# Calendar: 1852-1853 Page 332

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328 GENERAL LITERATURE AND SCIENCE II What is the algebraic condition that three points may be in the same straight line If from any point Ρ in an ellipse line PL be drawn to meet the minor axis in and cutting the major in PM hemispheroid and paraboloid have the same base and altitude compare their volumes Find the length of the perpendicular let fall from given point on given line in space Show how section of surface made by plane passing through the origin may be found Example -The paraboloid vertex the origin Find the law of force tending to the focus of an ellipse and determine the periodic time body describes an ellipse round the focus Sy Ρ Π ρ is λ chord through the other focus show that at Ρ at ρ is constant right-angle Β Ρ is moved so that Β and are always on two axes at right angles to each other find the locus of and show that if Β CP the area traced by Ρ 7r CP Between two unequally inclined planes forming an angle being the lowest point two equal hemispheres are placed with their convex surfaces in contact determine their position 10 Integrate the following differentials xdx dx 11 Any number of rectangles being inscribed in triangle find the locus of their centres 12 Hx2- -y2 Ax -f- be the equation to circle the axis of χ will be tangent to it if ss A3 13 Prove Lagrange's Theorem and expand it by sin when -f sin according to the powers of

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