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angles application arbitrary axes axis becomes centre chord circle circumscribing co-ordinates coefficients conic section conjugate consequently considered constant corresponding curve deduced denote described determined diameter direction distance divided draw drawn eliminating equal equation evident expression extremities figure former four functions geometrical given given points gives hence inscribed intersection involution joining known manner means meet method multiply obtain opposite origin parabola parallel pass perpendicular plane polar pole porism position preceding principle quantities radii radius ratios reducing reference relation represent respectively result roots segments sides similar Similarly solution sphere square straight line substituting suppose surface tangent theorem third touch triangle values variable Whence
Page 132 - ... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line.
Page 277 - Into a cubical cistern, eight feet deep, and having an unknown leak, water is poured from two pumps, worked by two men, A and B. They pump together till the vessel is half filled, when B falls asleep ; A continues pumping till it is threefourths filled, and then goes away.
Page 329 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 108 - The elementary character of the subject was the professed objection: his recondite mode of treating it, was the professed passport for its admission.
Page 95 - ... the product of three alternate segments taken in order is equal to the product of the other three segments.
Page 108 - The consequence of this attempt, was the paper now about to be submitted to the public for the first time, after lying more than twenty years altogether unknown. The first objection made to it was its length : the author curtailed it, under the impression made upon his mind, that it would be printed when so altered : the end of all his labour was,—tlrat it was
Page 108 - ... recondite mode of treating it, was the professed passport for its admission. " That paper has been reprinted in the Ladies' Diary for 1838 ; and most of our readers are doubtless acquainted with it. That the mode in which it is drawn up is in one respect fortunate, there can be no doubt, since that finally secured its publication ; whilst on the other hand, it may be considered unfortunate by its requiring so much higher mathematical learning to understand the reasoning than the nature of :ie...
Page 76 - Find the straight line of quickest descent from a given point to a given straight line, the point and the line being in the same vertical plane.
Page 46 - ABC being given by pofition, and alfo a ftraight line DE, which, does not cut the circle, a point K may be found, fuch...
Page 85 - A sin a cos B = cos b sin c —• sin b cos c cos A.