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

46 INTRODUCTION TO MATHEMATICS
held by Kepler, the actual velocity itself required preservation by force. Thus he looked
for tangential forces, as in the accompanying
figure (4). But according to the Newtonian
law, apart from some force the planet would
move for ever with its existing velocity in a
straight line, and thus depart entirely from
the sun. Newton, therefore, had to search
for a force which would bend the motion
Planet
f;/~Torce
Sun
Fig. 5.
round into its elliptical orbit. This he showed
must be a force directed towards the sun, as in
the next figure (5). In fact, the force is the
gravitational attraction of the sun acting
according to the law of the inverse square of
the distance, which has been stated above.
The science of mechanics rose among the
Greeks from a consideration of the theory of
the mechanical advantage obtained by the