An introduction to mathematics, by A. N. Whitehead.

CONIC SECTIONS 139
These laws proved to be only a stage towards a more fundamental development of
ideas. Newton (born 1642 A.D. and died
1727 A.D.) conceived the idea of universal
gravitation, namely, that any two pieces of
matter attract each other with a force proportional to the product of their masses and
inversely proportional to the square of their
distance from each other. This sweeping
general law, coupled with the three laws of
motion which he put into their final general
shape, proved adequate to explain all astronomical phenomena, including Kepler's laws,
and has formed the basis of modern physics.
Among other things he proved that comets
might move in very elongated ellipses, or in
parobolas, or in hyperbolas, which are nearly
parabolas. The comets which return-such
as Halley's comet-must, of course, move in
ellipses. But the essential step in the proof of
the law of gravitation, and even in the suggestion of its initial conception, was the verification of Kepler's laws connecting the
motions of the planets with the theory of
conic sections.
From the seventeenth century onwards the
abstract theory of the curves has shared in
the double renaissance of geometry due to
the introduction of coordinate geometry and
of projective geometry. In projective geometry the fundamental ideas cluster round