Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. differential calculus
from the GNU version of the Collaborative International Dictionary of English
 n.pl. See fluxion, 6(b).
Etymologies
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Examples

In Germany Mr. Leibnitz was considered as the inventor of the differences or moments, called fluxions, and Mr. Bernoulli claimed the integral calculus.
Letter XVIIOn Infinites in Geometry, and Sir Isaac Newton’s Chronology

Between French, therefore, and fluxions, and moreover, the French method of fluxions, which is somewhat peculiar, I have had my hands pretty full.
Memoirs of 30 Years with the Indian Tribes on the American Frontiers

In Germany Mr. Leibnitz was considered as the inventor of the differences or moments, called fluxions, and Mr. Bernouilli claimed the integral calculus.

This is, as any troglodyte with an abacus can tell you, that branch of fluxions pertaining to the bits of reality that are changing too fast for the proper application of regular fluxions.

He integrated Leibniz's differential calculus and Newton's method of fluxions into mathematical analysis.

And I've forgotten all the fluxions I ever learned.

The problem of determining a tangent to a curve is transformed into the problem of finding the relationship between the fluxions xÂ· and zÂ· when presented with an equation representing the relationship between the fluents x and z.

De quadratura curvarum he remarks that there is no necessity to introduce into the method of fluxions any argument about infinitely small quantities.

(A quadrature is the inverse problem, that of determining the fluents when the fluxions are given.)

“There is no space in void,” exclaimed Leibnitz, after having admitted a void; but when he admitted a void, he had not embroiled himself with Newton, nor disputed with him on the calculus of fluxions, of which Newton was the inventor.
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stpeter commented on the word fluxions
"Nature and Nature's Laws lay hid in night;
God said, 'Let Newton be!'  And all was light."
December 16, 2008