It took us about 45 minutes to find the answer this evening. Apparently Leibniz came up with the word calculus in conjunction with various suffix words to describe the new concepts he had worked out:
calculus differentialis became the method for finding tangents and the calculus summatorius or calculus integralis the method for finding areas.The etymology of calculus comes from the Latin calx meaning stone. The diminutive, calculi, indicates tiny stones, which people used for counting purposes. The words calculation thus came about to describe all manners of addition, subtraction, and so forth. Leibniz apparently chose the word calculus to describe a new manner of counting to arrive at solutions to problems. He used the phrases in his works published in 1684 and 1686.
Link:
http://www.math10.com/en/maths-history/history5/origins-differential-integral2.html
http://www-history.mcs.st-andrews.ac.uk/PrintHT/The_rise_of_calculus.html
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