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algebraical angles angular points anharmonic ratios arbitrary axes axis bisecting centre Chasles circumscribing circumscribing circle co-ordinates coefficients conic section conical surface conjugate conjugate lines cosec cosº cotr curve deduced denote Desargues determined diameter drawn eliminating ellipse enunciated equal equation expression formula Gentleman's Diary Geometry given circles given lines given points hence hyperbola indeterminate inscribed involution involution system locus Mathematician method multiply mutual contact obtain parabola parallel pass perpendicular points of contact points of intersection polar pole porism porismatic quadrilateral quantities radical axis radii radius respectively result roots Scholium second degree second order segments sides Similarly sinAC sinAD solution SoLUTION.—Mr sphere straight line substituting surface theorem Thomas Dobson three given touch tryo values variable Weddle Whence zero
Pàgina 132 - ... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line.
Pàgina 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.
Pàgina 329 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Pàgina 108 - The elementary character of the subject was the professed objection: his recondite mode of treating it, was the professed passport for its admission.
Pàgina 95 - ... the product of three alternate segments taken in order is equal to the product of the other three segments.
Pàgina 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
Pàgina 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...
Pàgina 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.
Pàgina 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...