The road to calculus is steadily being built. Mathematicians are constantly making breakthroughs but they could not do it if the foundation had not been laid down properly. The very first stones of the road were laid down in Greece, as are most of the foundations for math. The first stone was laid down in 450B.C. Calculus has traveled a long road since then, with a lot of stones placed in the foundations by various mathematicians.
Zeno of Elea(450B.C.) was the first person to place a stone on the road to calculus. He gave the world problems concerning the infinite. He said that motion was impossible because a body could not move anywhere. That everyplace a body moved to it had to reach the midpoint before it could reach the destination. That no matter what point the body was on there would always be another midpoint to go through. Leucippus, Democritus, and Antiphon were the next ones to place stones on the road.
They all contributed in their own way to the method of exhaustion. Following them on the road was Eudoxus(370B.C.).He placed the method of exhaustion on a scientific basis.
Archimedes(225B.C.) was one of the most influential gentlemen to work on the foundation of the road to calculus. All of his work involved area and volume. H invented an early example of integration to come up with the area of a circle and a parabola. He integrated the volume and surface areas of a sphere, cone, the surface area of an ellipse, as well as many others.
Luca Valerio(1606) was the next person to place a stone on the road t6o calculus. He published 'De quadratura parabolae', it involved problems involving gravity. Kepler came along at about the same time. He used a crude form of integration to...