Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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THE
BALLANCE
OF
Signeur GALILEO GALILEI;

In which, in immitation of Archimedes in the
Problem of the Crown, he ſheweth how to
find the proportion of the Alloy of
Mixt-Metals; and how to make
the ſaid Inſtrument.

As it is well known, by ſuch who take the pains to read
old Authors, that Archimedes detected the Cheat of
the Goldſmith in the Crown of ^{*} Hieron, ſo I think it

hitherto unknown what method this Great Philoſo-
pher obſerved in that Diſcovery: for the opinion, that he did per-
form it by putting the Crown into the Water, having firſt put in-

to it ſuch another Maſs of pure Gold, and another of Silver ſeve-
rally, and that from the differences in their making the Water
more or leſs riſe and run over, he came to know the Mixture or
Alloy of the Gold with the Silver, of which that Crown was
compounded; ſeems a thing (if I may ſpeak it) very groſs, and
far from exactneſs. And it will ſeem ſo much the more dull to
ſuch who have read and underſtood the exquiſite Inventions of ſo
Divine a Man amongſt the Memorials that are extant of him; by
which it is very manifeſt that all other Wits are inferiour to that
of Archimedes. Indeed I believe, that Fame divulging it abroad,
that Archimedes had diſcovered that ſame Fraud by means of the
Water, ſome Writer of thoſe Times committed the memory there-
of to Poſterity, and that this perſon, that he might add ſomething
to that little which he had heard by common Fame, did relate that
Archimedes had made uſe of the Water in that manner, as ſince
hath been by the generality of men believed.

* King of Sicily,
and Kinſman to
that Great Ma-
thematician.

Plutarch in Vit.
Marcel.

But in regard I know, that that method is altogether fallacious,
and falls ſhort of that exactneſs which is required in Mathematical
Matters, I have often thought in what manner, by help of the
Water, one might exactly find the Mixture of two Metals, and
in the end, after I had diligently peruſed that which Archimedes
demonſtrateth in his Books De inſidentibus aquæ, and thoſe others

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