the beginning of the year 1665 I found the Method of approximating
series & the Rule for reducing any dignity of any Binomial into such a series.
The same year in May I found the method of Tangents of Gregory & Slusius,
& in November had the direct method of fluxions & the next year in January
had the Theory of Colors & in May following I had entrance into the inverse
method of fluxions. And the same year I began to think of gravity extending
to the orb of the Moon & (having found out how to estimate the force with
which a globe revolving within a sphere presses the surface of the sphere)
from Kepler's rule of the periodical times of the Planets being in sesquialterate
proportion of their distances from the centers of their Orbs, I deduced that the
forces which keep the Planets in their Orbs must be reciprocally as the squares
of their distances from the centers about which they revolve: and thereby
compared the force requisite to keep the Moon in her Orb with the force
of gravity at the surface of the earth, and found them answer pretty nearly.
All this was in the two plague years of 1665 and 1666. For in those days
I was in the prime of my age of invention & minded Mathematics &
Philosophy more than at any time since."