Mathematical Questions and Solutions, from the "Educational Times.", Volume 19F. Hodgson, 1873 |
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Common terms and phrases
ABCD ax² axes axis bisected centre centroid cone conic coordinates cos² curve diagonals diameter distance draw drawn ellipse epicycloid equal equation fixed circle fixed point foci focus four G. S. CARR geometrical hence hexagon hyperbola hypocycloid imaginary inscribed intersection J. J. SYLVESTER latus rectum locus M.A. Let meet middle point obtain pa² parabola parallel particle pass pedal perpendicular point of contact Professor TOWNSEND Professor WOLSTENHOLME Proposed by J. J. Proposed by Professor prove quadric surface quadrics quadrilateral quartic question radii radius respect right angles roots sides sin² Solution by Professor sphere square STEPHEN WATSON straight line surface tangent plane tetrahedron theorem triangle ABC umbilic values velocity vertex vertices whence
Popular passages
Page xv - A large nation, of whom we will only concern ourselves with the adult males, N in number, and who each bear separate surnames, colonise a district. Their law of population is such that, in each generation...
Page xv - ... a female calf every year ; and that each calf begins to breed in like manner at the end of three years, bringing forth a cow calf every year ; and that these last breed in the same manner, &c.
Page 110 - An epicycloid is the path described by a point on the circumference of a circle which rolls on the circumference of another fixed circle touching it on the outside.
Page 93 - The normal at any point of an ellipse bisects the angle between the focal distances.
Page 103 - Their law of population is such that, in each generation, «0 per cent, of the adult males have no male children who reach adult life ; ai have one such male child ; oj have two ; and so on up to 0.5 who have five. Find (1) what proportion of the surnames will have become extinct after r generations ; and (2) how many instances there will be of the same surname being held by m persons.
Page 107 - ... when referred to the same pole and initial line. Show that the radius of curvature at any point of this locus is J of the length of the radius vector to the corresponding point on the original curve. for a plane curve, the upper or lower sign being taken according as the curve is convex or concave to the axis of x, The normal at the point P of the conic Zabx = Ьхг + ay1 meets the axis of x at G.