1Priſme, or Cylinder, to wit, that hath its two flat Superficies,
our and inferiour, alike and equall, and at Right Angles with the
ther laterall Superficies, and let its thickneſs I O be equall to the
greateſt Altitude of the Banks of water: I ſay, that if it be put upon
the water, it will not ſubmerge: for the Altitude
A I being equall to the Altitude I O, the
of the Air A B C I ſhall be equall to the Maſs
10[Figure 10]
the Solid C I O S: and the whole Maſs A O S
double to the Maſs I S; And ſince the
of the Air A C, neither encreaſeth nor
niſheth the Gravity of the Maſs I S, and the Solid I S was
double in Gravity to the water; Therefore as much water as
Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
A O S B: but when ſuch a Maſs of water, as is the ſubmerged part
the Solid, weighs as much as the ſaid Solid, it deſcends not farther,
but reſteth, as by (a) Archimedes, and above by us, hath been de>
monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
ſhall float, as long as its thickneſs be not above twice as much as the
greateſt Altitude of the Ramparts of water, that is, of A I. For I S
being Seſquialter in Gravity to the water, and the Altitude O I
being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
Seſquialter in Maſs to the Solid I S. And becauſe the Air A C,
neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
Maſs ſhall reſt. And briefly in generall.
our and inferiour, alike and equall, and at Right Angles with the
ther laterall Superficies, and let its thickneſs I O be equall to the
greateſt Altitude of the Banks of water: I ſay, that if it be put upon
the water, it will not ſubmerge: for the Altitude
A I being equall to the Altitude I O, the
of the Air A B C I ſhall be equall to the Maſs
the Solid C I O S: and the whole Maſs A O S
double to the Maſs I S; And ſince the
of the Air A C, neither encreaſeth nor
niſheth the Gravity of the Maſs I S, and the Solid I S was
double in Gravity to the water; Therefore as much water as
Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
A O S B: but when ſuch a Maſs of water, as is the ſubmerged part
the Solid, weighs as much as the ſaid Solid, it deſcends not farther,
but reſteth, as by (a) Archimedes, and above by us, hath been de>
monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
ſhall float, as long as its thickneſs be not above twice as much as the
greateſt Altitude of the Ramparts of water, that is, of A I. For I S
being Seſquialter in Gravity to the water, and the Altitude O I
being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
Seſquialter in Maſs to the Solid I S. And becauſe the Air A C,
neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
Maſs ſhall reſt. And briefly in generall.
Of Natation
Lib. 1. Prop. 3.
Lib. 1. Prop. 3.
THEOREME. VI.
When ever the exceſs of the Gravity of the Solid above
the Gravity of the Water, ſhall have the ſame
portion to the Gravity of the Water, that the
tude of the Rampart, hath to the thickneſs of the
Solid, that Solid ſhall not ſink, but being never ſo
tle thicker it ſhall.
the Gravity of the Water, ſhall have the ſame
portion to the Gravity of the Water, that the
tude of the Rampart, hath to the thickneſs of the
Solid, that Solid ſhall not ſink, but being never ſo
tle thicker it ſhall.
The
on of the
eſt thickneſs of
Solids, beyond
which
ſed they ſink.
on of the
eſt thickneſs of
Solids, beyond
which
ſed they ſink.
Let the Solid I S be ſuperior in Gravity to the water, and of ſuch
thickneſs, that the Altitude of the Rampart A I, be in
on to the thickneſs of the Solid I O, as the exceſs of the
ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall
to the Maſs I S, is to the Gravity of the Maſs of water equall to the
thickneſs, that the Altitude of the Rampart A I, be in
on to the thickneſs of the Solid I O, as the exceſs of the
ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall
to the Maſs I S, is to the Gravity of the Maſs of water equall to the