Mathematical Questions and Solutions, from the "Educational Times.", Volume 22F. Hodgson, 1875 |
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Common terms and phrases
a² cos² a²b² a²y² ABCD asymptote axes axis of homology b²x² BOOTH's New Geometrical centre chance chord complete quotients conic coordinates cosec curve diameter directrix drawn E. B. ELLIOTT ellipse ellipsoid envelope equal G. S. CARR given in position gives Hence HOLDITCH'S Theorem hyperbola inscribed integral intersection JAMES COCKLE locus M.A. Let major axis middle point parabola parallel pentagon perpendicular plane point at infinity points of contact polygon Professor TOWNSEND Proposed by Professor Proposed by T. T. quadric quadrilateral question radius remainder semicircle sides sin² Solution by G. S. Solution by Professor sphere square straight line tan² tangent tangential equation TEBAY theorem triangle ABC values velocity whence µ²
Popular passages
Page 86 - CE is equal to the difference of the segments of the base made by the perpendicular.
Page xi - [t]o determine the nature of the catenaria volvens, or the figure which a perfectly flexible chain of uniform density and thickness will assume, when it revolves with a constant angular velocity about an axis, to which it is fastened at its extremities, in free and non gravitating spaces.
Page 34 - ... 0 has repeatedly come before us, it has always been with the understanding that no two of the roots were equal, and the order of the determinant has never been greater than the %th.
Page 65 - ¿t'y -(-(я5 -7* +2) у + 4 = 0, (y» + y)a?-7y* + 2ír + 4 = 0. The original form shows that if x is between 1 and 2, у is positive ; but that x being beyond these limits, у is negative ; and as regards the first case, x between 1 and 2, we at once establish the existence of an oval, meeting the line у = 1 in the points x = 2 and f , and the line у = 2 in the points x = 1 and \ ; it is further easy to see that the horizontal tangents of the oval are у = ^ (25 ±v/ÏÎ3), = say 2'2 and 0-9.
Page 35 - If two points are given on the circumference of a given circle, another fixed circle can be found such that if any two lines be drawn from the given points to intersect...
Page 92 - ... connected with a common point 0 by four inextensible cords OA, OB, OC, OD, repel each other with forces varying directly as their masses and mutual distances conjointly ; shew that, in their configuration of relative equilibrium, BCDO : CDAO : DABO : ABCO = a...
Page 46 - ... conductor is uninsulated, the charge induced on it by a unit charge at a distance / from the origin and of angular coordinates 6, <f> is approximately 52.
Page 46 - A uniform circular wire of radius a, charged with electricity of line-density e, surrounds an uninsulated concentric spherical conductor of radius e; prove that the electrical density at any point of the surface of the conductor is . 2 a2 where Q,, Q* Q...
Page 65 - The point at infinity on the axis of у is in fact a flecnode, the tangent to the flecnodal branch being x = 0, and that of the ordinary branch x = 2. Similarly, from the second quadric equation, it appears that the line у = 0 is an asymptote ; the point at infinity on the axis of ж is in fact a cusp, the axis in question у = 0 being the cuspidal tangent. The equation of the curve (2) may also be written in the forms «y + (x3 - 1x + 2) у + 4 = 0, (f + y)x*- Тух + Zy + 4 = 0.
Page 63 - ... (x = b, y= a), and 4 other points, 16 = 5 + 5 + 2 + 4. As to the points at infinity, observe that, as regards the first curve, the point at infinity on the line x = 0 is a flecnode having this line for a tangent to the flecnodal branch ; and, as regards the second curve, the same point is a cusp, having this line for its tangent; hence the point in question counts as 2 + 3, = 5 intersections ; and the like as to the point at infinity on the line y — 0.