Analysis is a branch of mathematics based on the idea of limit, and includes concepts such as derivatives and integrals. Because it deals with abstract variables, it is considered an advanced branch of algebra.

It is also known as calculus, particularly in modern texts. However, this does not usually hold for more advanced branches like complex analysis.

A*nal"y*sis (#), n.; pl. Analyses (#). [Gr. αναλυσις, fr. αναλυσαι to unloose, to dissolve, to resolve into its elements; ανα up + λυσαι to loose. See Loose.]


A resolution of anything, whether an object of the senses or of the intellect, into its constituent or original elements; an examination of the component parts of a subject, each separately, as the words which compose a sentence, the tones of a tune, or the simple propositions which enter into an argument. It is opposed to synthesis.

2. Chem.

The separation of a compound substance, by chemical processes, into its constituents, with a view to ascertain either (a) what elements it contains, or (b) how much of each element is present. The former is called qualitative, and the latter quantitative analysis.

3. Logic

The tracing of things to their source, and the resolving of knowledge into its original principles.

4. Math.

The resolving of problems by reducing the conditions that are in them to equations.

5. (a)

A syllabus, or table of the principal heads of a discourse, disposed in their natural order.


A brief, methodical illustration of the principles of a science. In this sense it is nearly synonymous with synopsis.

6. Nat. Hist.

The process of ascertaining the name of a species, or its place in a system of classification, by means of an analytical table or key.

Ultimate, Proximate, Qualitative, Quantitative, and Volumetric analysis. Chem. See under Ultimate, Proximate, Qualitative, etc.


© Webster 1913.

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