A Discourse Presented to the Most Serene Don Cosimo II., Great Duke of Tuscany, Concerning the Natation of Bodies Vpon, and Submersion In, the Water.Galilei, Galileo
Science
A Discourse Presented to the Most Serene Don Cosimo II., Great Duke of Tuscany, Concerning the Natation of Bodies Vpon, and Submersion In, the Water.
Galilei, Galileo
Hydrostatics; Specific gravity
_Which Vertue dependes not only on the simple Gravity, but on the
Velocity of the Motion, and on the diverse Inclinations of the
Spaces along which the Motion is made: For a descending Weight
makes a greater Impetus in a Space much declining, than in one less
declining; and in summe, what ever is the occasion of such Vertue,
it ever retaines the name of Moment; nor in my Judgement, is this
sence new in our Idiome, for, if I mistake not, I think we often
say; This is a weighty businesse, but the other is of small moment:
and we consider lighter matters and let pass those of Moment; a
Metaphor, I suppose, taken from the Mechanicks._
As for example, two weights equall in absolute Gravity, being put
into a Ballance of equall Arms, they stand in _Equilibrium_, neither
one going down, nor the other up: because the equality of the
Distances of both, from the Centre on which the Ballance is supported,
and about which it moves, causeth that those weights, the said
Ballance moving, shall in the same Time move equall Spaces, that is,
shall move with equall Velocity, so that there is no reason for which
this Weight should descend more than that, or that more than this; and
therefore they make an _Equilibrium_, and their Moments continue of
semblable and equall Vertue.
The second Principle is; That
AXIOME II.
_The Moment and Force of the Gravity, is encreased by the Velocity
of the Motion._
So that Weights absolutely equall, but conjoyned with Velocity
unequall, are of Force, Moment and Vertue unequall: and the more
potent, the more swift, according to the proportion of the Velocity of
the one, to the Velocity of the other. Of this we have a very
pertinent example in the Balance or Stiliard of unequall Arms, at
which Weights absolutely equall being suspended, they do not weigh
down, and gravitate equally, but that which is at a greater distance
from the Centre, about which the Beam moves, descends, raising the
other, and the Motion of this which ascends is slow, and the other
swift: and such is the Force and Vertue, which from the Velocity of
the Mover, is conferred on the Moveable, which receives it, that it
can exquisitely compensate, as much more Weight added to the other
slower Moveable: so that if of the Arms of the Balance, one were ten
times as long as the other, whereupon in the Beames moving about the
Centre, the end of that would go ten times as far as the end of this,
a Weight suspended at the greater distance, may sustain and poyse
another ten times more grave absolutely than it: and that because the
Stiliard moving, the lesser Weight shall move ten times faster than
the bigger. It ought alwayes therefore to be understood, that Motions
are according to the same Inclinations, namely, that if one of the
Moveables move perpendicularly to the Horizon, then the other makes
its Motion by the like Perpendicular; and if the Motion of one were to
be made Horizontally; that then the other is made along the same
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