Calendar: 1891-1892 Page 822

cxxxiv engineering department having its vertex downwards and axis vertical under the action of two constant forces one horizontal the other vertical Find the velocity of the particle when it reaches the vertex SECOND AND THIRD YEARS Define the polar triangle of given triangle and shew that if A'B'O is the polar of ABC then ABC is the polar of A'B' Prove A' 7r Prove geometrically that in spherical triangle right- angled at cos cos cos Find to what relation in plane geometry this corresponds From the vertex of spherical triangle an arc AD is drawn perpendicular to BCy meeting BC at distance χ from its middle point Prove sin AD sin sin ג יי and tan χ tan-tan -- cot 10 Shew that the area of spherical triangle described on sphere of unit radius is equal to the circular measure of the excess of its three angles above two right angles 11 Shew that in any spherical triangle cos tan Β --- cot cos If in spherical triangle the sum of two angles is equal to two right angles then is also the sum of the opposite sides equal to two right angles