Welcome to the Svobodny Historical Sketches: Calculus I
The Greeks, especially Archimedes, were able to construct the tangent line to a given point on many different curves, including conics and spirals. However this became much easier to do after the development of the theory of algebraic curves of Chuquet and Viete, and the development of the modern number system by Stevin and Napier. It became particularly easy after the invention of Anaytic Geometry of Descartes.
Using the coordinates of Descartes, and improving on some early attempts of Cavalieri, Roberval and Napier, Fermat was able to compute the tanget and to attach significance to it. For example, he developed the notion of maxima and minima. As a matter of fact, Fermat was able to solve many of the problems that the student in Calc I solves. Fermat is clearly the hero of Calc I.
About this time, Mechanics started to develop. With the inspiration of Copernicus and Leonardo, Galileo carried out experiments, in an attempt to find fundamental laws of Mechanics. He defined velocity and showed, using functions, the difference between uniform motion and motion subject to a uniform force. Also about this time, Kepler discovered the laws of planetary motion.
The
notion of Derivative as a limit of slopes of lines secant to the graph
of a function seems to be due to Torricelli and Barrow. Barrow was the
teacher of Newton.They, along with Leibniz are the heroes of Calc II.
However, the modern understanding of limit had to wait until Bolzano.
