# Why were mathematicians interested in tangents ( before calculus was discovered)? ( On the origin of differential calculus)

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?

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