Calendar: 1853-1854 Page 337

GENERAL LITERATURE AND SCIENCE 333 II -fHcrijamcsi i2ctoton £i princtpia £י tonic tin of Cijvcc JDimcnStonS Find the centre of gravity of portion of parabolic area cut oft1 by focal chord body revolves in an ellipse at what point is the approach to the centre twice as great as that towards the focus paraboloid axis coincident with axis of and vertex in the origin is cut by plane ax find the equation to the section and its axes right cone vertical angle is cut by plane distances λ and from the vertex find the surface and solidity of the part cut off π ι Π tan Surface ac tan π Solidity -ך sin sin 2a Two unequal beams AC CB jointed at are supported find position of equilibrium and the distance of centre of gravity from body revolves in parabola find the law offeree tending to the focus If when the body arrives at the vertex of the parabola the velocity is then suddenly doubled find the eccentricity of the new orbit The chord arc and tangent vanish in ratios of equality Ρ is an arc of vertical circle the lowest point Ρ Τ tangent meeting the diameter produced in Τ show that ultimately the velocity acquired down the chord Ρ velocity down Ρ Τ 10 plane intersects cube at distances from one of its corners show that the surface of the truncated corner of the cube aH2 a2ca c3 11 Given the radius of curvature of the normal section of solid find that of the oblique section