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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/1148.jpg" pagenum="455"/>
            <p type="head">
              <s>THE OREME XII.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              That it is poſſible to fo m Solid Bodies, of what Figure
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1523"/>
                <lb/>
                <emph type="italics"/>
              and greatneſs ſoever, that of their own Nature goe
                <lb/>
              to the Bottome; But by the help of the Air
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              tained in the Rampart, reſt without ſubmerging.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1523"/>
              Solids of any
                <lb/>
              Figure &
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              neſſe, that
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              rally ſink, may
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              by help of the
                <lb/>
              Air in the
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              part ſwimme.</s>
            </p>
            <p type="main">
              <s>The truth of this Propoſition is ſufficiently manifeſt in all thoſe
                <lb/>
              Solid Figures, that determine in their uppermoſt part in a plane
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              Superficies: for making ſuch Figures of ſome Matter
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              cally as grave as the water, putting them into the water, ſo that the
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              whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
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              places, provided, that ſuch a Matter equall in weight to the water,
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              may be exactly adjuſted: and they ſhall by conſequence, reſt or
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              lie even with the Levell of the water, without making any Rampart.
                <lb/>
              </s>
              <s>If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
                <lb/>
              without ſubmerging, though deprived of the help of the Rampart,
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              it is manifeſt, that they may admit ſo much encreaſe of Gravity,
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              (without encreaſing their Maſſes) as is the weight of as much water
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              as would be contained within the Rampart, that is made about their
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              upper plane Surface: by the help of which being ſuſtained, they
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              ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
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              made graver than the water. </s>
              <s>In Figures, therefore, that determine
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              above in a plane, we may cleerly comprehend, that the Rampart
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              added or removed, may prohibit or permit the deſcent: but in thoſe
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              Figures that go leſſening upwards towards the top, ſome Perſons
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              may, and that not without much ſeeming Reaſon, doubt whether
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              the ſame may be done, and eſpecially by thoſe which terminate in a
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              very acute Point, ſuch as are your Cones and ſmall Piramids. </s>
              <s>
                <lb/>
              ing theſe, therefore, as more dubious than the reſt, I will endeavour
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              to demonſtrate, that they alſo lie under the ſame Accident of going,
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              or not going to the Bottom, be they of any whatever bigneſs. </s>
              <s>Let
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              therefore the Cone be A B D, made of a matter
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              ſpecifically as grave as the water; it is manifeſt
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                <figure id="id.040.01.1148.1.jpg" xlink:href="040/01/1148/1.jpg" number="317"/>
                <lb/>
              that being put all under water, it ſhall reſt in
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              all places (alwayes provided, that it ſhall weigh
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              exactly as much as the water, which is almoſt
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              impoſſible to effect) and that any ſmall weight
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              being added to it, it ſhall ſink to the bottom:
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              but if it ſhall deſcend downwards gently, I ſay,
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              that it ſhall make the Rampart E S T O, and
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              that there ſhall ſtay out of the water the point A S T, tripple in
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              height to the Rampart E S: which is manifeſt, for the Matter of the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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