# Definition:Integral Sign/Historical Note

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## Historical Note on Integral Sign

The integral sign $\displaystyle \int \ldots \rd x$ originated with Gottfried Wilhelm von Leibniz

In a manuscript dated $29$th October $1675$ he introduced a long letter $S$ to suggest the first letter of the word **summa** (Latin for **sum**).

At the time he was using the notation $\operatorname {omn} l$ (that is: **omnes lineae**, meaning **all lines**).

Then he noted:

*It will be useful to write $\int$ for $\operatorname {omn}$, thus $\int \, l$ for $\operatorname {omn} l$, that is, the sum of those $l$'s.*

At the same time he introduced the differential symbol $\rd$.

Thus he was soon writing $\rd x$, $\rd y$, and $\int \ldots \rd x$ soon followed.

In his $1684$ article *Nova Methodus pro Maximis et Minimis*, published in *Acta Eruditorum*, he casually drops the notation in place with very little explanation.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($1646$ – $1716$) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World: Leibniz