I am working with hyperbolic functions and was wondering where they actually came from. I am under the understanding that Ricotta (and I think Johann Heinrich Lambert also did work in this area), did major work in this area however I am wondering how he got to the final definition of sinh and cosh using the exponential function.
Did Ricotta or Lambert ever publish a research paper which I can access somehow? I really want to understand where they come from (or if someone can show me).
Another question I had was why people required finding the Taylor expansion for both sing and cosh, what is the purpose? Why is it useful?
Thank you so much,
A rather complete history in Enter, Stage Center: The Early Drama of the Hyperbolic Functions.