a general sense, implies the resolution of something compounded into its original and constituent parts. The word is Greek, and derived from \(\alpha\eta\lambda\alpha\sigma\tau\iota\sigma\), to resolve.

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 arguments, 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 contemplation 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 specific arithmetic or algebra. See Algebra.

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

logic, signifies the method of tracing things backward to their source, and of resolving knowledge into its original principles. This is also called the method of resolutions; 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 relations.

rhetoric, is that which examines the connections, tropes, figures, and the like, inquiring into the proposition, division, passions, arguments, and other apparatus of rhetoric.

Several authors, as Freigius and others, have given analyses of Cicero's Orations, wherein they reduce them to their grammatical and logical principles; strip them of all the ornaments and additions of rhetoric which otherwise disguise their true form, and conceal the connection between one part and another. The design of these authors is to have those admired harmonies just such as the judgment dispensed them, without the help of imagination; so that here we may coolly view the force of each proof, and admire the use Cicero made of rhetorical figures to conceal the weak part of a cause.

A collection has been made of the analyses formed by the most celebrated authors of the 16th century, in 3 vols. folio.

Analysis is also used, in chemistry, for the decomposition of a mixed body, or the separation of the principles and constituent parts of a compound substance.

To analyze bodies, or resolve them into their component parts, is indeed the chief object of the art of chemistry. Chemistry furnishes several means for the decomposition of bodies, which are all founded on the differences of the properties belonging to the different principles of which the body to be analyzed is composed. If, for example, a body be composed of several principles, some of which have a great, and others a moderate degree of volatility, and, lastly, others are fixed, its most volatile parts may be first separated by a gradual heat in distilling vessels; and then the parts which are next in volatility will pass over in distillation; and lastly, those parts which are fixed, and capable of resisting the action of fire, will remain at the bottom of the vessel.

Analysis is also used for a kind of syllabus, or table of the principle heads or articles of a continued discourse, disposed in their natural order and dependency. Analyses are more scientific than alphabetical indexes; but they are less used, as being more intricate.

Analysis is likewise used for a brief, but methodical, illustration of the principles of a science; in which Analytic sense it is nearly synonymous with what we otherwise call a synthesis.