ANALYSIS, in mathematics, is properly the method of resolving problems by means of algebraical equations; whence we often find that these two words, analysis and algebra, are used as synonymous.
Analysis, under its present improvements, must be allowed the apex or height of all human learning: it is this method which furnishes us with the most perfect examples of the art of reasoning; gives the mind an uncommon readiness at deducing and discovering, from a few data, things unknown; and, by using signs for ideas, presents things to the imagination, which otherwise seemed out of its sphere: by this, geometrical demonstrations may be greatly abridged, and a long series of argumentations, wherein the mind cannot without the utmost effort and attention discover the connection of ideas, are hereby converted into sensible signs, and the several operations required therein effected by the combination of those signs. But, what is more extraordinary, by means of this art, a number of truths are frequently expressed by a single line, which in the common way of explaining and demonstrating things would fill whole volumes. Thus, by mere contempla-
tion of one single line, whole sciences may be sometimes learnt in a few minutes time, which otherwise could scarcely be attained in many years.
ANALYSIS is divided, with regard to its object, into that of finite, and infinite.