Calendar: 1873-1874 Page 545

GENERAL LITERATURE AND SCIENCE 545 13 Given cos θ sin θ show that du 1-r ν άθ and hence find th exponential values of cos β and sin By this process establish Demoivre's Theorem 14 Trace the curve 2a comttrj antt flnjjlitteal eometrg In given triangle inscribe triangle similar to given triangle Describe circle passing through two given points and touching given straight line given circle Define harmonic ratio and investigate the harmonic pro- perties of the complete quadrilateral Find the polar equation to the chord of given conic the focus being the pole and deduce the equation to the tangent Find the equation to the pair of straight lines bisecting the angle between two straight lines whose equation is given and thence deduce the equation to the axes of the central conic whose equation is ax1 4- ihxy by' 2gx 2fy Find the condition that the two straight lines la -f ny יי l'a j3 71' may be perpendicular to each other Investigate fully the conditions that the general equation of ז be general degree may represent two parallel straight lines two coincident straight lines Μ Μ