Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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