CALCULUS, diferendalis,is a method of differencing quantities, that is, of finding an infinitely small quantity, which, being taken an infinitive number of times, shall be equal to a given quantity. An infinite ly small quantity, or infinitesimal, is a portion of a quantity less than any assign able one ; it is therefore accounted as no thing; and hence two quantities, only dif fering by an infinitesimal, are reputed equal. The word infinitesimal is merely respective, and implies a relation to ano ther quantity ; for example, in astronomy the diameter of the earth is an infinitesi mal in respect to the distance of the fix ed stars. Infinitesimals are likewise call ed differentials, or differential quantities, when they are considered as the differ ence of two quantities. Sir Isaac New ton calls them moments, considering them as momentary increments of quantities ; for instance, of a line generated by the flux of a point, of a surface by the flux of a line, or of a solid by the flux of a sur face. The calculus differential's, there fore, and the doctrine of fluxions, are the same thing, under different names, the latter given by Sir Iaac Newton, and the former by Mr. Leibnitz, who disputes
with Sir Isaac the honour of the discove ry. There is, however, one difference between them, which consists in the man ner of expressing the differentials of quantities : Mr. Leibnitz, and most fo reigners, express them by the same let ters as variable ones, prefixing only the letter d : thus the differential of x is call ed d x, and the differential of y, dy: and d x is a positive quantity, if x continually increase ; and a negative quantity, if x de crease. We, on the other hand, follow ing Sir Isaac Newton, instead of dx write x, (with a dot over it,) and instead of d y, y. But foreigners reckon this method not so commodious as the former, because, if differentials were to be differenced again, the dots would occasion great confusion ; not to mention, that printers are more apt to overlook a point than a letter. See FLuxioss.