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

Table of figures

< >
[Figure 201]
Page: 990
[Figure 202]
Page: 990
[Figure 203]
Page: 991
[Figure 204]
Page: 992
[Figure 205]
Page: 993
[Figure 206]
Page: 994
[Figure 207]
Page: 998
[Figure 208]
Page: 999
[Figure 209]
Page: 1006
[Figure 210]
Page: 1007
[Figure 211]
Page: 1008
[Figure 212]
Page: 1008
[Figure 213]
Page: 1009
[Figure 214]
Page: 1010
[Figure 215]
Page: 1012
[Figure 216]
Page: 1014
[Figure 217]
Page: 1014
[Figure 218]
Page: 1015
[Figure 219]
Page: 1015
[Figure 220]
Page: 1017
[Figure 221]
Page: 1018
[Figure 222]
Page: 1020
[Figure 223]
Page: 1021
[Figure 224]
Page: 1021
[Figure 225]
Page: 1022
[Figure 226]
Page: 1023
[Figure 227]
Page: 1030
[Figure 228]
Page: 1031
[Figure 229]
Page: 1032
[Figure 230]
Page: 1034
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1022.jpg" pagenum="328"/>
              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>
            <p type="head">
              <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
                <lb/>
              the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orces, of which and of all their parts the Lines of Dire­
                <lb/>
              ction are parallel to one another, and perpendicular to the Balance,
                <lb/>
              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
                <lb/>
              ſhall be to one another in Reciprocal proportion of their Arms,
                <lb/>
              which we think to be ſo manifeſt to you, that we thence ſhall de­
                <lb/>
              rive the Demonſtration of this Univerſal Propoſition to which we
                <lb/>
              haſten.</s>
            </p>
            <p type="head">
              <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
                <lb/>
              reciprocal to that of the Perpendicular Lines drawn from the
                <lb/>
              Center or Point of the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              ulciment unto the Lines of Direction
                <lb/>
              of the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orces, drawing the one againſt the other, they ſhall make
                <lb/>
              an
                <emph type="italics"/>
              Equilibrium,
                <emph.end type="italics"/>
              and drawing on one and the ſame ſide, they ſhall
                <lb/>
              have a like Effect, that is to ſay, that they ſhall have as much
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce
                <lb/>
              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,
                <lb/>
              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
                <lb/>
              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
                <lb/>
              draw; and that there is the ſame rate
                <lb/>
                <figure id="id.040.01.1022.1.jpg" xlink:href="040/01/1022/1.jpg" number="225"/>
                <lb/>
              of the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce D to the Force E as there
                <lb/>
              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
                <lb/>
              the other, I ſay, that they will make an
                <lb/>
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              upon the Balance
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              A B.
                <lb/>
              </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
                <lb/>
              unto F, ſo as that
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              F may be equal to
                <lb/>
                <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
                <lb/>
              ſtreight Balance, of which let the Center be
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              : and let there be
                <lb/>
              ſuppoſed two Forces G and H, of which and of all their parts the
                <lb/>
              Lines of Direction are parallel to the Line C E, and that the
                <lb/>
              Force G be equal to the Force D, and H to E, the one, to wit G, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum