When Newton left Cambridge in April 1696 to take up, at the age of
53, a new career at the London Mint, he did not entirely 'leave off
Mathematicks' as he so often publicly declared. This last volume of
his mathematical papers presents the extant record of the
investigations which for one reason and another he pursued during
the last quarter of his life. In January 1697 Newton was tempted to
respond to two challenges issued by Johann Bernoulli to the
international community of mathematicians, one the celebrated
problem of identifying the brachistochrone; both he resolved within
the space of an evening, producing an elegant construction of the
cycloid which he identified to be the curve of fall in least time.
In the autumn of 1703, the appearance of work on 'inverse fluxions'
by George Cheyne similarly provoked him to prepare his own
ten-year-old treatise De Quadratura Curvarum for publication, and
more importantly to write a long introduction to it where he set
down what became his best-known statement of the nature and purpose
of his fluxional calculus.
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