Calendar: 1878-1879 Page 633

cloth-workers' science exhibition 631 II ttcltli iomttrical Conui &c Define parallelogram Prove that its opposite sides and angles are equal and that the diameters bisect each other Parallelograms upon the same base and between the same parallels are equal Divide straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square of the other part Draw pair of tangents to given circle from an external point and prove that the straight line joining the centre and given point is perpendicular to the chord of contact On given straight line describe segment of circle containing an angle equal to given angle β Describe an isosceles triangle having each of the angles at the base double the third angle Inscribe regular quindecagon in given circle Triangles of the same altitude are to one another as their bases Similar triangles are to one another in the duplicate ratio of their homologous sides Bisect triangle by straight line parallel to one side Also trisect it 10 Describe rectilineal figure similar to one and equal to another rectilineal figure 11 In parabola the tangents at the extremities of focal chord intersect at right angles in the directrix 12 In the parabola prove that V2 SP Ρ 13 In the ellipse prove that SY S'Y' BC2 where SY S'Y1 denote perpendiculars from the foci upon any tangent 14 Express the area of triangle in terms of the co-ordinates of its angular points When the co-ordinates are rectangular In polar co-ordinates