detailed examination of the elements or structure of something.

Merriam-Webster Online Dictionary
analysis (noun)
separation of a whole into its parts - component
a) the identification or separation of ingredients of a substance
b) a statement of the of a mixture - constituents
a) of a mathematical proposition by assuming the result and deducing a valid statement by a series of reversible steps - proof
b) (1) a branch of mathematics concerned mainly with limits, , and infinite series - continuity
(2) - calculus
a) an examination of a , its elements, and their relations - complex
b) a statement of such an analysis
a) a method in philosophy of resolving complex expressions into simpler or more basic ones
b) clarification of an expression by an of its use in discourse - elucidation
the use of instead of inflectional forms as a characteristic device of a language - function words
- psychoanalysis
analysis (Wikipedia)
For other uses, see Analysis (disambiguation).

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.

The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking up", from ana- "up, throughout" and lysis "a loosening").

As a formal concept, the method has variously been ascribed to Alhazen,René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).

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