How did the name "The Calculus" come about, was there a reason or just good marketing?
The original latin name fluctuated between calculus and analysis from the beginning.
See:
- Gottfried Wilhelm von Leibniz, Mathematische Schriften (ed.C.I.Gerhardt 1858):
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:
Leonhard Euler, Introductio in analysin infinitorum (1748)
Leonhard Euler, Institutiones calculi differentialis (1755):
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:
- Augustin-Louis Cauchy, Résumé des leçons sur le calcul infinitésimal (1823):
the general project is a Cours d'analyse including the calcul infinitésimal, in turn composed of: calcul différentiel and calcul intégral.
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", ...