An Elementary Treatise on the Differential and Integral Calculus (Classic Reprint)

By a method, simU ar to that of M. Poisson I have shewn that Wi=( j?-f A) can always be put under the form u+ Ah -U hf whence we obtain the equation Ui -u =J h+ Uh?. The term JA is defined to be the differential of w, and A jor the coefficient of A, is called the differential coefiicient. And from these definitions, the Rules forD ifferentiation have been in general derived. But as the algebraical labour of finding A may sometimes be greatly diminished, if, after dividing both sides of the equation u-uA h-- Uh by A, we make A =0, this method is in a few instances made use of. The symbol for the differential coefficient of w=(), invented by Leibnitz, and used almost without exception by the continental writers, is here retained I mention the fact, since the notation du for the same term has lately been revived by some Cambridge Mathematicians I do du not pretend to decide the question which of the two -dw or dggU estimated by its power of best representing the differential coefiicient ought to be preferred, but I see that the latter is, to say the least, an imperfect notation, and is liable to the important objection that the sufiix ,in the calculus of finite differences has a meaning entirely different from that indicated by the xin
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