# Who introduced the finite difference notation using $\Delta$?

We all know that Leibniz introduced the differential notation $dx, dy$, and that in developing his calculus for infinitesimal differences he was inspired by his previous work on finite diffences. Today we usually denote such finite differences $\Delta x, \Delta y$. But did Leibniz use this notation? If not, who originated it?

• Does it even matter? The word difference obviously starts with a d, so the Greek letter delta seems like an appropriate choice, as does the differential d in calculus. – Lucian Apr 30 '14 at 12:54
• First uses of mathematical terms are of interest to many people and there is even a well-developed site. The history of notation has also interested many historians, e.g. F. Cajori. – Mikhail Katz Apr 30 '14 at 13:10

According to Florian Cajori, A history of mathematical notations (1928 - Dover reprint) :

"A provisional, temporary notation $\Delta$ for differential coefficient or différences des fonctions was used in 1706 by Johann Bernoulli." (see Cajori, page 205 of 2nd vol).

L.Euler introduced the symbolism for finite differences in Institutiones calculi differentialis (Petersburgh, 1755), p.3-7 (see Cajori, page 265).