Calendar: 1876-1877 Page 590

590 GENERAL LITERATURE AND SCIENCE find the minimum value of PT and prove that when it is minimum the other common tangent to the ellipse and the circle of curvature at Ρ pass through 12 Investigate the equation to plane under the form χ cos cos β cos Ύ and find the perpendicular distance of any point from it Three planes are at perpendicular distances plt pv p3 from the origin three planes are drawn through the lines of intersection of any two perpendicular to the third shew that the last three planes will intersect in straight line passing through the origin if pt cos p2 cos Β p3 cos when are the angles between the first three planes 13 Shew that hyperboloid of one sheet can be generated by two systems of straight lines and that no two lines of the same system intersect Given two generating lines that intersect and two points on hyperboloid shew that the locus of the centre is another hyperboloid bisecting the straight lines joining the two points to the intersection of the generators 14 Four spheres whose radii are intersect at right angles shew that tlie volume of the tetrahedron whose angles are their centres is abed XX -algebra auU CI c£1n of Equations Prove that tf yy χ t£ zf yY yz xz xy If are in harmonic progression so also are ab ac be c' β If p3 represent the number of permutations uf quantities taken together then