Calendar: 1850-1851 Page 331

APPLIED SCIENCES 327 If two circles intersect the common chord produced bisects the common tangent 10 In square inscribe square th of the original and find the least value of 11 If be the sides of ABC andif tan β- cot a- -b י then log log log sin log cos Θ 12 Find cos mA in terms of the powers of cos and if sin sin sin 30 find 13 Find two numbers such that their difference shall be equal to the difference of their cubes 14 If be the angles of triangle and their cosines be in arithmetical progression ο Λ Β cos cos sin cos 15 If &c be series of positive fractions increasing or decreasing in value then will between b" &c the greatest and least of them 16 The edges of rectangular parallelopiped are and feet approximate to the diagonal by means of continued fraction Euclid Book Prop XIII Euclid Book Prop XIII Euclid Book Prop Solve the equations- x2 ax by י ל y2 bx ay x4 y4 369 The minute hand of watch is half-an-hour before the hour- hand which latter shows true time find the time when the hands are together between and