Why does “propositional calculus” have the word “calculus” in it?

Question

We define “calculus” like this:

“Calculus is the mathematical study of continuous change.”

But if that’s the case, then why is the study of (true or false) propositions and their relations called:

“Propositional calculus”?

These are some example statements from both fields:

This is something from calculus: $\int_{0}^{3} x^2 dx = 3$

This is something from propositional calculus: $((A \rightarrow B)\land A) \rightarrow B$

What I know from a historical standpoint is that “calculus” was originally a word for “small pebble” and then evolved into a word for “calculation”. However, I also know that propositional calculus was developed somewhere in the 19th century, which is way after calculus was used for “calculation”.

Why are both of these using the term “calculus”? Is its meaning as “calculation” related?

Answer 1

Definition :

Douglas N. Clark "DICTIONARY of Analysis, Calculus, and Differential Equations" gives this Entry, with my highlighting and emphasis:

calculus (1.) The study of properties of
functions of one or several variables, using
derivatives and integrals. Differential calcu-
lus usually refers to the one variable study
of the derivative and its applications and in-
tegral calculus to the study of the Riemann
integral of a function of one variable. Classi-
cally, it has been referred to as "the" calculus.
(2.) Any system of computations based upon
some unifying idea, such as the calculus of
residues or calculus of variations.

Overview :

Etymologically , "calculi" & "calculus" come from PEBBLE which was used for measuring geographical distances and such.
[[ Currently, "calculate" is the most general term covering all mathematical computations and even more. ]]

With that came "infinitesimal calculus" , which is generally shortened to just "calculus" , the most common abd well known type.

• "Propositional Calculus" involves calculating truth values of Statements , hence it uses the word "Calculus".
• We have "Predicate Calculus" , where we calculate truth values with Statements involving various quantifiers & variables.
• "Variational Calculus" is concerned with calculating & optimizing functionals.
• "Lambda Calculus" is the mathematical theory of computation the calculations involve Expressions, variables, functions, and various abstractions including Turing Machines.
  In general, these terms are not shortened.

All these are about calculations and computations, within various domains.

Summary:

When we have "W Calculus" or "X Calculus" or "Y Calculus" or "Z Calculus", we make calculations involving type W or type X or type Y or type Z. To avoid confusion, we do not shorten it.

When we have "infinitesimal calculus", we make calculations involving infinitesimal quantities, ratios, limits & real numbers. We shorten that to just "calculus" since it is the most common.

Answer 2

The proper term for the study of integrals, derivatives, etc, is "differential calculus". It is incorrectly shortened to "calculus". You can probably tell from words like "calculator" or "calculation" that "calculus" can refer to a lot more than methods of manipulating differentials.