Archimedes - Natation of bodies

Archimedes, Natation of bodies, 1662

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NIC. You ſay truth.

RIC. I have another queſtion to aske you, which is this, Why the Author
uſeth the word Liquid, or Humid, inſtead of Water.

NIC. It may be for two of theſe two Cauſes; the one is, that Water being the
principal of all Liquids, therefore ſaying Humidum he is to be underſtood to mean
the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of
this Book of his, do not only hold true in Water, but alſo in every other Liquid,
as in Wine, Oyl, and the like: and therefore the Author might have uſed the word
Humidum, as being a word more general than Aqua.

RIC. This I underſtand, therefore let us come to the firſt Propoſition, which, as
you know, in the Original ſpeaks in this manner.

PROP. I. THEOR. I.

If any Superficies ſhall be cut by a Plane thorough any
Point, and the Section be alwaies the Circumference
of a Circle, whoſe Center is the ſaid Point: that Su-
perficies ſhall be Spherical.

Let any Superficies be cut at pleaſure by a Plane thorow the
Point K; and let the Section alwaies deſcribe the Circumfe-
rence of a Circle that hath for its Center the Point K: I ſay,
that that ſame Superficies is Sphærical. For were it poſſible that the
ſaid Superficies were not Sphærical, then all the Lines drawn
through the ſaid Point K unto that Superficies would not be equal,
Let therefore A and B be two
Points in the ſaid Superficies, ſo that

[Figure 2]

drawing the two Lines K A and
K B, let them, if poſſible, be une-
qual: Then by theſe two Lines let
a Plane be drawn cutting the ſaid
Superficies, and let the Section in
the Superficies make the Line
D A B G: Now this Line D A B G
is, by our pre-ſuppoſal, a Circle, and
the Center thereof is the Point K, for ſuch the ſaid Superficies was
ſuppoſed to be. Therefore the two Lines K A and K B are equal:
But they were alſo ſuppoſed to be unequal; which is impoſſible:
It followeth therefore, of neceſſity, that the ſaid Superficies be
Sphærical, that is, the Superficies of a Sphære.

RIC. I underſtand you very well; now let us proceed to the ſecond Propoſition,
which, you know, runs thus.

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