Archimedes - Natation of bodies

Archimedes, Natation of bodies, 1662

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NIC. The Cauſe of all theſe Effects is aſſigned by Archimedes, the Siracuſan, in

that Book De Incidentibus (^{*}) Aquæ, by me publiſhed in Latine, and dedicated to
your ſelf, as I alſo ſaid in the beginning of that my Induſtrions Invention.

* Aquæ, tanſlated
by me Humido, as
the more Compre-
henſive word, for
his Doctrine holds
true in all Liquids
as well as in Wa-
ter, ſoil. in Wine,
Oyl, Milk, &c.

RIC. I have ſeen that ſame Archimedes, and have very well underſtood thoſe
two Books in which he treateth De Centro Gravitatis æquerepentibus, or of the
Center of Gravity in Figures plain, or parallel to the Horizon; and likewiſe thoſe
De Quadratura Parabolæ, or, of Squaring the Parabola; but ^{*}that in which he treat-
eth of Solids that Swim upon, or ſink in Liquids, is ſo obſcure, that, to ſpeak the
truth, there are many things in it which I do not underſtand, and therefore before

we proceed any farther, I ſhould take it for a favour if you would declare it to me
in your Vulgar Tongue, beginning with his firſt Suppoſition, which ſpeaketh in this
manner.

* He ſpeaks of but
one Book, Tartag-
lia having tranſla-
ted no more.

SVPPOSITION I.

It is ſuppoſed that the Liquid is of ſuch a nature, that
its parts being equi-jacent and contiguous, the leſs
preſſed are repulſed by the more preſſed. And
that each of its parts is preſſed or repulſed by the
Liquor that lyeth over it, perpendicularly, if the
Liquid be deſcending into any place, or preſſed any
whither by another.

NIC. Every Science, Art, or Doctrine (as you know, Honoured Companion,)
hath its firſt undemonſtrable Principles, by which (they being
granted or ſuppoſed) the ſaid Science is proved, maintained, or de-
monſtrated. And of theſe Principles, ſome are called Petitions,
and others Demands, or Suppoſitions. I ſay, therefore, that the Science or Doctrine
of thoſe Material Solids that Swim or Sink in Liquids, hath only two undemon-
ſtrable Suppoſitions, one of which is that above alledged, the which in compliance
with your deſire I have ſet down in our Vulgar Tongue.

RIC. Before you proceed any farther tell me, how we are to underſtand the
parts of a Liquid to be Equijacent.

NIC. When they are equidiſtant from the Center of the World, or of the
Earth (which is the ſame, although ^{*} ſome hold that the Centers of the Earth
and Worldare different.)

RIC. I underſtand you not unleſs you give me ſome Example thereof in
Figure.

* The Coperni-
cans.

NIC. To exemplifie this particular, Let us ſuppoſe a quantity of Liquor (as
for inſtance of Water) to be upon the Earth; then let us with the Imagination
cut the whole Earth together with that Water into two equal parts, in ſuch a
manner as that the ſaid Section may paſs ^{*} by the Center of the Earth: And let
us ſuppoſe that one part of the Superficies of that Section, as well of the Water
as of the Earth, be the Superficies A B, and that the Center of the Earth be the
point K. This being done, let us in our Imagination deſcribe a Circle upon the

ſaid Center K, of ſuch a bigneſs as that the Circumference may paſs by the Super-
ficies of the Section of the Water: Now let this Circumference be E F G: and
let many Lines be drawn from the point K to the ſaid Circumference, cutting the
ſame, as KE, KHO, KFQ KLP, KM. Now I ſay, that all theſe parts of
the ſaid Water, terminated in that Circumference, are Equijacent, as being all

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