What does the word "analysis" mean when we say real/mathematical analysis or analytic geometry?

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The choice of the word "analysis" has always confounded me. Is it because we're literally analyzing mathematical objects/relationships till we have a clear understanding of things?

Is it quite literally "to analyze" that we have this word or is there more to it than meets the eye?

I can "grossly simplify" analysis into saying "algebraic/arithmetic POV" devoid of geometry. However, why was the word "analysis" chosen and when did it first become formally attached to the various fields?