Why "integralis" over "summatorius"?

It is written that Johann Bernoulli suggested to Leibniz that he (Leibniz) change the name of his calculus from "calculus summatorius" to "calculus integralis", but I cannot find their correspondence wherein Bernoulli explains why he thinks "integralis" is preferable to "summatorius." Can someone enlighten me? Thank you.

Solution 1:

Bernoulli writes this to Leibniz in 20/30 April 1695. His justification for this choice of words is that "differentials are part of a whole" ("integer" being Latin for whole).

Leibniz replies (6/16 May 1695) that this appellation does not displease him, but that he considers his preferred term "sum" more illuminating and closer to the source of the notion.

See the Akademie-Ausgabe, III6A, pp. 348, 356: http://www.leibniz-edition.de/Baende/ReiheIII.htm

Solution 2:

If you wanted the correspondence. Maybe, this would be sure, the initial quotation states the exact point. As for the reason, some say that it was to rival Newton on proving that he had invented calculus first. The Bernoulli's too were involved in the controversy.This page explains the controversy.