Galilei, Galileo, Mechanics, 1665

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              <s>
                <pb xlink:href="070/01/035.jpg" pagenum="305"/>
              weigh equally it would be neceſſary to hang it nearer to the
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              Perpendicular C, as
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              v. </s>
              <s>gr.
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              in E: and look how many times the Di­
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              ſtance C A ſhall contain A E, ſo many times ſhall the Metal
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              weigh more than the Water. </s>
              <s>Let us therefore ſuppoſe that the
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              Weight in B be Gold, and that weighed in the Water it with­
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              draws the Counterpoiſe D into E; and then doing the ſame with
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              pure Silver, let us ſuppoſe that its Counterpoiſe, when afterwards
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              it is weighed in the Water, returneth to F: which point ſhall be
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              nearer to the point C, as Experience ſheweth, becauſe the Silver
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              is leſs grave than the Gold: And the Diſtance that is between
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              A and F ſhall have the ſame Difference with the Diſtance A E,
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              that the Gravity of the Gold hath with that of the Silver. </s>
              <s>But if
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              we have a Mixture of Gold and Silver, it is clear, that by reaſon it
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              participates of Silver, it ſhall weigh leſs than the pure Gold, and
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              by reaſon it participates of Gold, it ſhall weigh more than the
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              pure Silver: and therefore being weighed in the Air, and deſiring
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              that the ſame Counterpoiſe ſhould counterpoiſe it, when that
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              Mixture ſhall be put into the Water it will be neceſſary to draw
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              the ſaid Counterpoiſe more towards the Perpendicular C, than the
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              point E is, which is the term of the Gold; and more from C
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              than F is, which is the term of the pure Silver; Therefore it ſhall
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              fall between the points E and F: And the proportion into which
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              the Diſtance EF ſhall be divided, ſhall exactly give the proportion
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              of the two Metals which compound that Mixture. </s>
              <s>As for exam­
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              ple: Let us ſuppoſe the Mixture of Gold and Silver to be in B,
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                <figure id="id.070.01.035.1.jpg" xlink:href="070/01/035/1.jpg" number="29"/>
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              counterpoiſed in
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              the Air by D,
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              which Counter­
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              poiſe when the
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              Compound Me­
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              tal is put into the Water returneth into G: I ſay now, that the
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              Gold and the Silver which compound this Mixture are to one ano­
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              ther in the ſame proportion, as the Diſtance F G is to the Diſtance
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              G E. </s>
              <s>But you muſt know that the Diſtance G F terminated in
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              the mark of the Silver, ſhall denote unto us the quantity of the
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              Gold, and the Diſtance G E, terminated in the mark of the Gold,
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              ſhall ſhew us the quantity of the Silver: inſomuch that if F G
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              ſhall prove double to G E, then that Mixture ſhall be two parts
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              Gold, and one part Silver: and in the ſame method proceeding in
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              the examination of other Mixtures, one ſhall exactly find the
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              quantity of the ſimple Metals.</s>
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              <s>To compoſe the Ballance, therefore, take a Rod at leaſt a yard
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              long, (and the longer it is, the exacter the Inſtrument ſhall be)
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              and divide it in the midſt, where place the Perpendicular: then
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              adjuſt the Arms that they may ſtand in
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              Equilibrium,
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              by filing or </s>
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