Mathematical Questions and Solutions, from the "Educational Times.", Volume 36F. Hodgson, 1881 |
Contents
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Common terms and phrases
asymptote axes axis centre of gravity chord circumscribed circle coefficient conic contour coordinates cos² cosec cot A+ cubic curve denote diameter directrices distance dx dy E. W. SYMONS ellipse equal equation fixed point G. F. WALKER G. S. CARR hence HEPPEL hyperbola infinity inscribed circle integral intersection locus nine-point circles nodal cubic pairs parabola perpendicular plane points of contact polar circle Professor PROPOSER prove quartic radius of curvature range rectangular right angles roots sec² semicircle sides sin² Solution by G Solution by G. F. Solution by W. J. C. sphere square straight line symmetry T. R. TERRY tangents theorem touching values velocity vertical vis viva W. B. GROVE W. J. C. SHARP
Popular passages
Page 123 - ... MAXIMA AND MINIMA 1. Of all equivalent parallelograms that have equal bases, the rectangle has the minimum perimeter. 2. Of all equivalent rectangles, the square has the minimum perimeter. 3. Of all triangles that have the same base and the same altitude, the isosceles has the minimum perimeter. 4. Of all triangles that can be inscribed in a given circle, the equilateral is the maximum and has the maximum perimeter. 5. To inscribe in a semicircle the maximum rectangle. 6. Find the area of the...
Page 114 - If fig. 179 were spun about OA, what figure would be generated (i) by the circle, (ii) by AP, (iii) by PQ? Hence find the locus of the points of contact of tangents from a fixed point to a fixed sphere. Ex.
Page xxi - Ь)»] ; (2) when b = 0, so that the curve is the locus of the vertex of a triangle on a given base, having the sum of its two sides equal to the sum of the perpendicular from the vertex on the...
Page 85 - A ; prove that, if в he the inclination to the vertical of the line joining the centre of the sphere to the centre of the rod, sin (л + л') 2 cos (a + Л) cos (a — A') ' and examine the case where a + A = Jir.
Page 108 - If a quadrilateral be circumscribed to a circle and a fifth variable tangent be drawn, the rectangles under perpendiculars on it from each pair of opposite angles are in a constant ratio.
Page 45 - I is the moment of inertia, where k is the radius of gyration of the area about the axis in the surface of the fluid.
Page 114 - CHEF, and the latter only at the two points R and S of its contact with two of the system of conies through ABEF. When the two points E and F, common to...