I recently delved into a discussion about a statement attributed to the renowned mathematician and philosopher, Benjamin Peirce. In this statement, he refers to mathematics as "the science that draws necessary conditions." This has piqued my curiosity about the linguistic origins and historical context of the term "necessary condition" in mathematics.
Interpreting "$q$ is a necessary condition for $p$" seems to be a formal way to express that "$p$ implies $q$" ($p \Rightarrow q$). This realization has led me to several questions:
Main question: Who was the first person that introduced the term "necessary condition" in mathematical discourse?
second important related question: Was there a specific rationale or historical backdrop that necessitated the introduction of this term?
How has the understanding and utilization of this term evolved in the landscape of mathematical language over time?
I am genuinely interested in uncovering the historical nuances surrounding the inception and adoption of this phrase in the mathematical community.