Galilei, Galileo, Discourse concerning the natation of bodies, 1663

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 77 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="414"/>
            <p type="head">
              <s>THEOREME
                <lb/>
                <arrow.to.target n="marg1416"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1416"/>
              The proportion
                <lb/>
              of water
                <lb/>
              ſite to make a
                <lb/>
              Solid ſwim.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically
                <lb/>
              than the Water, being put into a Veſſel, as above, of
                <lb/>
              whatſoever greatneſſe, and the Water, be afterwards
                <lb/>
              infuſed, the Solid ſhall reſt in the bottom, unraiſed, till
                <lb/>
              the Water arrive to that part of the Altitude, of the
                <lb/>
              ſaid Priſme, to which its whole Altitude hath the
                <lb/>
              ſame proportion, that the Specificall Gravity of the
                <lb/>
              Water, hath to the Specificall Gravity of the ſaid
                <lb/>
              Solid: but infuſing more Water, the Solid ſhall aſcend.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let the Veſſell be M L G N of any bigneſs, and let there be
                <lb/>
              ced in it the Solid Priſme D F G E, leſs grave
                <emph type="italics"/>
              in ſpecie
                <emph.end type="italics"/>
              than the
                <lb/>
              water; and look what proportion the
                <emph type="italics"/>
              S
                <emph.end type="italics"/>
              pecificall Gravity of
                <lb/>
              the water, hath to that of the Priſme, ſuch let the Altitude D F, have
                <lb/>
              to the Altitude F B. </s>
              <s>I ſay, that infuſing water to the Altitude F B,
                <lb/>
              the Solid D G ſhall not float, but ſhall ſtand in
                <emph type="italics"/>
              Equilibrium,
                <emph.end type="italics"/>
              ſo, that
                <lb/>
              that every little quantity of water, that is infuſed, ſhall raiſe it. </s>
              <s>Let
                <lb/>
              the water, therefore, be infuſed to the Levell A B C, and, becauſe
                <lb/>
              the Specifick Gravity of the Solid D G, is to the Specifick Gravity of
                <lb/>
              the water, as the altitude B F is to the altitude F D; that is, as the Maſs
                <lb/>
              B G to the Maſs G D; as the proportion of the Maſs B G is to the
                <lb/>
              Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they
                <lb/>
              compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore,
                <lb/>
              the Maſs B G is to the Maſs A F, in a proportion compounded of the
                <lb/>
              proportions of the Specifick Gravity of the Solid G D, to the
                <lb/>
              fick Gravity of the water, and of the Maſs G D
                <lb/>
              to the Maſs A F: But the ſame proportions
                <lb/>
                <figure id="fig266" number="5"/>
                <lb/>
              of the Specifick Gravity of G D, to the Specifick
                <lb/>
              Gravity of the water, and of the Maſs G D to
                <lb/>
              the Maſs A F, do alſo by the precedent
                <emph type="italics"/>
              Lemma,
                <emph.end type="italics"/>
                <lb/>
              compound the proportion of the abſolute
                <lb/>
              vity of the Solid D G, to the abſolute Gravity
                <lb/>
              of the Maſs of the water A F: Therefore,
                <lb/>
              as the Maſs B G is to the Maſs A F, ſo is the
                <lb/>
              Abſolute Gravity of the Solid D G, to the
                <lb/>
              ſolute Gravity of the Maſs of the water A F. </s>
              <s>But as the Maſs B G
                <lb/>
              is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface
                <lb/>
              of the water AB; and ſo is the deſcent of the water A B, to the
                <lb/>
              Elevation of the Priſme D G; Therefore, the deſcent of the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum