ANALYSIS

(Yunanca köken — orijinale bakınız.) A Greek word, which signifies the resolution of a thing into its component parts In Logic, anal3'sis is used in opposition to synthesis, as a method of arriving at adequate definitions. In the synthetical method, we begin by a uming some quahty which the subject is known to po e . Finding this to be common to other subjects than the one we wish to define, we add on some further property and BO on, until we have adequately distinguished it from all other things. Thus, man is an animal, man is a hot blooded animal, man is a hot-blooded viviparous animal, . ., maybe taken as a specimen of a synthetical proce . In analysis we should reverse the method; a uming the most distinguishing characteristic, and descending, through succe ive gradations, to that which is least so. Correspondently with this distinction, an analytical proposition is one in which the subject is implied in the predicate: e. g. " matter is extended." A synthetical proposition, on the contrary, is that in which the terms have no nece ary connection: e. g. "John is tall:" " the world is round." As applied to mental phenomena, analysis is the referring them to the acts or faculties of the mind which thejr nece arily imply, either as contemporaneously contributing to their production, or as rendering their production po ible by their past operation. The distinction frequently made between analytic and synthetic reasoning, rests on a somewhat vague use of language. Strictly speaking, all reasoning can be but of one kind. A proce of ratiocination admits, however, of being reversed: i.e. we may make certain a umptions, and from them form certain legitimate deductions; and we may then proceed to take the truths thus deduced for granted, and by a counter-proce arrive, as inferences, at what, in the former case, were the grounds from which we started. Here it is evident that the distinction lies not in the reasoning, but in the subject-matter concerning which we reason. Analysis. In Chemistry, this term is applied to the resolution of compound bodies into their elements. It is either qualitative or quantitative. Qualitative analysis consists in the determination of the component parts, merely as respects their nature, and without reference to their relative proportions: it is an imperfect, and often a very easy, operation, as compared with quantitative analysis, by which we determine not merely the 44 ANALYSIS. components of a compound, but their relative proportions: to effect this, much scientific skill and practical dexterity are required, more especially in the identification of new substances. The theory of definite proportionals, or the Atomic Theory, as it is usually called, has materially facilitated many analytical proce es, and is especially valuable as furnishing an unerring test or criterion of the general accuracy of the results. In reference to chemical analysis generally, but more especially as regards organic products, we often employ the terms proximate and ultimate analysis: the former referring to the immediate combinations which form the subject of experiment; the latter, to their final resolution into elementary principles/ Thus, in regard to sulphate of lime, it is resolved by proximate anal5rsis into sulphuric acid and lime, and these are called its proximate elements; but sulphuric acid is itself a compound of ox3'gen and sulphur; and lime, of oxygen and calcium; oxygen, sulphur, and calcium, therefore, are the results of the ultimate analysis of sulphate of lime; and there are many theoretical points in chemistry dependent upon the views which are taken of the various groupings of these ultimate principles. Wheat flour is a compound of starch and gluten; starch is compounded of oxygen, hydrogen, and carbon; and gluten, of the same elements with the addition of nitrogen; so that the ultimate components of wheat, are oxygen, hydrogen, carbon, and nitrogen. Analysis. In Geometry, a method of conducting geometrical inquiries, invented by the philosophers of the school of Plato, or, according to The on of Alexandria, by Plato himself, and one of the most ingenious and beautiful contrivances in the Mathematics. The e ence of the analytic method of establishing the truth of a proposition consists in a uming the proposition enunciated to be true, and deducing consequences from that supposition till a conclusion is arrived at manifestly true or manifestly false; or at least known to be true or false by its agreement or disagreement with some proposition which has already been demonstrated. Analysis IS thus the converse of synthesis, or composition, — a form of reasoning by which we ascend, through a series of propositions, from some known truth to the conclusion we are in search of. The distinction between analysis and synthesis, as well as the definition of the two terms in the sense in which they were understood by the ancient geometers, is concisely given by Pappus, in the Preface to the Seventh Book of his Mathematical Collections. "Analysis," says Pappus, "is the course which, setting out from the thing sought, and which for the moment is taken for granted, conducts by a series of. consequences to something already known, or placed among the number of principles admitted to l)e true. By this method, therefore, we ascend from a truth or a proposition to its antecedents; and we call it analysis, or resolution, as if indicating an inverted solution. In synthesis, on the contrary, we set out from the proposition which is the last in the analysis; and proceed by arranging, according to their nature, the antecedents which present themselves as consequents in the analytic method, and combining them together till we arrive at the conclusion sought. Analysis may be distinguished into two kinds: in the first, which may be called comtemplative analysis, we propose to discover the truth or falsehood of an aflSrmed proposition; the other belongs to the solution of problems, or the invest i gat on of unknown truths. In the first we a ume the subject of the proposition advanced to be true, and proceed through the consequences of the hypothesis till we arrive at something known. If this result is true, the proposition is true also, and the direct demonstration is obtained by stating in an inverse order the different parts of the analysis. If the ultimate consequence at which we arrive is false, the proposition was also false. In the case of a problem, we first suppose it to be resolved, and deduce the consequences resulting from that proposition till we arrive at something known. If the last consequence involves only something which can be executed, or is comprised among what geometers called data, the proposed problem can be solved; and the demonstration, or rather m this case the construction, is -obtained, as in the former case, by taking the different parts of the analysis in an inverse order. If the last result is impo ible, the thing demanded is also impo ible." The names of the ancient writers on the geometrical analysis have been preserved by Pappus in the preface before referred to: they are, Kuclid, in his Data and Porism at a; A poll on i us, in his treatise De Sectione Ration is, and in his Conic Sections; Arista^us, De Locis Solid is; and Eratosthenes, De Mediis Proportional i bus; but of these only the Data of Euclid, and some fragments of A poll on i us, have come down to our times. The subject lias, however, been fully investigated by the moderns, and a complete system of the ancient geometrical analysis may be found in the works of Dr. Simson of Glasgow. (See also Leslie's Geometrical Analysis.) By the term analysis the ancient geometers understood [s. 57]