# Definition:Differential Calculus/Historical Note

## Historical Note on Differential Calculus

The technique used by Archimedes of Syracuse to find the Tangent to Archimedean Spiral at Point is often suggested as anticipating the **differential calculus**.

Pierre de Fermat had the basic idea of differential calculus in its modern form in about $1628$ or $1629$, but he did not publish these ideas until a decade or so later.

Much of the early work developing **differential calculus** was done by Isaac Newton.

His initial work on this was done during the years $1665$ to $1667$ when he was at home in Woolsthorpe.

He suggested that Isaac Barrow include his ideas in his *Lectiones Geometricae* of $1670$.

Newton referred to a function as a **fluent**, and its derivative as a **fluxion**.

At the same time that Newton was arranging his thesis, Gottfried Wilhelm von Leibniz was publishing many papers himself on the same subject.

H.T.H. Piaggio states that Leibniz first published his account of **differential calculus** in $1684$.

Newton, on the other hand, finally published his ideas in his *Philosophiae Naturalis Principia Mathematica* in $1687$.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs - 1952: H.T.H. Piaggio:
*An Elementary Treatise on Differential Equations and their Applications*(revised ed.) ... (previous) ... (next): Historical Introduction - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3$: Appendix $\text B$: Newton - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.18$: Newton ($\text {1642}$ – $\text {1727}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**calculus** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**calculus**