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

#### Table of figures

< >
[Figure 201]
[Figure 202]
[Figure 203]
[Figure 204]
[Figure 205]
[Figure 206]
[Figure 207]
[Figure 208]
[Figure 209]
[Figure 210]
[Figure 211]
[Figure 212]
[Figure 213]
[Figure 214]
[Figure 215]
[Figure 216]
[Figure 217]
[Figure 218]
[Figure 219]
[Figure 220]
[Figure 221]
[Figure 222]
[Figure 223]
[Figure 224]
[Figure 225]
[Figure 226]
[Figure 227]
[Figure 228]
[Figure 229]
[Figure 230]
< >
page |< < of 701 > >|
<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
without impediment by this Line, the Force and the Line ſhall
<lb/>
take ſome certain poſition in which they ſhall reſt, and the Line
<lb/>
ſhall of neceſſity be ſtreight, let that Line be termed
<emph type="italics"/>
the Pendant,
<emph.end type="italics"/>
<lb/>
or
<emph type="italics"/>
Line of Direction of the Force.
<emph.end type="italics"/>
And let the Point by which it is
<lb/>
faſtned to the Fulciment be called
<emph type="italics"/>
the Point of Suſpenſion
<emph.end type="italics"/>
: which
<lb/>
may ſometimes be the Arm of a Leaver or Ballance; and then let
<lb/>
the Line drawn from the Center of the Fulciment of the Leaver
<lb/>
or Ballance to the Point of Suſpenſion be named
<emph type="italics"/>
the Diſtance
<emph.end type="italics"/>
or
<lb/>
<emph type="italics"/>
the Arm of the Force
<emph.end type="italics"/>
: which we ſuppoſe to be a Line fixed, and
<lb/>
conſidered without Gravity. </s>
<s>Moreover, let the Angle comprehen­
<lb/>
ded betwixt the Arm of the Force and the Line of Direction be
<lb/>
termed
<emph type="italics"/>
the Angle of the Direction of the Force.
<emph.end type="italics"/>
</s>
</p>
<s>AXIOM I.</s>
</p>
<p type="main">
<s>After theſe Definitions we lay down for a Principle, that in the
<lb/>
Leaver, and in the Ballance, Equal Forces drawing by Arms
<lb/>
that are equal, and at equall Angles of Direction, do draw equal­
<lb/>
ly. </s>
<s>And if in this Poſition they draw one againſt the other they
<lb/>
ſhall make an
<emph type="italics"/>
Equilibrium
<emph.end type="italics"/>
: but if they draw together, or towards
<lb/>
the ſame part, the Effect ſhall be double.</s>
</p>
<p type="main">
<s>If the Forces being equal, and the Augles of Direction alſo
<lb/>
equal, the Arms be unequal, the Force that ſhall be ſuſpended at
<lb/>
the greater Arm ſhall work the greater Effect.</s>
</p>
<p type="main">
<s>As in this Figure, the Center of the Ballance or Leaver being A,
<lb/>
<lb/>
if the Arms A B and A C are equal,
<lb/>
as alſo the Angles A B D, and A C E,
<lb/>
the equal Forces D and E ſhall
<lb/>
draw equally, and make an
<emph type="italics"/>
Equili­
<lb/>
brium.
<emph.end type="italics"/>
So likewiſe the Arm A F be­
<lb/>
ing equal to A B, the Angle A F G
<lb/>
to the Angle A B D, and the Force
<lb/>
G to D, theſe two Forces ^{*} G and D
<lb/>
<arrow.to.target n="marg1124"/>
<lb/>
draw equally; and in regard that
<lb/>
they draw both one way, the Effect
<lb/>
ſhall be double.</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1124"/>
* In the M. S.
<lb/>
</s>
<s>Copy it is
<emph type="italics"/>
C and
<lb/>
D.
<emph.end type="italics"/>
</s>
</p>
<p type="main">
<s>In the ſame manner the Forces G and E ſhall make an
<emph type="italics"/>
Equilibri­
<lb/>
um
<emph.end type="italics"/>
; as alſo I and L ſhall counterpoiſe, if (being equal) the Arms
<lb/>
A K and A H, and the Angles A H T, and A K L be equal.</s>
</p>
<p type="main">
<s>The ſame ſhall befall in the Forces P and R, if all things be
<lb/>
diſpoſed as before. </s>
<s>And in this caſe we make no other diſtinction
<lb/>
betwixt Weights and other Forces ſave only this, that Weights all
<lb/>
tend towards the Center of Grave Bodies, and Forces may be un­
<lb/>
derſtood to tend all towards all parts of the Univerſe, with ſo
<lb/>
much greater or leſſer
<emph type="italics"/>
Impetus
<emph.end type="italics"/>
than Weights. </s>
<s>So that Weights and </s>
</p>
</chap>
</body>
</text>
</archimedes>