Archimedes, Natation of bodies, 1662

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ſhall be equal to the Triangle O X K; Therefore (by common
Notion) ſubſtracting thoſe two ſmall Triangles O P K and O X K
from the two others B E K and B R K, the two Remainders ſhall
be equal: one of which Remainders ſhall be the Quadrangle
B E O P, and the other B R X O.
And becauſe the whole Quadran-
gle B E O P is full of Liquor, and of the Quadrangle B R X O,
the part B A X O only is full, and the reſidue B R A is wholly void
of Water: It followeth, therefore, that the Quadrangle B E O P
is more ponderous than the Quadrangle B R X O.
And if the ſaid
Quadrangle B E O P be more Grave than the Quadrangle
B R X O, much more ſhall the Quadrangle B L O P exceed in Gra-
vity the ſaid Quadrangle B R X O: whence it followeth, that the
part O P is more preſſed than the part O X. But, by the firſt part
of the Suppoſition, the part leſs preſſed ſhould be repulſed by the
part more preſſed: Therefore the part O X muſt be repulſed by
the part O P: But it was preſuppoſed that the Liquid did not
move: Wherefore it would follow that the leſs preſſed would not
be repulſed by the more preſſed: And therefore it followeth of
neceſſity that the Line A B G D is the Circumference of a Circle,
and that the Center of it is the point K.
And in like manner ſhall
it be demonſtrated, if the Surface of the Liquid be cut by a Plane
thorow the Center of the Earth, that the Section ſhall be the Cir-
cumference of a Circle, and that the Center of the ſame ſhall be
that very Point which is Center of the Earth.
It is therefore mani-
feſt that the Superficies of a Liquid that is conſiſtant and ſetled
ſhall have the Figure of a Sphære, the Center of which ſhall be
the ſame with that of the Earth, by the firſt Propoſition; for it is
ſuch that being ever cut thorow the ſame Point, the Section or Di-
viſion deſcribes the Circumference of a Circle which hath for Cen-
ter the ſelf-ſame Point that is Center of the Earth: Which was to
be demonſtrated.
PROP. III. THEOR. III.

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