Galilei, Galileo, Mechanics, 1665

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            <pb xlink:href="070/01/033.jpg" pagenum="303"/>
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              <s>THE
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              BALLANCE
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              OF
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              Signeur GALILEO GALILEI
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              ;</s>
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              <s>In which, in immitation of
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              Archimedes
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              in the
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              Problem of the Crown, he ſheweth how to
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              find the proportion of the Alloy of
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              Mixt-Metals; and how to make
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              the ſaid Inſtrument.</s>
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              <s>As it is well known, by ſuch who take the pains to read
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              old Authors, that
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              Archimedes
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              detected the Cheat of
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              the Goldſmith in the Crown of ^{*}
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              Hieron,
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              ſo I think it
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              hitherto unknown what method this Great Philoſo­
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              pher obſerved in that Diſcovery: for the opinion, that he did per­
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              form it by putting the Crown into the Water, having firſt put in­
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              to it ſuch another Maſs of pure Gold, and another of Silver ſeve­
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              rally, and that from the differences in their making the Water
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              more or leſs riſe and run over, he came to know the Mixture or
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              Alloy of the Gold with the Silver, of which that Crown was
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              compounded; ſeems a thing (if I may ſpeak it) very groſs, and
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              far from exactneſs. </s>
              <s>And it will ſeem ſo much the more dull to
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              ſuch who have read and underſtood the exquiſite Inventions of ſo
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              Divine a Man amongſt the Memorials that are extant of him; by
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              which it is very manifeſt that all other Wits are inferiour to that
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              of
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              Archimedes.
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              Indeed I believe, that Fame divulging it abroad,
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              that
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              Archimedes
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              had diſcovered that ſame Fraud by means of the
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              Water, ſome Writer of thoſe Times committed the memory there­
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              of to Poſterity, and that this perſon, that he might add ſomething
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              to that little which he had heard by common Fame, did relate that
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                <emph type="italics"/>
              Archimedes
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              had made uſe of the Water in that manner, as ſince
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              hath been by the generality of men believed.</s>
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            <p type="margin">
              <s>
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              * King of
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              Sicily,
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              and Kinſman to
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              that Great Ma­
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              thematician.</s>
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            <p type="margin">
              <s>
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              Plutarch in Vit.
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              </s>
              <s>Marcel.
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              </s>
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            <p type="main">
              <s>But in regard I know, that that method is altogether fallacious,
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              and falls ſhort of that exactneſs which is required in Mathematical
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              Matters, I have often thought in what manner, by help of the
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              Water, one might exactly find the Mixture of two Metals, and
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              in the end, after I had diligently peruſed that which
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              Archimedes
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              demonſtrateth in his Books
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              De inſidentibus aquæ,
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              and thoſe others </s>
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          </chap>
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