From the second edition (1989):
(əˈnælɪsɪs) Pl. analyses (-iːz). [a. med. (or early mod.) L. analysis (found c 1470), a. Gr. ἀνάλυσις, n. of action f. ἀναλύ-ειν to unloose, undo, f. ἀνά up, back + λύ-ειν to loose: see -sis.]

I. Generally.

1. The resolution or breaking up of anything complex into its various simple elements, the opposite process to synthesis; the exact determination of the elements or components of anything complex (with or without their physical separation).a. of things material. Obs., exc. as fig. from spec. uses.

1667 H. Stubbe in Phil. Trans. II. 501, I tryed some Analysis of Bodies by letting Ants eat them. 1867 Sir J. Herschel Fam. Lect. Sc. 70 A mechanical analysis of the contents of your basket.

b. of things immaterial.

1581 Kirke Spenser's Sheph. Cal. Argt., Which difinition albe‥it agree with the nature of the thing, yet no whit answereth with the analysis and interpretation of the worde. 1590 Nashe in Greene's Arcad. Pref. 7 These men‥doe bound their base humours in the beggerly straights of a hungry Analysis. 1753 Chambers Cycl. Supp., Analysis is most proper for the discovery of truth, and synthesis for teaching and explaining it in a systematical way. 1797 Godwin Enquirer i. vi. 46 The habits of investigation and analysis. 1825 Macaulay Ess., Milton, Analysis is not the business of the Poet. His office is to portray, not to dissect. 1866 G. Macdonald Ann. Q. Neighb. 470 A time favourable to the analysis of feeling. 1873 H. Spencer Sociol. 322 Analysis has for its chief function to prepare the way for synthesis.

c. in the last (or final) analysis [after F. en dernière analyse], when reduced to its fundamental elements; at the conclusion of the investigation or examination involved; all things duly considered and weighed.

[1791 J. Mackintosh Vindiciae Gallicae i. 89 Corporate property is here as sacred as individual, because in the ultimate analysis it is the same. 1844 E. A. Poe in Chambers's Jrnl. 30 Nov. 345/2 Now this mode of reasoning in the schoolboy, whom his fellows termed ‘lucky’,—what, in its last analysis, is it?] 1877 Independent 29 Mar. 13/2 In the last analysis there will be a painless universe! 1885 Harper's Mag. Mar. 648/1 The loveliest doll in the last analysis is merely sawdust. 1902 W. H. Fitchett Let. 18 Oct. in D. P. Hughes Life H. P. Hughes (1904) xix. 535, I have always felt that, in the last analysis, the question of union was a religious one. 1918 B. Russell Logic & Knowl. (1956) 194 Analysis‥always depends, in the last analysis, upon direct acquaintance with the objects which are the meanings of certain simple symbols. 1957 L. F. Brosnahan Genes & Phonemes 12 The total experience incorporated in a language, in the vocabulary, morphology and syntax, must, in the last analysis, have been gained through the senses. 1963 V. Nabokov Gift iii. 188 In the final analysis all girls aspire to be beauties.

2. concr. A tabular statement or other form embodying the results of the above process; an abridgement exhibiting the essential heads; a synopsis or conspectus; as an analysis of a text-book, of a General Charges account. bowling analysis: in Cricket, a register of the result of each ball bowled.

1668 Wilkins Real Char. ii. i. §1. 22 A Scheme or Analysis of all the Genus's or more common heads of things belonging to this design. 1816 Gentl. Mag. LXXXVI. i. 11 So good an analysis of Mr. Park's ‘History of Hampstead.’ 1854 F. W. Lillywhite Guide to Cricketers 22 The analysis of the Bowling is given of all those matches possessing the most interest. 1862 Robertson (title) Analysis of Mr. Tennyson's In Memoriam. 1882 Daily Tel. 27 May, The fielding of the Australians‥was as nothing compared with the bowling, the analysis of which we append below. 1904 Warner How we recovered Ashes iii. 57 His [sc. Rhodes's] analysis—two wickets for seventy-eight runs—is misleading, as analyses very often are.

II. Specifically.

3. Chem. The resolution of a chemical compound into its proximate or ultimate elements; the determination of the elements of which it is composed; or, in the case of a substance of known composition, such as water, of the foreign substances which it may contain.
When the analysis determines only what the elements are, it is qualitative; when it determines the quantity of each present, it is quantitative; the latter is gravimetrical or volumetrical according as the weights or the volumes of the elements are measured.

a1655 Let. in Hartlib Ref. Commw. Bees 27 Manna‥hath [not] the like nature as Honey, which in its Analysis more easily is apparent. 1686 W. Harris Lemery's Chem. ii. xxii. 621 Let us examine now whether any such thing can probably be found in opium by the Analysis I have made of it. 1791 Hamilton Berthollet's Dyeing I. i. i. iii. 51 The quantity of charcoal which they yield by analysis. 1831 T. P. Jones New Convers. Chem. xxviii. 282 Sugar, starch, and gum are proximate principles, and these we obtain by proximate analysis. 1878 Huxley Physiogr. 83 A large number of analyses of air from various localities.

4. Optics. The resolution of light into its prismatic constituents.

1831 Brewster Optics xxiii. 205 The polarisation of the incident light, and the analysis of the transmitted light. 1860 Tyndall Glac. ii. §6. 253 A delicate prismatic analysis of white light.

5. Literature. The investigation of any production of the intellect, as a poem, tale, argument, philosophical system, so as to exhibit its component elements in simple form.

1644 E. Huit (title) The whole Prophecie of Daniel Explained by a Paraphrase, Analysis and Briefe Comment. 1789 Belsham Ess. II. xxxiv. 244 Of these [theories] I shall not descend to a particular analysis. 1860 Motley Netherl. (1868) I. vi. 357 Such, in brief analysis, was the memorable Declaration of Elizabeth. 1862 Stanley Jew. Ch. (1877) I. v. 105 The critical analysis of the text.

6. Gram. The ascertainment of the elements composing a sentence or any part of it. esp. (since 1852) logical analysis, syntactic analysis, or sentence analysis: the resolution of the sentence into elements performing distinct functions in the expression of thought, and thus having definite relations to the whole sentence and to each other, as subject and predicate with their respective enlargements.

1612 Brinsley Lud. Lit. viii. (1627) 104 Of the analysis or resolving a sentence. 1724 Watts Logic iv. i. Wks. 1813 VII. 511 The word analysis has three or four senses‥When a sentence is distinguished into the nouns, the verbs, pronouns, and other particles of speech which compose it, then it is said to be analysed grammatically. When the same sentence is distinguished into subject, predicate‥then it is analysed logically, and metaphysically. 1852 Min. Comm. Council I. 23 Geography, history, the analysis of language, arithmetic. 1852 Morell (title) Analysis of Sentences explained. 1869 Farrar Fam. of Speech i. 31 The name for grammar in Sanscrit means analysis.

7. Math. ancient analysis, the proving of a proposition by resolving it into simpler propositions already proved or admitted. modern analysis, the resolving of problems by reducing them to equations.

1656 Hobbes Elem. Philos. (1839) 309 Analysis is continual reasoning from the definitions of the terms of a proposition we suppose true‥and so on, till we come to some things known. 1660 Stanley Hist. Philos. (1701) 162/2 Analysis as defined by the Scholiast upon Euclid, is a sumption of the thing sought, by the consequents (as if it were already known) to find out the truth. 1753 Chambers Cycl. Supp. s.v., Simple Analysis is that employed in solving problems reducible to simple equations. 1798 Hutton Course Math. (1827) I. 3 Analysis or the Analytic Method‥is that which is commonly used in Algebra. 1879 Thomson & Tait Nat. Phil. I. i. 171 Spherical harmonic analysis, has for its object the expression of an arbitrary periodic function of two independent variables in the proper form for a large class of physical problems involving arbitrary data over a spherical surface. 1902 E. T. Whittaker (title) A Course of Modern Analysis. Ibid. Pref., The first half of this book contains an account of those methods and processes of higher mathematical analysis, which seem to be of greatest importance at the present time;‥it is chiefly concerned with the properties of infinite series and complex integrals, and their applications to the analytical expression of functions. 1959 G. & R. C. James Math. Dict. 10/2 Analysis, that part of mathematics which uses, for the most part, algebraic and calculus methods—as distinguished from such subjects as synthetic geometry, number theory, and group theory.

8. Logic. The tracing of things to their source, and the resolution of knowledge into its original principles; the discovery of general principles underlying concrete phenomena.

a1680 Glanvill (J.) We cannot know any thing of nature but by an analysis of its true initial causes. 1724 Watts Logic iv. i. (1822) 372 Analysis finds out causes by their effects. 1877 Caird Philos. Kant vii. 319 Analysis‥is simply going back on the path which the mind has already travelled, proceeding from the more to the less determinate.

9. Philos. a. The resolution into their elements, as a philosophical procedure, of complex things, facts, propositions, and concepts. Freq. with defining word, as logical (cf. also sense b), philosophical analysis.

1828 J. S. Mill in Westm. Rev. IX. 144 To perform the logical analysis of an argument, in the manner pointed out by the doctrine of the syllogism, is not the best means of discovering whether it contain a flaw. Ibid. 171 The philosophical analysis of Predication, the explanation of what is the immediate object of belief when we assent to a proposition, is yet to be performed. 1883 F. H. Bradley Logic i. ii. 95 It is wholly unjustifiable to take up a complex, to do any work we please upon it by analysis, and then simply predicate as an adjective of the given these results of our abstraction. 1901 W. James Mem. & Stud. (1911) vii. 169 Some psychologists are fascinated‥by the dissecting out, whether by logical analysis or by brass instruments, of whatever elementary mental processes may be [in living action]. 1903 B. Russell Princ. Math. iv. 42 The correctness of our philosophical analysis of a proposition may‥be usefully checked by‥assigning the meaning of each word in the sentence expressing the proposition. Ibid. vii. 83 A less complete analysis of propositions into subject and assertion has also been considered. Ibid. liii. 466 A distinction is made‥between conceptual analysis and real division into parts. 1918 —— Logic & Knowl. (1956) 192 The analysis of apparently complex things‥can be reduced‥to the analysis of facts which are apparently about those things.

b. (Freq. in recent Philos.) The procedure or the result of finding an expression exactly equivalent to a given word, phrase, or sentence, for the purposes of clarification.
At first an analysis was intended simply to reveal the logical structure of the analysandum, but later was often intended as leading to, or justifying, the metaphysical claim that an element eliminated by the analysis was not real, or was not fundamental: then sometimes called reductive analysis, etc. (see quot. 1956).

1910 Whitehead & Russell Principia Mathematica iii. 69 In all such cases, the proposition must be capable of being so analysed that what was the grammatical subject shall have disappeared. Thus when we say ‘the round square does not exist’, we may, as a first attempt at such analysis, substitute ‘it is false that there is an object x which is both round and square’. 1912 Russell Probl. Philos. v. 91 The fundamental principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted. 1949 Mind LVIII. 46 A later and more radical form of reductive analysis is characterised by the complete repudiation of ‘consciousness’ and the replacement of mental ‘acts’ as the constituents of mind by events which are common to both mental and physical complexes. 1956 J. O. Urmson Philos. Analysis iii. 39 The elimination of logical constructions‥is then another sort of analysis. It was variously called new-level (as opposed to same-level), or philosophical (as opposed to logical), or directional, or reductive, analysis. Different names were patronized by different analysts. 1958 G. J. Warnock Eng. Philos. since 1900 ii. 27 Moore involved both himself and others in difficulties resulting from the unquestioned assumption that any analysis must be of a standard pattern. It was always to consist in providing a verbal paraphrase of what was to be analysed, in the form of a longer, more explicit, but strictly synonymous phrase or sentence. 1960 [see analysandum].

c. philosophical analysis: as a branch of Philosophy, that conducted by means of, or understood as consisting in, analysis (senses a or b); philosophy concerned with the clarification of existing concepts and knowledge, by a method of reformulation, rather than with conceptual revision or addition to knowledge; esp. the analytic movement associated with Bertrand Russell, Moore, Wittgenstein and others.

1843 Mill Logic I. ii. ii. 238 Philosophical analysis confirms the indication of common sense, that the function of names is but that of enabling us to remember and to communicate our thoughts. 1887 S. H. Hodgson Let. 8 Apr. in R. B. Perry Tht. & Char. W. James (1935) I. 642 What is ‘the mind’?‥ I suspect it is a mere façon de parler‥which has a basis neither in psychological construction nor in philosophical analysis. 1936 Ayer Lang., Truth & Logic ii. 62 The possibility of philosophical analysis is independent of any empirical assumptions. 1943 Mind LII. 275 The subject [sc. mathematical logic]‥ may claim an important place in the corpus of philosophical analysis. 1956 J. O. Urmson (title) Philosophical Analysis: Its development between the two world wars.

10. Mus. A critical description of a musical work, designed to make clear its structure.

1885 [see analyse v. 8]. 1935 D. F. Tovey Ess. Mus. Analysis I. 1 Some of the analyses‥were written on occasions where there was no opportunity for musical quotations.

11. Psychol. The mental process of discrimination, by separate attention, of the separable elements in a totality of simultaneous sensory impressions, or in any other complex experience.

1890 W. James Princ. Psychol. I. xiii. 502 Our first way of looking at a reality is often to suppose it simple, but later we may learn to perceive it as compound. This new way of knowing the same reality may conveniently be called by the name of Analysis. It is manifestly one of the most incessantly performed of all our mental processes. 1938 R. S. Woodworth Exper. Psychol. xxv. 645 To judge the lines and angles of a figure requires analysis which is difficult because the observer is engrossed in the appearance of the figure as a whole.

12. Psychiatry. Short for psychoanalysis.

1907 Brain XXX. 179 In hysteria with very little trouble the complex may be revealed by analysis, and with a good prospect of therapeutic advantage. 1912 A. A. Brill tr. Freud's Sel. Papers on Hysteria (ed. 2) iv. 76 It is very difficult to examine a case of neurosis before it has been subjected to a thorough analysis. 1913 Lancet 10 May 1345/2 Analysis might record some latent content having nothing to do with hunting and would perhaps show Dr. Brown that he no more fears hunting in dreams than he does awake. 1916 C. E. Long tr. Jung's Analytical Psychol. vii. 208 An attempt has‥been made to compare analysis with the reasoning method of Dubois, which is in itself a rational process. This comparison does not‥hold good, for the psychoanalyst strictly avoids argument and persuasion with his patients. 1958 Spectator 1 Aug. 160/1 He [sc. Freud] was always attracted by telepathy (so much so that he alarmed his English followers, who feared that it would give their enemies an excuse to sneer at analysis as occultism).