Archimedes, Natation of bodies, 1662

Table of figures

< >
[Figure 1]
Page: 6
[Figure 2]
Page: 7
[Figure 3]
Page: 8
[Figure 4]
Page: 10
[Figure 5]
Page: 11
[Figure 6]
Page: 12
[Figure 7]
Page: 14
[Figure 8]
Page: 15
[Figure 9]
Page: 16
[Figure 10]
Page: 18
[Figure 11]
Page: 18
[Figure 12]
Page: 19
[Figure 13]
Page: 20
[Figure 14]
Page: 22
[Figure 15]
Page: 22
[Figure 16]
Page: 22
[Figure 17]
Page: 22
[Figure 18]
Page: 23
[Figure 19]
Page: 24
[Figure 20]
Page: 25
[Figure 21]
Page: 26
[Figure 22]
Page: 27
[Figure 23]
Page: 27
[Figure 24]
Page: 28
[Figure 25]
Page: 28
[Figure 26]
Page: 29
[Figure 27]
Page: 30
[Figure 28]
Page: 31
[Figure 29]
Page: 33
[Figure 30]
Page: 34
< >
page |< < of 68 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="073/01/016.jpg" pagenum="345"/>
              But now that that Solid is lighter in the Liquid than out of it, as
                <lb/>
              is affirmed in the ſecond part, ſhall be demonſtrated in this man­
                <lb/>
              ner. </s>
              <s>Take a Solid, as ſuppoſe A, that is more grave than the Li­
                <lb/>
              quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
                <lb/>
              </s>
              <s>And of a Maſs of
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquor of the ſame bigneſs with the Solid A, ſup­
                <lb/>
              poſe the Gravity to be B: It is to be demonſtrated that the Solid
                <lb/>
              A, immerged in the Liquid, ſhall have a Gravity equal to G. </s>
              <s>And
                <lb/>
              to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
                <lb/>
              more light than the Liquid, but of ſuch a quality as that its Gravi­
                <lb/>
              ty is equal to B: and let this D be of ſuch a Magnitude, that a
                <lb/>
              Maſs of
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquor equal to it hath its Gravity equal to the Gravity
                <lb/>
              B G. </s>
              <s>Now theſe two Solids D and A being compounded toge­
                <lb/>
              ther, all that Solid compounded of theſe two ſhall be equally
                <lb/>
              Grave with the Water: becauſe the Gravity of theſe two Solids
                <lb/>
              together ſhall be equal to theſe two Gravities, that is, to B G, and
                <lb/>
                <figure id="id.073.01.016.1.jpg" xlink:href="073/01/016/1.jpg" number="9"/>
                <lb/>
              to B; and the Gravity of a Liquid that hath its
                <lb/>
              Maſs equal to theſe two Solids A and D, ſhall be
                <lb/>
              equal to theſe two Gravities B G and B.
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              et
                <lb/>
              theſe two Solids, therefore, be put in the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid,
                <lb/>
                <arrow.to.target n="marg1136"/>
                <lb/>
              and they ſhall ^{*} remain in the Surface of that
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              i­
                <lb/>
              quid, (that is, they ſhall not be drawn or driven
                <lb/>
              upwards, nor yet downwards:) For if the Solid
                <lb/>
              A be more grave than the Liquid, it ſhall be
                <lb/>
              drawn or born by its Gravity downwards to­
                <lb/>
              wards the Bottom, with as much Force as by the Solid D it is thruſt
                <lb/>
              upwards: And becauſe the Solid D is lighter than the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, it
                <lb/>
              ſhall raiſe it upward with a Force as great as the Gravity G: Be­
                <lb/>
              cauſe it hath been demonſtrated, in the ſixth
                <emph type="italics"/>
              Propoſition,
                <emph.end type="italics"/>
              That So­
                <lb/>
              lid Magnitudes that are lighter than the Water, being demitted in
                <lb/>
              the ſame, are repulſed or driven upwards with a Force ſo much the
                <lb/>
              greater by how much a
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid of equal Maſs with the Solid is more
                <lb/>
              Grave than the ſaid Solid: But the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid which is equal in Maſs
                <lb/>
              with the Solid D, is more grave than the ſaid Solid D, by the Gra­
                <lb/>
              vity G: Therefore it is manifeſt, that the Solid A is preſſed or
                <lb/>
              born downwards towards the Centre of the World, with a Force
                <lb/>
              as great as the Gravity G: Which was to be demonſtrated.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1136"/>
              * Or, according to
                <lb/>
                <emph type="italics"/>
              Commandine,
                <emph.end type="italics"/>
              ſhall
                <lb/>
              be equall in Gravi­
                <lb/>
              ty to the Liquid,
                <lb/>
              neither moving up­
                <lb/>
              wards or down­
                <lb/>
              wards.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This hath been an ingenuous Demonſtration; and in regard I do ſuffici­
                <lb/>
              ently underſtand it, that we may loſe no time, we will proceed to the ſecond
                <emph type="italics"/>
              Suppo­
                <lb/>
              ſition,
                <emph.end type="italics"/>
              which, as I need not tell you, ſpeaks thus.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum