Treatise on the Differential and Integral Calculus (Classic Reprint)

But as the algebraical labour of finding A may sometimes be greatly diminished if after dividing both sides of the equation Ui-u =A k+ Uh by k, we make A =0, this method is in a few instances made use of. du The symbol -7- for the differential coefficient of u=f{x), 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 not pretend to decide the quesdu tion which of the two -7- ordu estimated by its power of best representing the differential coefficient 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 suffix a, in the calculus of finite differences has a meaning entirely different from that indicated by the xin d,. But the most important objection is that already alluded to, that when the proposed notation has been learned in our own elementary works, the eye must become familiarized with that of Leibnitz, before the works of Lacroix and Laplace can be read with advantage. Lastly, if it be considered necessary to offer an inducement to any one to enter upon the study of a science which is the result of one of Newton smost brilliant discoveries, let him know that it is a high privilege, not a duty, to study this language of pure unmixed truth. The laws by which God has thought good to govern the universe are surely subjects of lofty contemplation, and the study of that symbolical language by which alone these laws can be fully decyphered, is well deserving of his noblest efforts Professor Sedgwick on theS tudies of the University.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History,