>In article <49A8C201.firstname.lastname@example.org>, > "Stephen J. Herschkorn" <email@example.com> wrote: > > > >>What is the history of the trick to find the indefinite integral of the >>secant function? Who first used it, and when? >> >> > >Which trick? >z = tan(x/2)? >Inverse gudermannian? > >The correspondence predates the invention of the formal >integral calculus. The same numbers appeared while compiling >tables for the loxodrome and for log(tan(x)). I imagine >that after the integral calculus was invented, there was >no mystery about int sec(x) dx. > I refer to the trick of noting that sec x = sec x (sec x + tan x) / (sec x + tan x). (I was teaching this the other day and pointed out that I would never expect the students to come up with this on their own.) I see what you are saying - people noticed a numerical identification in a different context, nearly two centuries before Newton and Leibniz. So mathematicians had a specific formula and could look for ways to derive it. I still wonder when this trick was first known. For example, does it go back to Newton or Leibniz?
This is one of the things that makes sci.math really great. For example, firstname.lastname@example.org points me to the page of an article on a different subject. Thanks for that.
-- Stephen J. Herschkorn email@example.com Math Tutor on the Internet and in Central New Jersey