Calendar: 1858-1859 Page 421

GENERAL LITERATURE AND SCIENCE 423 In the parabola the subtangent is twice the abscissa and the subnormal is constant The tangents at the extremities of any focal chord of parabola intersect at right angles in the directrix and the line drawn from the point of intersection to the focus is perpendicular to the chord The square of the semi-ordinate of any diameter is four times the rectangle contained by the focal distance of its extremity and the abscissa The perpendiculars from the foci on the tangent at any point of an ellipse intersect the tangent in the circumference of the circle described on the major axis 10 Define conjugate diameters of an ellipse If be con י jugate to CP CP will be conjugate to CD 11 Find the equation to the hyperbola when the centre is origin and trace the curve The rectangle contained by the ab- scissEe is to the square of the semi-ordinate as the square of the axis major is to the square of the axis minor 12 The parallelograms formed by tangents at the extremities of pairs of conjugate diameters of hyperbola have all the same area II -Differential anH integral Calculus Investigate from the definition the differential coefficients of xn x2 sin log χ Prove the rule foridiiTerentiatinq fraction Ex Differentiate ύ -" יי sin -1 x" xq Xp Xl' -1 ain χ Expand to five terms in powers of χ by Maclaurin's Theorem Investigate the method of evaluating vanishing fraction