# Fundamental Theorem of Calculus/Historical Note

## Historical Note on the Fundamental Theorem of Calculus

In $1668$, James Gregory published *Geometriae Pars Universalis*, in which the Fundamental Theorem of Calculus first makes its appearance, although only for a limited class of functions.

It is believed that the earliest complete statement and proof was made by Isaac Newton.

This can be seen in a letter to Leibniz from $1676$ or $1677$, collected as item $190$ of 1959 -- 1961: H.W. Turnbull: *The Correspondence of Isaac Newton*.

Isaac Barrow is also cited by some as being the first to establish it.

Leibniz himself, in his own turn, claimed to have made the same startling realisation on reading Blaise Pascal's $1658$ work *Traité des Sinus du Quart de Cercle*.

In Leibniz's $1684$ article *Nova Methodus pro Maximis et Minimis*, published in *Acta Eruditorum*, he takes this result as given, stating that $\int$ and $\mathrm d$ are each other's converse, with no attempt at proof.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VII}$: Master of All Trades - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3$: Appendix $\text B$: Newton: Footnote $1$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.18$: Newton ($1642$ – $1727$): Footnote $2$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($1646$ – $1716$)