THEOREME III.

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.

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

[Figure 3]

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 abſo

lute 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 pro

portion as the aſcent of the Priſme when it riſeth, hath to the deſcent

of the water circumfuſed C E.

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

[Figure 3]

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 abſo

lute 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 pro

portion as the aſcent of the Priſme when it riſeth, hath to the deſcent

of the water circumfuſed C E.

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 re

fiſts the repulſe and violence done it by the Moment of the water:

Therefore, the Priſme ſhall be raiſed.

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 re

fiſts the repulſe and violence done it by the Moment of the water:

Therefore, the Priſme ſhall be raiſed.

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.

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.