Galilei, Galileo - Discourse concerning the natation of bodies

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

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ment or ebbing of the water A C, hath to the riſe or elevation of
the ſaid Solid M. Therefore, by Perturbation of proportion, in the
aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
the abaſement of the water E N S F, hath the ſame proportion, that the
Surface of the water E F, hath to the Surface of the water A D;
that is, that the whole Maſs of the water E N S F, hath to the whole
Maſs A B C D, being equally high: It is manifeſt, therefore, that
in the expulſion and elevation of the Solid M, the water E N S F
ſhall exceed in Velocity of Motion the water A B C D, aſmuch as it
on the other ſide is exceeded by that in quantity: whereupon their
Moments in ſuch operations, are mutually equall.

And, for ampler confirmation, and clearer explication of this, let us
conſider the preſent Figure, (which if I be not deceived, may ſerve to
detect the errors of ſome Practick Mechanitians, who upon a falſe founda
tion ſome times attempt impoſſible enterprizes,) in which, unto the large
Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and ſup
poſe water infuſed into them, unto the Levell L G H, which water ſhall
reſt in this poſition, not without admiration in ſome, who cannot conceive

[Figure 7]

how it can be, that the heavie charge of the great
Maſs of water G D, preſſing downwards, ſhould
not elevate and repulſe the little quantity of the
other, contained in the Funnell or Pipe C L, by
which the deſcent of it is reſisted and hindered:
But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
the water G D to be abaſed only to Q D, and
ſhall afterwards conſider, what the water C L
hath done, which to give place to the other, which
is deſcended from the Levell G H, to the Levell
Q O, ſhall of neceſſity have aſcended in the ſame
time, from the Levell Lunto A B. And the
aſcent L B, ſhall be ſo much greater than the de
ſcent G Q, by how much the breadth of the Veſſell
G D, is greater than that of the Funnell I C;
which, in ſumme, is as much as the water G D,
is more than the water L C: but in regard that the Moment of the Velocity
of the Motion, in one Moveable, compenſates that of the Gravity of ano
ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
reſiſt the ſlow deſcent of the greater G D?

The ſame, therefore, happens in this operation, as in the Stilliard,
in which a weight of two pounds counterpoyſeth an other of 200,
asoften as that ſhall move in the ſame time, a ſpace 100 times great
er than this: which falleth out when one Arme of the Beam is an

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