Newton's memorandum of the two plague years
In the beginning of the year 1665 I found the Method of approximating series
and the Rule for reducing any power of any Binomial into such a series.
The same year in May I found the method of Tangents of Gregory and Slusius,
and in November had the direct method of fluxions and the next year in
January had the Theory of colours and 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, and having found out how to
estimate the force with which a globe revolving within a sphere presses
the surface of the sphere, from Keplers Rule of the periodical times of
the Planets being in sesquialternate proportion of their distances from
the centers of their Orbs, 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 to 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 for invention and minded Mathematicks
and Philosophy more than at any time since.
What Mr Hugens has published
since about centrifugal forces I suppose he had before me. At length in
the winter between the years 1676 and 1677 I found the Proposition that
by a centrifugal force reciprocally as the square of the distance a
Planet must revolve in an Ellipsis about the center of the force placed
in the lower umbilicus of the Ellipsis and with the radius drawn to that
center describe areas proportional to the times. And in the winter
between the years 1683 and 1684 this Proposition with the Demonstration
was entered in the Register book of the Royal Society. And this is the
first instance upon record of any Proposition in the higher Geometry found
out by the Method in dispute. In the year 1689 Mr Leibnitz endeavouring
to rival me published a Demonstration of the same Proposition upon another
supposition but his Demonstration proved erroneous, for want of skill in
the Method.
The Great Plague of 1665-1666 killed close to 70,000 people in London,
about one-fourth of the population. Samuel Pepys recorded in his
Diary that "I have stayed in the city till about 7400 died in
one week and of them about 6000 of the plague, and little noise heard
day or night but tolling of bells." Cambridge University was closed
and Newton stayed at his family farm in Woolsthorpe.