Galilei, Galileo, Mechanics, 1665

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The way is by help of a Ballance, whoſe Conſtruction and Uſe
ſhall
be ſhewn by and by, after we ſhall have declared what is
neceſſary
for the knowledge thereof.
You muſt know there­
fore
, that the Solid Bodies that ſink in the Water weigh ſo much
leſs
in the Water than in the Air, as a Maſs of Water equal to
the
ſaid Solid doth weigh in the Air: which hath been demon­
ſtrated
by Archimedes. But, in regard his Demonſtration is very
mediate
, becauſe I would not be over long, laying it aſide, I ſhall
declare
the ſame another way.
Let us conſider, therefore, that
putting
into the Water v. g. a Maſs of Gold, if that Maſs were
of
Water it would have no weight at all: For the Water moveth
neither
upwards, nor downwards in the Water: It remains,
therefore
, that the Maſs of Gold weigheth in the Water only ſo
much
as the Gravity of the Gold exceeds the Gravity of the Wa­
ter
.
And the like is to be underſtood of other Metals. And be­
cauſe
the Metals are different from each other in Gravity, their
Gravity
in the Water ſhall diminiſh according to ſeveral proporti­
ons
.
As for example: Let us ſuppoſe that Gold weigheth twenty
times
more than Water, it is manifeſt by that which hath been
ſpoken
, that the Gold will weigh leſs in the Water than in the
Air
by a twentieth part of its whole weight.
Now, let us ſuppoſe
that
Silver, as being leſs Grave than Gold, weigheth 12 times more
than
Water: this then, being weighed in the Water, ſhall di­
miniſh
in Gravity the twelfth part of its whole weight.
Therefore
the
Gravity of Gold in the Water decreaſeth leſs than that of
Silver
; for that diminiſheth a twentieth part, and this a twelfth.
If therefore in an exquiſite Ballance we ſhall hang a Metal at the
one
Arm, and at the other a Counterpoiſe that weigheth equally
with
the ſaid Metal in the Water, leaving the Counterpoiſe in the
Air
, to the end that it may equivalate and compenſate the Me­
tal
, it will be neceſſary to hang it nearer the Perpendicular or
Cook
.
As for example, Let the Ballance be A B, its Perpendicu­
28[Figure 28]
lar
C, and let a
Maſs
of ſome
Metal
be ſu­
ſpended
at B,
counterpoiſedby

the
Weight D: putting the Weight B into the Water, the
Weight
D in A would weigh more: therefore that they may

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