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 is divided, with regard to its object, into that of finites and infinites. Analysis of Finite Quantities is what we otherwise call specious arithmetic or algebra. Analysis of Infinites, called also the New Analysis, is particularly used for the method of fluxions, or the differential calculus.

Mental Philosophy, signifies the process of decompounding our thoughts into their simplest elements, or of resolving our intellectual operations into their primary principles.

Physics, and in Chemistry, also denotes decomposition, that is, the separation of what is complex into its constituent parts. The different meanings of the term Analysis, as used in mathematics and the other branches of science, are well explained in Stewart's Philosophy of the Mind, vol. ii. chap. iv. § 3.