Mathematical Questions and Solutions, Volume 58F. Hodgson, 1893 - Mathematics |
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A₁ asymptotes axes bisects centre of gravity centroid cercle chord circonférence circumcircle collinear concyclic cone conic courbe curve deux diagonals diameter draw drawn droites dy dx ellipse equal equation equilateral triangle feet H. J. WOODALL H. W. CURJEL Hence hk cos hyperbola inscribed KNOWLES line joining locus LVIII meet opposite sides orthocentre parabola parallel particle perpendicular plane points of intersection polar Prof Professor G. B. M. ZERR Professor ZERR prove R. F. DAVIS radical axis radius ratio rencontre respect right angles sin² sin³ Solution by H. J. Solution by Professor Solution by T. W. K. sphere square straight line T. W. K. CLARKE theorem triangle ABC velocities vertex vertices W. J. GREENSTREET
Popular passages
Page 134 - It is required to find three numbers in arithmetical progression, such, that the sum of every two of them may be a square.
Page 134 - Into a hollow cone, whose vertical angle is 2a, are put a number of spheres one above another, each sphere touching the one above, the one below, and the sheet of the cone; show that the radii of the spheres...
Page 55 - Q', in opposite senses from B with such velocities that at the first impact all three have equal velocities ; prove that throughout the motion the line joining any pair is either horizontal or passes through one of two fixed points, and that the intervals of time between successive impacts are all equal.
Page 134 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Page 134 - A quantity of corn is to be divided among n persons, and is calculated to last a certain time if each of them receive a peck every week ; during the distribution it is found that one person dies every week, and then the corn lasts twice as long as was expected ; find the quantity of corn and the time it lasts.
Page 130 - In the same case, 21. In a given O inscribe a A, so that two of its sides may pass through given points, and that the third side may be a maximum. 22. What theorem analogous to 18 holds for escribed 0s? 23. Draw from the vertical L of an obtuse-angled A a line to a point in the base, such that its square will be equal to the rectangle contained by the segments of the base. 24. If the line AD, bisecting the vertical LA of the A ABC, meets the...
Page vii - In a triangle, having given the base, the sum of the other two sides, and the length of a line drawn from the vertical angle to the middle of the base, to find the sides of the triangle.
Page 84 - If the tangent at any point P of a parabola meet the axis in T, and the circle of curvature meet the curve in Q, then 43.
Page 131 - We have to express analytically the fact that the area of the triangle formed by joining the feet of...