Calendar: 1852-1853 Page 378

574 THE SCHOOL Prove that- sin sin cos cos Af cos It tan -- then η sin tan tan The angles of quadrilateral inscribed in circle taken in order when multiplied by the numbers are in arith- metical progression find them If and -f Β be three angles whose cosines are in harmonical proportion prove that cos cos £ Given the sum of two angles and the ratio of their tan- gents find the sine of the difference of the angles If- 2χ sin £ 2x sin φ ג sin Φ find ע in terms of α δ person wanting to find his distance from an inaccessible object discovers three places on level plane from which the elevation of the object is the same show that his distance cosec MECHANICS Ρ and balance on straight lever whose length is --צ- of Ρ and of being taken away find the alteration in the fulcrum 10 Three forces of and 10 lbs act upon point the second makes an angle of 30 the third an angle of 60 with the first find the magnitude of the resultant and the direction of the reaction 11 In the screw Ρ χ circumference of the power -JFx dis- tance between the threads 12 Find the centre of gravity of triangle and of two unequal circles which touch externally 13 beam of given weight rests in given position against smooth wall with one end on the ground show that there must be friction from the ground and determine its value 14 Two unequal spheres are placed in hemispherical bowl determine their position of rest