no similar figures, and the area of a triangle varies as the excess of the sum of its angles above two right angles. The so-called space-constant is positive. There are no parallels and no non-intersectors to a given...

...Find the value of x which gives a maximum value to sin x. cos x 11. Find the value of 13. Prove that the area of a spherical triangle is proportional to the excess of the sum of its three angles above two right angles. 14. In a spherical triangle sin C cot A=Cot a gin b-cosb cos C....

...further than Saccheri. He actually showed that on the hypothesis of ' he obtuse angle the area of a triangle is proportional to the excess of the sum of its angles over two right angles, which is the case for the geometry on the sphere, and he concluded that the...

...equation , ax , / ix- л cos-1 = 2 tan"1 . / . ж Л я 5. Show that the expression becomes o. Prove that the area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles. DR. TBAILL. 7. Given base, and difference of cosines of sides in a spherical...

...triangles are equivalent in surface. The area of a spherical triangle is to that of the whole sphere as the excess of the sum of its angles above two right angles is to eight right angles. When a portion of a regular polygon, inscribed in the generating circle of...

...15-2V§-2Vl5 + 3V2"-2 N/6+2 Vs"-2 V30. 2. Prove that the surface of any spherical triangle is measured by the excess of the sum of its angles above two right angles. 3. Spatia quae corpus urgente quacunque vi finita describit, sive vis ilia determinata et iramutabilis...