_A Prisme or regular Cylinder, of a substance specifically less
grave than Water, if it should be totally submerged in Water,
stayes not underneath, but riseth, though the Water circumfused
be very little, and in absolute Gravity, never so much inferiour
to the Gravity of the said Prisme._
Let then the Prisme A E F B, be put into the Vessell C D F B, the same
being less grave _in specie_ than the Water: and let the Water infused
rise to the height of the Prisme: I say, that the Prisme left at
liberty, it shall rise, being born up by the Water circumfused C D E
A. For the Water C E being specifically more grave than the Solid A F,
the absolute weight of the water C E, shall have greater proportion to
the absolute weight of the Prisme A F, than the Mass C E hath to the
Mass A F (in regard the Mass hath the same proportion to the Mass,
that the weight absolute hath to the weight absolute, in case the
Masses are of the same Gravity _in specie_.) But the Mass C E is to
the Mass A F, as the Surface of the water A C, is to the Superficies,
or Base of the Prisme A B; which is the same proportion as the ascent
of the Prisme when it riseth, hath to the descent of the Water
circumfused C E.
[Illustration]
Therefore, the absolute Gravity of the water C E, hath greater
proportion to the absolute Gravity of the Prisme A F; than the Ascent
of the Prisme A F, hath to the descent of the said water C E. The
Moment, therefore, compounded of the absolute Gravity of the water C
E, and of the Velocity of its descent, whilst it forceably repulseth
and raiseth the Solid A F, is greater than the Moment compounded of
the absolute Gravity of the Prisme A F, and of the Tardity of its
ascent, with which Moment it contrasts and resists the repulse and
violence done it by the Moment of the water: Therefore, the Prisme
shall be raised.
[Sidenote: The Proportion according to which the Submersion &
Natation of Solids is made.]
It followes, now, that we proceed forward to demonstrate more
particularly, how much such Solids shall be inferiour in Gravity to
the water elevated; namely, what part of them shall rest submerged,
and what shall be visible above the Surface of the water: but first it
is necessary to demonstrate the subsequent Lemma.