Archimedes - Natation of bodies

Archimedes, Natation of bodies, 1662

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* I add the word
ſetled, as neceſſary
in making the Ex-
periment.

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.

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

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