in a general sense, implies the resolu- tion of something compounded into its original and constituent parts. The word is Greek, and derived from ἀναλύω, to resolve.

in mathematics, is properly the method of resolving problems by means of algebraical equa- tions; whence we often find that these two words, anal- ysis and algebra, are used as synonymous.

Analysis, under its present improvements, must be al- lowed 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 un- common readiness at deducing and discovering, from a few data, things unknown; and, by using signs for i- deas, presents things to the imagination, which other- wise seemed out of its sphere: by this, geometrical demonstrations may be greatly abridged, and a long series of argumentations, wherein the mind cannot with- out the utmost effort and attention discover the connec- tion 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 scarce be attained in many years.

Analysis is divided, with regard to its object, into that of finites, and infinites.

Analysis of Finite Quantities, is what we otherwise call spurious arithmetic or algebra. See Algebra.

Analysis of Infinites, called also the New Analysis, is particularly used for the method of fluxions, or the differential calculus. See Fluxions.

logic, signifies the method of tracing things backwards to their source, and of resolving know- ledge into its original principles. This is also called the method of resolution; and stands opposed to the synthetic method, or that of composition.—The art of logical analysis consists principally in combining our perceptions, clasping them together with address, and contriving proper expressions for conveying our thoughts, and representing their several divisions, classes, and re- lations.

chemistry, the reducing of an hetero- geneous or mixed body, into its original principles or component parts. See Chemistry.

Analysis is also used for a brief but methodical illu- stration of the principles of a science; in which sense, it is nearly synonymous with what we otherwise call a synopsis.