Calendar: 1871-1872 Page 528

528 GENERAL LITERATURE AND SCIENCE Thence deduce the harmonic properties of the complete quadrilateral 10 Prove that the three diagonals of quadrilateral circum- scribing conic form self-conjugate triangle with respect to the conic 11 Find in trilinear co-ordinates the polar reciprocal of the general conic with respect to the conic a2 Also find the polar reciprocal of the conic circumscribing the triangle of reference with respect to the same conic 12 Find geometrically the polar reciprocal of circle with respect to given circle 13 Show that the directrix and principal axis of the parabola Xs 2xy 2dx 2ey de are given by the equations x-y -- fmix -- 14 Find the conditions which must be satisfied in order that the equation ita2 νβ2 wy 2η1βγ 2v1ay 21ρ1αβ may represent circle rectangular hyperbola 15 The locus of the vertices of an equilateral triangle described about the ellipse is the curve a2 by V1 orb2 VI -Cuclft Describe an equilateral triangle on given finite straight line If an equal triangle be described on the other side of the given line what figure will the two triangles form If two triangles have two sides of the one equal to two sides of the other each to each and have also the angles contained by those sides equal to one another they shall also have their bases or third sides equal and the two triangles shall