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

#### Table of figures

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
of Direction
<emph type="italics"/>
A
<emph.end type="italics"/>
D H and
<emph type="italics"/>
A
<emph.end type="italics"/>
E I are Right
<emph type="italics"/>
A
<emph.end type="italics"/>
ngles, we ſuppoſe that
<lb/>
theſe two
<emph type="italics"/>
F
<emph.end type="italics"/>
orces I and H weigh alike upon the Center
<emph type="italics"/>
A
<emph.end type="italics"/>
as if they
<lb/>
were nearer to the Center, at the equal Diſtances
<emph type="italics"/>
A
<emph.end type="italics"/>
B and A C,
<lb/>
and we alſo ſuppoſe the ſame if theſe very
<emph type="italics"/>
F
<emph.end type="italics"/>
orces were ſuſpended
<lb/>
both together in
<emph type="italics"/>
A,
<emph.end type="italics"/>
the
<emph type="italics"/>
A
<emph.end type="italics"/>
ngles of Directions being ſtill Right
<lb/>
<emph type="italics"/>
A
<emph.end type="italics"/>
ngles.</s>
</p>
<s>PROPOSITION I.</s>
</p>
<p type="main">
<s>Theſe Principles agreed upon, we will eaſily demonſtrate,
<lb/>
in Imitation of
<emph type="italics"/>
Archimedes,
<emph.end type="italics"/>
that upon a ſtraight Balance
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the
<emph type="italics"/>
F
<emph.end type="italics"/>
orces, of which and of all their parts the Lines of Dire­
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ction are parallel to one another, and perpendicular to the Balance,
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ſhall couuterpoiſe and make an
<emph type="italics"/>
Equilibrium,
<emph.end type="italics"/>
when the ſaid
<emph type="italics"/>
F
<emph.end type="italics"/>
orces
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ſhall be to one another in Reciprocal proportion of their Arms,
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which we think to be ſo manifeſt to you, that we thence ſhall de­
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rive the Demonſtration of this Univerſal Propoſition to which we
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haſten.</s>
</p>
<s>PROPOS. II.</s>
</p>
<p type="main">
<s>In every Balance or Leaver, if the proportion of the
<emph type="italics"/>
F
<emph.end type="italics"/>
orces is
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reciprocal to that of the Perpendicular Lines drawn from the
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Center or Point of the
<emph type="italics"/>
F
<emph.end type="italics"/>
ulciment unto the Lines of Direction
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of the
<emph type="italics"/>
F
<emph.end type="italics"/>
orces, drawing the one againſt the other, they ſhall make
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an
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Equilibrium,
<emph.end type="italics"/>
and drawing on one and the ſame ſide, they ſhall
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have a like Effect, that is to ſay, that they ſhall have as much
<emph type="italics"/>
F
<emph.end type="italics"/>
orce
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the one as the other, to move the Balance.</s>
</p>
<p type="main">
<s>In this
<emph type="italics"/>
F
<emph.end type="italics"/>
igure let the Center of the Balance be
<emph type="italics"/>
A,
<emph.end type="italics"/>
the
<emph type="italics"/>
A
<emph.end type="italics"/>
rm
<emph type="italics"/>
A
<emph.end type="italics"/>
B,
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bigger than
<emph type="italics"/>
A
<emph.end type="italics"/>
C, and firſt let the
<emph type="italics"/>
L
<emph.end type="italics"/>
ines of Direction B D, and E C
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be perpendicular to the
<emph type="italics"/>
A
<emph.end type="italics"/>
rms
<emph type="italics"/>
A
<emph.end type="italics"/>
B and
<emph type="italics"/>
A
<emph.end type="italics"/>
C, by which Lines the
<lb/>
<emph type="italics"/>
F
<emph.end type="italics"/>
orces D and E (which may be made of Weights if one will) do
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draw; and that there is the ſame rate
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<lb/>
of the
<emph type="italics"/>
F
<emph.end type="italics"/>
orce D to the Force E as there
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is betwixt the
<emph type="italics"/>
A
<emph.end type="italics"/>
rm
<emph type="italics"/>
A
<emph.end type="italics"/>
C to the Arm
<lb/>
<emph type="italics"/>
A
<emph.end type="italics"/>
B: the Forces drawing one againſt
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the other, I ſay, that they will make an
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<emph type="italics"/>
Equilibrium
<emph.end type="italics"/>
upon the Balance
<emph type="italics"/>
C
<emph.end type="italics"/>
A B.
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</s>
<s>For let the
<emph type="italics"/>
A
<emph.end type="italics"/>
rm C
<emph type="italics"/>
A
<emph.end type="italics"/>
be prolonged
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unto F, ſo as that
<emph type="italics"/>
A
<emph.end type="italics"/>
F may be equal to
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<emph type="italics"/>
A
<emph.end type="italics"/>
B: and let C
<emph type="italics"/>
A
<emph.end type="italics"/>
F be conſidered as a
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ſtreight Balance, of which let the Center be
<emph type="italics"/>
A
<emph.end type="italics"/>
: and let there be
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ſuppoſed two Forces G and H, of which and of all their parts the
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Lines of Direction are parallel to the Line C E, and that the
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Force G be equal to the Force D, and H to E, the one, to wit G, </s>
</p>
</chap>
</body>
</text>
</archimedes>