Calendar: 1863-1864 Page 524

524 GENERAL LITERATURE AND SCIENCE If ζ x"J -f yn φ show that Prove Lagrange's Theorem and find in terms of when χ logy If excoaecos sinfl cosi cos sin0- If be homogeneous function of &c to η dimen- sions prove that du du dκ nu χ --Υ ζ -j- &c dx dy dz ם xyz Ex --- χ by cz If tf2 5y2 12 12y be an equation to rectangular co-ordinates show that it is an ellipse and find its area The equation to parabola being y2 ax and y1 y$ being the ordinates of the angular points of triangle inscribed in it show that its area is 01 03 -y2 ys In spherical triangle find cos in terms of the cosines and sines of the sides The angles at the base of an isosceles spherical triangle are equal In right-angled spherical triangle if CD be drawn perpendicularly to the hypothenuse show that cot2 CD cot cot 10 Prove that in any oblique angled spherical triangle cos £ cos cos sin £ cos sin sin -f sin 11 If find the form of 12 Find the equation to the surface of an oblique cylinder the base being circular