Calendar: 1855-1856 Page 371

GENERAL LITERATURE AND SCIENCE β 10 If through any point in the triangle Β lines Β be drawn to the opposite sides then shall Ac Ba Cb aC bA cB 11 If two straight lines be parallel and one of them is at right angles to plane the other also shall be at right angles to the same plane 12 If from point above plane Β be drawn perpen- dicular to the plane and perpendicular to straight line Β in the plane and Β Che joined Β shall be perpendicular to DC 13 Given the perimeter of triangle and its angles find the radius of the inscribed circle 14 If be any angles show that if- Sin cos cos sin that cot cot cot 90 ν sin If -- cos cos s1n tan Sin -7 tan 15 Given the logarithms of 71 and find that of 71 16 If in triangle ABC tan 71 tan and tan Β η tan then shall sin 71 sin 17 Prove that- sin sin sin &c to 71 terms rill Ώ -- -- cos 4- cos cos &c to 71 term 18 Find the circular measure of and if the radius of the earth be 000 miles and the dip of the horizon from the top of mountain be 5810 find the mountain's height 19 The difference between polygon of η sides inscribed in circle and one of an equal number of sides described about it 71 being very great area of circle