I think it is often said that one great motivation for the invention of calculus was to have a tool allowing to calculate the slope of a tangent to a curve C at a given point P, and even, to find the equation of this tangent.

What made this goal so important for mathematicians ( and more broadly for scientists) at that time?

In which contexts did the tangent-problem reveal so crucial?

  • $\begingroup$ Euclid has tangents to circles. Archimedes has tangents to parabolas. $\endgroup$ – Gerald Edgar Nov 24 '19 at 13:19

I'd imagine that part of the reason tangents were so important was that they were of the easiest ways to calculate the rate of something.

Since many scientists were working on physics questions (esp. classical mechanics) at the time, I would imagine that rates were instrumental to those theories.

I would rather put this down as a comment rather than an answer, but I don't have enough reputation. I hope this helps!

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