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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="448"/>
            <p type="head">
              <s>THEOREME
                <lb/>
                <arrow.to.target n="marg1510"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1510"/>
              The heavieſt
                <lb/>
              Bodies may
                <lb/>
              ſwimme.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              All Matters, how heavy ſoever, even to Gold it ſelf,
                <lb/>
              heavieſt of all Bodies, known by us, may float upon
                <lb/>
              the Water.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Becauſe its Gravity being conſidered to be almoſt twenty times
                <lb/>
              greater than that of the water, and, moreover, the greateſt Alti­
                <lb/>
              tude that the Rampart of water can be extended to, without break
                <lb/>
              ing the Contiguity of the Air, adherent to the Surface of the Solid,
                <lb/>
              that is put upon the water being predetermined, if we ſhould make
                <lb/>
              a Plate of Gold ſo thin, that it exceeds not the nineteenth part ofthe
                <lb/>
              Altitude of the ſaid Rampart, this put lightly upon the water ſhall
                <lb/>
              reſt, without going to the bottom: and if Ebony ſhall chance to be
                <lb/>
              in ſeſquiſeptimall proportion more grave than the water, the greateſt
                <lb/>
              thickneſs that can be allowed to a Board of Ebony, ſo that it may be
                <lb/>
              able to ſtay above water without ſinking, would be ſeaven times
                <lb/>
              more than the height of the Rampart Tinn,
                <emph type="italics"/>
              v. </s>
              <s>gr.
                <emph.end type="italics"/>
              eight times
                <lb/>
              grave than water, ſhall ſwimm as oft as the thickneſs of its Plate,</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1511"/>
                <lb/>
              exceeds not the 7th part of the Altitude of the Rampart.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1511"/>
                <emph type="italics"/>
              He elſewhere
                <lb/>
              cites this as a
                <lb/>
              Propoſition,
                <lb/>
              fore I make it of
                <lb/>
              that number.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>And here I will not omit to note, as a ſecond Corrollary dependent
                <lb/>
              upon the things demonſtrated, that,</s>
            </p>
            <p type="head">
              <s>THEOREME
                <lb/>
                <arrow.to.target n="marg1512"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1512"/>
              Natation and
                <lb/>
              Submerſion,
                <lb/>
              lected from the
                <lb/>
              thickneſs,
                <lb/>
              ding the length
                <lb/>
              and breadth of
                <lb/>
              Plates.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The Expanſion of Figure not only is not the Cauſe of
                <lb/>
              Natation of thoſe grave Bodies, which
                <lb/>
              do ſubmerge, but alſo the determining what be
                <lb/>
              Boards of Ebony, or Plates of Iron or Gold that
                <lb/>
              ſwimme, depends not on it, rather that ſame
                <lb/>
              tion is to be collected from the only thickneſs of
                <lb/>
              Figures of Ebony or Gold, wholly excluding the
                <lb/>
              ſideration of length and breadth, as having no way
                <lb/>
              any ſhare in this Effect.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>It hath already been manifeſted, that the only cauſe of the
                <lb/>
              tion of the ſaid Plates, is the reduction of them to be leſs grave
                <lb/>
              than the water, by means of the connexion of that Air, which
                <lb/>
              ſcendeth together with them, and poſſeſſeth place in the water;
                <lb/>
              which place ſo occupyed, if before the circumfuſed water diffuſeth
                <lb/>
              it ſelf to fill it, it be capable of as much water, as ſhall weigh equall
                <lb/>
              with the Plate, the Plate ſhall remain ſuſpended, and ſinke
                <lb/>
              farther.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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