He developed Hudde's Rule involving the derivative and provided an ingenious method to find multiple roots of an equation. Johann Hudde (1628 - 1704) worked on maxima and minima and the theory of equations. Bonaventura Cavalieri (1598 - 1647) developed a method of indivisibles, an important factor in the development of the integral calculus.įact 8: Who invented Calculus? The Renaissance Scientists: Rene Descartes (1596 - 1650) developed an important method of determining normals based on double intersection. Gilles Roberval (1602 - 1675) developed significant methods in the study of integration. Johannes Kepler (1571 - 1630) provided three fundamental laws of planetary motion and worked on a basic form of integration.įact 7: Who invented Calculus? The Renaissance Scientists: Pierre de Fermat (1601 - 1665) was famous for his work in number theory. Luca Valerio (1552 - 1618) worked to find volumes and centres of gravity of solid bodies. Archimedes was a genius in geometry and his methods anticipated the integral calculus 2,000 years before Gottfried Leibniz and Sir Isaac Newton.įact 6: Who invented Calculus? The Renaissance Scientists: Important Renaissance mathematicians and scientists made significant advances in the invention of Calculus. Leucippus and Democritus originated the atomic theory of indivisibles.įact 5: Who invented Calculus? The Greeks: Eudoxus was a Greek astronomer who mapped the stars and compiled a map of the known world. It is broken into two subgroups called differential calculus and integral calculus.įact 4: Who invented Calculus? The Greeks: Zeno of Elea was a famous Greek philosopher who posed so-called paradoxes about motion to challenge the ideas of Greek mathematicians. Calculus helps formulate concepts and predictions through the use of limits, derivatives, integrals, functions and astronomy. As we will see later this assumption leads to difficulties.īoth Newton and Leibniz were satisfied that their calculus provided answers that agreed with what was known at the time.Fact 1: Who invented Calculus? Calculus was invented independently by Isaac Newton and Gottfried Leibniz in the mid 1700's during the Industrial Revolution era of inventions (1700 - 1860).įact 2: Who invented Calculus? Although both Isaac Newton and Gottfried Leibniz are credited with the invention the first steps were taken by Ancient Greek mathematicians such as Zeno of Elea, Leucippus, Democritus, Eudoxus and Archimedes.įact 3: Who invented Calculus? Prominent Renaissance mathematicians and scientists such as Luca Valerio, Johannes Kepler, Pierre de Fermat, Gilles Roberval, Rene Descartes, Johann Hudde, Christiaan Huygens, Bonaventura Cavalieri, Evangelista Torricelli and Isaac Barrow also played a significant role in the invention.įact 3: Who invented Calculus? Calculus is used in the present day to help formulate concepts such as as heat, motion, electricity and light. This was consistent with the thinking of the time and for the duration of this chapter we will also assume that all quantities are differentiable. In a sense, these topics were not necessary at the time, as Leibniz and Newton both assumed that the curves they dealt with had tangent lines and, in fact, Leibniz explicitly used the tangent line to relate two differential quantities. In fact, the term derivative was not coined until 1797, by Lagrange. Notice that there is no mention of limits of difference quotients or derivatives. You may decide for yourself how convincing his demonstration is. His attention there was on physics, not math, so he was really just trying to give a convincing demonstration of his methods. In Newton’s defense, he wasn’t really trying to justify his mathematical methods in the Principia. If we take any other increments in \(x\) and \(v\) whose total lengths are \(∆x\) and \(∆v\) it will simply not work. This argument is no better than Leibniz’s as it relies heavily on the number \(1/2\) to make it work. Which is the total change of \(R = xv\) over the intervals \(∆x\) and \(∆v\) and also recognizably the Product Rule.
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