THEOREME IV.

If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically

than the Water, being put into a Veſſel, as above, of

whatſoever greatneſſe, and the Water, be afterwards

infuſed, the Solid ſhall reſt in the bottom, unraiſed, till

the Water arrive to that part of the Altitude, of the

ſaid Priſme, to which its whole Altitude hath the

ſame proportion, that the Specificall Gravity of the

Water, hath to the Specificall Gravity of the ſaid

Solid: but infuſing more Water, the Solid ſhall aſcend.

than the Water, being put into a Veſſel, as above, of

whatſoever greatneſſe, and the Water, be afterwards

infuſed, the Solid ſhall reſt in the bottom, unraiſed, till

the Water arrive to that part of the Altitude, of the

ſaid Priſme, to which its whole Altitude hath the

ſame proportion, that the Specificall Gravity of the

Water, hath to the Specificall Gravity of the ſaid

Solid: but infuſing more Water, the Solid ſhall aſcend.

Let the Veſſell be M L G N of any bigneſs, and let there be pla

ced in it the Solid Priſme D F G E, leſs grave in ſpecie than the

water; and look what proportion the Specificall Gravity of

the water, hath to that of the Priſme, ſuch let the Altitude D F, have

to the Altitude F B. I ſay, that infuſing water to the Altitude F B,

the Solid D G ſhall not float, but ſhall ſtand in Equilibrium, ſo, that

that every little quantity of water, that is infuſed, ſhall raiſe it. Let

the water, therefore, be infuſed to the Levell A B C, and, becauſe

the Specifick Gravity of the Solid D G, is to the Specifick Gravity of

the water, as the altitude B F is to the altitude F D; that is, as the Maſs

B G to the Maſs G D; as the proportion of the Maſs B G is to the

Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they

compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore,

the Maſs B G is to the Maſs A F, in a proportion compounded of the

proportions of the Specifick Gravity of the Solid G D, to the Speci

fick Gravity of the water, and of the Maſs G D

to the Maſs A F: But the ſame proportions

[Figure 5]

of the Specifick Gravity of G D, to the Specifick

Gravity of the water, and of the Maſs G D to

the Maſs A F, do alſo by the precedent Lemma,

compound the proportion of the abſolute Gra

vity of the Solid D G, to the abſolute Gravity

of the Maſs of the water A F: Therefore,

as the Maſs B G is to the Maſs A F, ſo is the

Abſolute Gravity of the Solid D G, to the Ab

ſolute Gravity of the Maſs of the water A F. But as the Maſs B G

is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface

of the water AB; and ſo is the deſcent of the water A B, to the

Elevation of the Priſme D G; Therefore, the deſcent of the

ced in it the Solid Priſme D F G E, leſs grave in ſpecie than the

water; and look what proportion the Specificall Gravity of

the water, hath to that of the Priſme, ſuch let the Altitude D F, have

to the Altitude F B. I ſay, that infuſing water to the Altitude F B,

the Solid D G ſhall not float, but ſhall ſtand in Equilibrium, ſo, that

that every little quantity of water, that is infuſed, ſhall raiſe it. Let

the water, therefore, be infuſed to the Levell A B C, and, becauſe

the Specifick Gravity of the Solid D G, is to the Specifick Gravity of

the water, as the altitude B F is to the altitude F D; that is, as the Maſs

B G to the Maſs G D; as the proportion of the Maſs B G is to the

Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they

compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore,

the Maſs B G is to the Maſs A F, in a proportion compounded of the

proportions of the Specifick Gravity of the Solid G D, to the Speci

fick Gravity of the water, and of the Maſs G D

to the Maſs A F: But the ſame proportions

[Figure 5]

of the Specifick Gravity of G D, to the Specifick

Gravity of the water, and of the Maſs G D to

the Maſs A F, do alſo by the precedent Lemma,

compound the proportion of the abſolute Gra

vity of the Solid D G, to the abſolute Gravity

of the Maſs of the water A F: Therefore,

as the Maſs B G is to the Maſs A F, ſo is the

Abſolute Gravity of the Solid D G, to the Ab

ſolute Gravity of the Maſs of the water A F. But as the Maſs B G

is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface

of the water AB; and ſo is the deſcent of the water A B, to the

Elevation of the Priſme D G; Therefore, the deſcent of the