Definition:Integral Sign/Historical Note

Historical Note on Integral Sign

The integral sign $\ds \int \ldots \rd x$ 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 $\d$.

Thus he was soon writing $\d x$ and $\d y$, and $\ds \int \ldots \rd x$ 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 ($\text {1646}$ – $\text {1716}$)
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $8$: The System of the World: Leibniz