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This is a historical and lighthearted question about etymology.

The area of mathematics that deals with limiting processes over real numbers (Real Analysis) or real vector spaces, or even complex vector spaces (I think it depends on who you ask) is variably referred to as "analysis" or "the Calculus".

My question is, why did this particular area of math get the somewhat grandiose name The Calculus, which, if taken literally, means something like "The way to reason". It seems like linear algebra, geometry, logic, and many other formal systems are just as worthy of this title in their areas of application, yet the mathematics that was developed by Newton, Leibniz, Weierstrass & Co. has taken this moniker without contest.

Any anyone fill in the history of why this particular branch of mathematics got this title? I know calculus is a great achievement, has lots of applications, etc...but I don't think that is the reason.

Half-jokingly, maybe it was just good marketing on the developers of Calculus...give it a great name so people pay attention to it ;-)

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The original latin name fluctuated between calculus and analysis from the beginning.

See:

De Geometría recondita et Analysi Indivisibilium atque infinitorum (Act.Erud.Lips., 1686)

Nova Calculi differentials applicatio et usus ad multiplicem linearum constructionem ex data Tangentium conditione (Act.Erudit.Lips., 1694).

See also:

Quid sit Calculus Differentialis , atque in genere Analysis Infinitorum ?

In the English speaking countries, "calculus" prevailed, while in many others the "local equivalent" of "analysis" is used.


See later:

the general project is a Cours d'analyse including the calcul infinitésimal, in turn composed of: calcul différentiel and calcul intégral.

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Calculus in the general sense is used to mean a system of reckoning or calculation. "The calculus" is a nowadays old-fashioned locution for the mother of all calculi, and an abbreviation of longer phrases like "the calculus of infinitesimals" that refer to the same. The phrase implies the possibility of other forms of calculus, such as (the) calculus of finite differences.

https://en.wikipedia.org/wiki/Calculus_%28disambiguation%29

The list of calculi at Wikipedia is far from complete. There are Kirby calculus (topology), Goodwillie calculus / calculus of functors (topology), calculus of fractions (category theory), stochastic calculus, Fox calculus (algebra), various things proposed as noncommutative "calculus", ...

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