The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
6. Fourthly, in what time soever the movent, whose centre is A (in fig.
2) moved in K L N, shall, by any number of revolutions, that is, when
the perimeters B I and K L N be commensurable, have described a line
equal to the circle which passes through the points B and I; in the same
time all the points of the floating body, whose centre is B, shall
return to have the same situation in respect of the movent, from which
they departed. For seeing it is as the distance B A, that is, as the
radius of the circle which passes through B I is to the perimeter itself
B I, so the radius of the circle K L N is to the perimeter K L N; and
seeing the velocities of the points B and K are equal, the time also of
the revolution in I B to the time of one revolution in K L N, will be as
the perimeter B I to the perimeter K L N; and therefore so many
revolutions in K L N, as together taken are equal to the perimeter B I,
will be finished in the same time in which the whole perimeter B I is
finished; and therefore also the points L, N, F and H, or any of the
rest, will in the same time return to the same situation from which they
departed; and this may be demonstrated, whatsoever be the points
considered. Wherefore all the points shall in that time return to the
same situation; which was to be proved.
From hence it follows, that if the perimeters B I and L K N be not
commensurable, then all the points will never return to have the same
situation or configuration in respect of one another.
[Sidenote: If a sphere have simple motion, its motion will more
dissipate heterogeneous bodies by how much it is more remote
from the poles.]
7. In simple motion, if the body moved be of a spherical figure, it hath
less force towards its poles than towards its middle to dissipate
heterogeneous, or to congregate homogeneous bodies.