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 a complete system. This tract was intended as an introduction to an edition of Kinckhuysen's Algebra, which he had undertaken to publish. "But the fear of being involved in disputes about this new discovery, or perhaps the wish to render it more complete, or to have the sole advantage of employing it in his physical researches, induced him to abandon this design."[33]

Excepting two papers on optics, all of his works appear to have been published only after the most pressing solicitations of his friends and against his own wishes.[34] His researches on light were severely criticised, and he wrote in 1675: "I was so persecuted with discussions arising out of my theory of light that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow."

The Method of Fluxions, translated by J. Colson from Newton's Latin, was first published in 1736, or sixty-five years after it was written. In it he explains first the expansion into series of fractional and irrational quantities,—a subject which, in his first years of study, received the most careful attention. He then proceeds to the solution of the two following mechanical problems, which constitute the pillars, so to speak, of the abstract calculus:—

"I. The length of the space described being continually (i.e. at all times) given; to find the velocity of the motion at any time proposed.

"II. The velocity of the motion being continually given; to find the length of the space described at any time proposed."

Preparatory to the solution, Newton says: "Thus, in the equation $\scriptstyle{y=x^2}$, if y represents the length of the space at any time described, which (time) another space x, by increasing with an uniform celerity $\scriptstyle{\dot x}$, measures and exhibits as described: then $$\scriptstyle{2x\dot x}$$ will represent the celerity by which the space y,