Mathematical Questions and Solutions, from the "Educational Times.", Volume 25

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F. Hodgson, 1876
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Page 82 - Shew that the attraction of an indefinitely thin doubleconvex lens on a point at the centre of one of its faces is equal to that of the infinite plate included between the tangent plane at the point and the parallel tangent plane of the other face of the lens.
Page 78 - Show that the area of the triangle formed by joining the centres of the escribed circles of the original triangle = -. -'— 7, where s is the semi-perimeter of the original triangle.
Page 35 - Q are the points of contact of a common tangent to two given conies.
Page 85 - Sin. b . Sin. с Cos. a— Cos. b . Cos. с Sin. b . Sin. с
Page 56 - T will at that instant be the axis of the centrifugal couple; and the perpendicular from the centre on the tangent plane to the ellipsoid...
Page 26 - A bright sphere, whose radius is e, has its centre at the focus of a paraboloid of revolution ; show that the total illumination on the portion of the paraboloid cut off by a plane through the focus perpendicular to the axis is ITT (т — 2) c2.
Page 41 - Given one sido of a right-angled triangle ; construct it, so that the difference between the other side and the adjacent segment of the hypotenuse, cut off by a perpendicular from the right angle, may Ъе a maximum.
Page 63 - If through the corners of a spherical triangle arcs are drawn bisecting the angles A, B, C, and meeting the opposite sides in D, E, F respectively ; prove that...
Page 80 - ... attraction for the ordinary law of the inverse square of the distance...
Page 107 - A uniform rod of length a, capable of making complete revolutions in a vertical plane about one extremity, is placed in a vertical position with its free end upward, and being slightly displaced moves from rest.

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