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NIC. In this Propoſition it is affirmed that thoſe Solid Magnitules that hap-

pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber-

ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap-

pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the

Bottom.

pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber-

ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap-

pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the

Bottom.

For ſuppoſing, on the contrary, that it were poſſible for one of

thoſe Solids being placed in the Liquid to lie in part without the

Liquid, that is above its Surface, (alwaies provided that the ſaid

Liquid be ſetled and undiſturbed,) let us imagine any Plane pro-

duced thorow the Center of the Earth, thorow the Liquid, and

thorow that Solid Body: and let us imagine that the Section of the

Liquid is the Superficies A B G D, and the Section of the Solid

Body that is within it the Superſicies E Z H T, and let us ſuppoſe

the Center of the Earth to be the Point K: and let the part of the

ſaid Solid ſubmerged in the Liquid be B G H T, and let that above

be B E Z G: and let the Solid Body be ſuppoſed to be comprized in

a Pyramid that hath its Parallelogram Baſe in the upper Surface of

the Liquid, and its Summity or Vertex in the Center of the Earth:

which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame

Plane in which is the Circumference A B G D, and let the Sections

[Figure 4]

of the Planes of the ſaid

Pyramid be K L and

K M: and in the Liquid

about the Center K let

there be deſcribed a Su-

perficies of another

Sphære below E Z H T,

which let be X O P;

and let this be cut by

the Superficies of the Plane: And let there be another Pyramid ta-

ken or ſuppoſed equal and like to that which compriſeth the ſaid

Solid Body, and contiguous and conjunct with the ſame; and let

the Sections of its Superficies be K M and K N: and let us ſuppoſe

another Solid to be taken or imagined, of Liquor, contained in that

ſame Pyramid, which let be R S C Y, equal and like to the partial

Solid B H G T, which is immerged in the ſaid Liquid: But the

part of the Liquid which in the firſt Pyramid is under the Super-

ficies X O, and that, which in the other Pyramid is under the Su-

perficies O P, are equijacent or equipoſited and contiguous, but

are not preſſed equally; for that which is under the Superficies

X O is preſſed by the Solid T H E Z, and by the Liquor that is

contained between the two Spherical Superficies X O and L M

and the Planes of the Pyramid, but that which proceeds accord-

ing to F O is preſſed by the Solid R S C Y, and by the Liquid

thoſe Solids being placed in the Liquid to lie in part without the

Liquid, that is above its Surface, (alwaies provided that the ſaid

Liquid be ſetled and undiſturbed,) let us imagine any Plane pro-

duced thorow the Center of the Earth, thorow the Liquid, and

thorow that Solid Body: and let us imagine that the Section of the

Liquid is the Superficies A B G D, and the Section of the Solid

Body that is within it the Superſicies E Z H T, and let us ſuppoſe

the Center of the Earth to be the Point K: and let the part of the

ſaid Solid ſubmerged in the Liquid be B G H T, and let that above

be B E Z G: and let the Solid Body be ſuppoſed to be comprized in

a Pyramid that hath its Parallelogram Baſe in the upper Surface of

the Liquid, and its Summity or Vertex in the Center of the Earth:

which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame

Plane in which is the Circumference A B G D, and let the Sections

[Figure 4]

of the Planes of the ſaid

Pyramid be K L and

K M: and in the Liquid

about the Center K let

there be deſcribed a Su-

perficies of another

Sphære below E Z H T,

which let be X O P;

and let this be cut by

the Superficies of the Plane: And let there be another Pyramid ta-

ken or ſuppoſed equal and like to that which compriſeth the ſaid

Solid Body, and contiguous and conjunct with the ſame; and let

the Sections of its Superficies be K M and K N: and let us ſuppoſe

another Solid to be taken or imagined, of Liquor, contained in that

ſame Pyramid, which let be R S C Y, equal and like to the partial

Solid B H G T, which is immerged in the ſaid Liquid: But the

part of the Liquid which in the firſt Pyramid is under the Super-

ficies X O, and that, which in the other Pyramid is under the Su-

perficies O P, are equijacent or equipoſited and contiguous, but

are not preſſed equally; for that which is under the Superficies

X O is preſſed by the Solid T H E Z, and by the Liquor that is

contained between the two Spherical Superficies X O and L M

and the Planes of the Pyramid, but that which proceeds accord-

ing to F O is preſſed by the Solid R S C Y, and by the Liquid