Calendar: 1873-1874 Page 542

542 GENERAL LITERATURE AND SCIENCE Define the term Logarithm Prove that the logarithm of product is equal to the sum of the logarithms of its factors Find log S3349 having given log log 10 person ascends tower 108 feet high and then observes the angles of depression of the top and bottom of another tower to be respectively 30 and 60 find its height 11 Having given that two points each 10 feet above the surface cease to be visible from each other over still water at distance of miles find the earth's radius 12 Prove that in any triangle ABC c1 a' 42 2ab cos Hence deduce that c2 a1 cos cos Adapt the formula φ a2 42 2ab cos 6' to logarithmic computation 13 Find the radius of circle circumscribing triangle Prove that if it be equal to the perpendicular from one of the angles on the opposite side the product of the sines of the angles adjacent to that side 14 Show how to find the area of regular polygon of η sides circumscribing circle of given radius Find an expression for the area of circle Two circles of equal radd intersect so that the common chord is equal to the radius find the area common to the two circles 15 The radius of circle inscribed in triangle can never be greater than half the radius of the circle described about the triangle 16 Prove If χ cosec θ sin Θ sec θ cos θ ai yi xi yi If r" coe β tan3 β tan