Archimedes - Natation of bodies

Archimedes, Natation of bodies, 1662

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equidiſtant from the point K, the Center of the World, which parts are G M,
M L, L F, F H, H E.

RIC. I underſtand you very well, as to this particular: But tell me a little; he
ſaith that each of the parts of the Liquid is preſſed or repulſed by the Liquid that
is above it, according to the Perpendicular: I know not what that Liquid is that
lieth upon a part of another Perpendicularly.

NIC. Imagining a Line that cometh from the Center of the Earth penetrating
thorow ſome Water, each part of the Water that is in that Line he ſuppoſeth to
be preſſed or repulſed by the Water that lieth above it in that ſame Line, and that
that repulſe is made according to the ſame Line, (that is, directly towards the
Center of the World) which Line is called a Perpendicular; becauſe every
Right-Line that departeth from any point, and goeth directly towards the Worlds
Center is called a Perpendicular. And that you may the better underſtand me, let

[Figure 1]

us imagine
the Line KHO,
and in that
let us imagine
ſeveral parts,
as ſuppoſe RS,
S T, T V, V H,
H O. I ſay,
that he ſup-
poſeth that
the part V H
is preſſed by
that placed a-
bove it, H O,
according to
the Line OK;
the which
O K, as hath been ſaid above, is called the Perpendicular paſſing thorow thoſe two
parts. In like manner, I ſay that the part T V is expulſed by the part V H, ac-
cording to the ſaid Line O K: and ſo the part S T to be preſſed by T V, according
to the ſaid Perpendicular O K, and R S by S T. And this you are to underſtand
in all the other Lines that were protracted from the ſaid Point K, penetrating the
ſaid Water, As for Example, in K G, K M, K L, K F, K E, and infinite others of the
like kind.

RIC. Indeed, Dear Companion, this your Explanation hath given megreat ſa-
tisfaction; for, in my Judgment, it ſeemeth that all the difficulty of this Suppoſition
conſiſts in theſe two particulars which you have declared to me.

NIC. It doth ſo; for having underſtood that the parts E H, H F, F L, L M, and
MG, determining in the Circumference of the ſaid Circle are equijacent, it is an
eaſie matter to underſtand the foreſaid Suppoſition in Order, which ſaith, That it is
ſuppoſed that the Liquid is of ſuch a nature, that the part thereof leſs preſſed or thrust is re-
pulſed by the more thruſt or preſſed. As for example, if the part E H were by chance
more thruſt, crowded, or preſſed from above downwards by the Liquid, or ſome
other matter that was over it, than the part H F, contiguous to it, it is ſuppoſed
that the ſaid part H F, leſs preſſed, would be repulſed by the ſaid part E H. And
thus we ought to underſtand of the other parts equijacent, in caſe that they be
contiguous, and not ſevered. That each of the parts thereof is preſſed and repul.
ſed by the Liquid that lieth over it Perpendicularly, is manifeſt by that which was
ſaid above, to wit, that it ſhould be repulſed, in caſe the Liquid be deſcending into
any place, and thruſt, or driven any whither by another.

RIC. I underſtand this Suppoſition very well, but yet me thinks that before
the Suppoſition, the Author ought to have defined thoſe two particulars, which
you firſt declared to me, that is, how we are to underſtand the parts of the Liquid
equijacent, and likewiſe the Perpendicular.

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