Galilei, Galileo - Discourse concerning the natation of bodies

Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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the Gravity of the water, yet the caſe ſtands ſo, that the Rampart
doth alſo contract it ſelf, and the Cylinder contained in it doth de
miniſh. Nevertheleſs it ſhall be demonſtrated, how that the Cone
A B D being of any ſuppoſed bigneſſe, and made at the firſt of a
Matter exactly equall in Gravity to the Water, if there may
be affixed to it ſome Weight, by means of which it may deſcend to
the bottom, when ſubmerged under water, it may alſo by vertue of
the Rampart ſtay above without ſinking.

Let, therefore, the Cone A B D be of any ſuppoſed greatneſſe,
and alike in ſpecificall Gravity to the water. It is manifeſt, that
being put lightly into the water, it ſhall reſt without deſcending;
and it ſhall advance above water, the Point

[Figure 18]

AS T, tripple in height to the height of the
Rampart E S: Now, ſuppoſe the Cone A B D
more depreſſed, ſo that it advance above wa
ter, only the Point A I R, higher by half than
the Point A S T, with the Rampart about it
C I R N. And, becauſe, the Cone A B D is
to the Cone A I R, as the cube of the Line S T
is to the cube of the Line I R, but the Cylin
der E S T O, is to the Cylinder C I R N, as the Square of S T to
the Square of I R, the Cone A S T ſhall be Octuple to the Cone
A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N:
But the Cone A S T, is equall to the Cylinder E S T O: Therefore,
the Cylinder C I R N, ſhall be double to the Cone A I R: and the
water which might be contained in the Rampart C I R N, would be
double in Maſs and in Weight to the Cone A I R, and, therefore,
would be able to ſuſtain the double of the Weight of the Cone AIR:
Therefore, if to the whole Cone A B D, there be added as much
Weight as the Gravity of the Cone A I R, that is to ſay, the eighth
part of the weight of the Cone A S T, it alſo ſhall be ſuſtained by
the Rampart C I R N, but without that it ſhall go to the bottome:
the Cone A B D, being, by the addition of the eighth part of the
weight of the Cone A S T, made ſpecifically more grave than the
water. But if the Altitude of the Cone A I R, were two thirds
of the Altitude of the Cone A S T, the Cone A S T would be to the
Cone A I R, as twenty ſeven to eight; and the Cylinder E S T O, to
the Cylinder C I R N, as nine to four, that is, as twenty ſeven to
twelve; and, therefore, the Cylinder C I R N, to the Cone A I R,
as twelve to eight; and the exceſs of the Cylinder C I R N, above
the Cone A I R, to the Cone A S T, as four to twenty ſeven: there
fore if to the Cone A B D be added ſo much weight as is the four
twenty ſevenths of the weight of the Cone A S T, which is a little
more then its ſeventh part, it alſo ſhall continue to ſwimme, and

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