The Mathematician, Volume 1

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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 108 - Gilbert, than te any respect to the author, his subject, or his mode of treating it, that the honour was accorded to him. The elementary character of the subject was the professed objection : his 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...
Page 108 - Science, at all events, is no valid ground of hope1 — ignorance no ground for despair. — ED. MM The Note to the Article on Homer's Algebraic Transformation. " No mathematician has contributed so largely as Mr. Horner to the improvement of the problem of the numerical solution of equations ; and perhaps no one has left the world with cause so just for considering himself treated with unmerited neglect, and even personal hostility, in connexion with his researches. It is not difficult to account...
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 108 - ... so as to secure an enforcement of his claims upon the public mind. A good deal of intrigue and a little science will effect more in the way of cotemporary reputation, than much science, without foreign aid, can ever effect for him. This, indeed, is a melancholy truth : nevertheless, a truth it is. Mr. Homer's first paper on equations was printed in the Philosophical Transactions for 181); and Air.
Page 277 - They return together and find the water 1$ inch lower than when B. left. The leak is now discovered and stopped, and by their joint efforts the Vessel is filled in half the time in which they had worked together at first. They remark also that 10 hours had elapsed since they first began pumping, and that B.
Page 41 - Show that the area of the triangle formed by joining the centres of the escribed circles is 8.R2 cos | A cos | B cos J C.
Page 108 - ... enquiry itself renders desirable. Mr. Horner was himself so sensible of this objection, that he immediately attempted a simplification of the principles. The consequence of this attempt was the papers 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...
Page 336 - ... the parts of this line, between the vertices of the triangles and the base, are in the same ratio to each other as the areas of the triangles.

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