ANALYSIS, in Logick, a Method of applying the Rules of Reasoning, to resolve a Discourse into its Principles; in order to a Discovery of its Truth, or Falsehood. See PRINCIPLE. Or, Analysis is an Examination of some Discourse, Proposition, or other Matter, by searching into its Principles, and separating and opening its Parts; in order to consider them more distinctly, and arrive at a more precise Knowledge of the Whole. See DISCOURSE, PROPOSITION, REDUCTION, etc. The Word is Greek, ἀνάλυσις (analysis), which literally signifies, Resolution; formed of ἀνά (ana), and λύω (luo), folvo, resolvo, I loosen, I resolve. Analysis makes one great Branch or Species of Method; called also Resolution. See METHOD, and RESOLUTION.
Analysis, in Mathematics, a Method of solving, or resolving Mathematical Problems. See PROBLEM. There are two general Methods of finding Truth in Mathematics; Synthesis, and Analysis.—Analysis is the Demonstration, or Consideration of the Consequences drawn from any Proposition; in which a Man proceeds, till he comes to some known Truth, by means whereof, he may be able to give a Solution of the Problem. See RESOLUTION. The Method of Analysis consists more in the Judgment and readiness of Apprehension, than in any particular Rules, where pure Geometry is made use of, as it was among the Ancients; but at present Algebra is principally used on this Occasion, which furnishes certain Rules to perform or arrive at the End proposed. See ANALYTIC.
This Method, under its present Improvements, must be allowed the Apex or Height of all human Learning; being the great Instrument or means whereby so many surprising Discoveries have been of late Years made, both in Mathematics, and Philosophy. It furnishes the most perfect Instances, and Examples of the Art of Reasoning; gives the Mind a surprising Readiness at deducing and discovering Things unknown, from a few Data; and by using Signs for Ideas, presents Things to the Imagination, which otherwise seemed out of its Sphere. By this, Geometrical Demonstrations may be wonderfully 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 yet 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 sometimes be learnt in a few Minutes time; which otherwise could scarce be attained in many Years. See MATHEMATICS, KNOWLEDGE, THEOREM, etc.
Analysis is divided, with regard to its Object, into that of Finites, and that of Infinites.
Analysis of finite Quantities, is what we otherwise call Specious Arithmetic, or Algebra. See ALGEBRA, and SPECIOUS ARITHMETIC.
Analysis of Infinites, called also the New Analysis, is particularly used for the Method of Fluxions, or Differential Calculus. See FLUXIONS, and CALCULUS.—See also Infinite. Analysis is also used in Chemistry, for the decompounding of a mixed Body; or the Reduction thereof into its Principles. See PRINCIPLE, REDUCTION, DECOMPOSITION, BODY, etc. To analyze Bodies, or resolve them into their component Parts, is the chief Object of the Art of Chemistry. See CHEMISTRY. The Analysis of Bodies is chiefly effected by means of Fire. See FIRE. All Bodies, by a Chemical Analysis, resolve into Water, Earth, Salt, Sulphur, and Mercury; though every Body does not afford all these Parts, but some more, some less, according to the Kingdom they belong to. See ELEMENT,—See also Water, Earth, Salt, etc.
The Analysis of Vegetables is easy; that of Fossils, particularly Metals and Semi-metals, difficult. See VEGETABLE, FOSSIL, METAL, etc. Some Bodies of the Fossil Tribe consist of Particles so very minute, and so firmly united, that the Corpuscles thereof need less heat to carry them off, than to separate them into their Principles: So that the Analysis is impracticable in such Bodies—Hence the difficulty of analyzing Sulphur. See SULPHUR.
The Anatomical Dissection of an Animal, is a kind of Analysis. See ANATOMY, and DISSECTION.
Analysis is also used for a kind of Syllabus, or Table of the principal Heads, or Articles of a continued Discourse; disposed in their natural Order, and Dependency.—Analyses are more scientifical than Alphabetical Indexes; but are less used, as being more intricate.
