Evanescent Increments

What are evanescent increments?

Part of the beauty of Calculus is– I don’t really know.  Not tangible, supremely debatable– Newton named them as a measure of the ratio of fluxions.

What seems like a million years ago in our information age, Berkeley scoffed at the idea.  And here is somewhere I find the absolute poetry of calculus.

It must, indeed, be acknowledged, that [Newton] used Fluxions, like the Scaffold of a building, as things to be laid aside or got rid of, as soon as finite Lines were found proportional to them. But then these finite Exponents are found by the help of Fluxions. Whatever therefore is got by such Exponents and Proportions is to be ascribed to Fluxions: which must therefore be previously understood. And what are these Fluxions?
The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the Ghosts of departed Quantities?

Maybe you can tell me exactly what an evanescent increment is; to me, they are a nebulous symbol of beauty quantifying the imaginary unknown.


Math is the meaning of life.

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