No, we have no proof of that. We just know that she published a paper explaining the trapezoidal rule.
(A) That approximation for 'nice' curves was known long before calculus. Calculus is about doing this in the limit (or with infinitesimals or whatever) and also wondering about mathematical niceties, and also some things about integration. (B) I'm fairly certain she would have had a bit of calculus at some point in her education, even if she remembered it badly enough to think she found something new.
I mean, it's possible she reinvented the wheel because what she really needed in her life is for the math department to laugh at her, but that seems far fetched to me.
No, we have no proof of that. We just know that she published a paper explaining the trapezoidal rule.
(A) That approximation for 'nice' curves was known long before calculus. Calculus is about doing this in the limit (or with infinitesimals or whatever) and also wondering about mathematical niceties, and also some things about integration. (B) I'm fairly certain she would have had a bit of calculus at some point in her education, even if she remembered it badly enough to think she found something new.