1the Superficies that proceed according to the Circumferences X O

and P O are equally preſſed; whereby the Gravity preſſed is equal.

233[Figure 233]

But the Gravity of the

Liquid which is in the

firſt Pyramid ^{*} without

the Solid B H T G, is

equal to the Gravity of

the Liquid which is in

the other Pyramid with

out the Liquid R S C Y:

It is manifeſt, therefore,

that the Gravity of the Solid E Z H T, is equal to the Gravity of

the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor

equal in Maſs to the part of the Solid ſubmerged is equal in Gra

vity to the whole Solid.

and P O are equally preſſed; whereby the Gravity preſſed is equal.

233[Figure 233]

But the Gravity of the

Liquid which is in the

firſt Pyramid ^{*} without

the Solid B H T G, is

equal to the Gravity of

the Liquid which is in

the other Pyramid with

out the Liquid R S C Y:

It is manifeſt, therefore,

that the Gravity of the Solid E Z H T, is equal to the Gravity of

the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor

equal in Maſs to the part of the Solid ſubmerged is equal in Gra

vity to the whole Solid.

* Without, i.e. that

being deducted.

being deducted.

RIC. This was a pretty Demonſtration, and becauſe I very well underſtand

it, let us loſe no time, but proceed to the ſixth Propoſition, ſpeaking thus.

it, let us loſe no time, but proceed to the ſixth Propoſition, ſpeaking thus.

PROP. VI. THEOR. VI.

Solid Magnitudes lighter than the Liquid being thruſt

into the Liquid, are repulſed upwards with a Force

as great as is the exceſs of the Gravity of a Maſs

of Liquor equal to the Magnitude above the Gra

vity of the ſaid Magnitude.

into the Liquid, are repulſed upwards with a Force

as great as is the exceſs of the Gravity of a Maſs

of Liquor equal to the Magnitude above the Gra

vity of the ſaid Magnitude.

NIC. This ſixth Propoſition ſaith, that the Solids lighter than the Liquid

demitted, thruſt, or trodden by Force underneath the Liquids Sur

face, are returned or driven upwards with ſo much Force, by

how much a quantity of the Liquid equal to the. Solid ſhall

exceed the ſaid Solid in Gravity.

demitted, thruſt, or trodden by Force underneath the Liquids Sur

face, are returned or driven upwards with ſo much Force, by

how much a quantity of the Liquid equal to the. Solid ſhall

exceed the ſaid Solid in Gravity.

And to delucidate this Propoſition, let the Solid A be lighter

than the Liquid, and let us ſuppoſe that the Gravity of the ſaid

Solid A is B: and let the Gravity of a Liquid, equal in Maſs to A,

be B G. I ſay, that the Solid A depreſſed or demitted with Force

into the ſaid Liquid, ſhall be returned and repulſed upwards with

a Force equal to the Gravity G. And to demonſtrate this Propo

ſition, take the Solid D, equal in Gravity to the ſaid G. Now

the Solid compounded of the two Solids A and D will be lighter

than the Liquid: for the Gravity of the Solid compounded of

them both is BG, and the Gravity of as much Liquor as equal

leth in greatneſs the Solid A, is greater than the ſaid Gravity BG,

than the Liquid, and let us ſuppoſe that the Gravity of the ſaid

Solid A is B: and let the Gravity of a Liquid, equal in Maſs to A,

be B G. I ſay, that the Solid A depreſſed or demitted with Force

into the ſaid Liquid, ſhall be returned and repulſed upwards with

a Force equal to the Gravity G. And to demonſtrate this Propo

ſition, take the Solid D, equal in Gravity to the ſaid G. Now

the Solid compounded of the two Solids A and D will be lighter

than the Liquid: for the Gravity of the Solid compounded of

them both is BG, and the Gravity of as much Liquor as equal

leth in greatneſs the Solid A, is greater than the ſaid Gravity BG,