...+gy* = 0; whence we have the condition fl*-2lmn+gm* = 0. 1 542 (Proposed by Professor CAYLEY.) — If a given line meet two given conies in the points...four points of intersection of the two given conies. Solution by ABCHEB STANLEY. The several conies which pass through the four intersections of the two...

...B") be the sibi-conjugate points (or foci) of the pairs (A, A') and (B, B'), or of the pairs (A, R) and (A', B), then (A", B") lie on a conic passing...four points of intersection of the two given conies. [Vol. п. pp. 97—100.] 1606. (Proposed by the EDITOR, [WJM]). — Solve the following problems: (a)...

...prove that the tangents to U at A and B intersect the tangents to V at C and D in four points which lie on a conic passing through the four points of intersection of UandV 67 11563. (Professor Lange, Ph.D.) — (1) Let A0, B0. 00 be the midpoints of the sides BC, CA,...

...0,2) = 0, where E is a constant proportional to the energy. It follows that the locus of 0 must be a conic passing through the four points of intersection of the two conies ntff + vf0f + H,20,2 = 0, 0it + 0f + 0f = 0. The four points in which these two conies intersect...

...0,') = 0, where E is a constant proportional to the energy. It follows that the locus of 0 must be a conic passing through the four points of intersection of the two conies uW + utff + uf6,2 = 0, The four points in which these two conies intersect correspond to the...