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

Table of figures

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              <s>
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              mit a Board of Ebony into the Water, you do not put therein a Solid
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              more grave
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              in ſpecie
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              than the Water, but one lighter, for be ſides the
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              Ebony, there is in the Water a Maſs of Air, united with the Ebony,
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              and ſuch, and ſo light, that of both there reſults a Compoſition leſs
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              grave than the Water: See, therefore, that you remove the Air, and
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              put the Ebony alone into the Water, for ſo you ſhall immerge a
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              lid more grave then the Water, and if this ſhall not go to the Bottom,
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              you have well Philoſophized, and I ill.</s>
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              <s>Now, ſince we have found the true Cauſe of the Natation of thoſe
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              Bodies, which otherwiſe as being graver than the Water, would
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              ſcend to the bottom, I think, that for the perfect and diſtinct
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              ledge of this buſineſs, it would be good to proceed in a way of
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              covering demonſtratively thoſe particular Accidents that do attend
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              theſe effects, and,</s>
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            <p type="head">
              <s>PROBL. I.</s>
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            <p type="main">
              <s>
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              To finde what proportion ſeverall Figures of different
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              </s>
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              <s>
                <arrow.to.target n="marg1507"/>
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                <emph type="italics"/>
              Matters ought to have, unto the Gravity of the
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              Water, that ſo they may be able by vertue of the
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              Contigucus Air to ſtay afloat.
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              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1507"/>
              To finde the
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              proportion
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              gures ought to
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              have to the
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              ters Gravity,
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              that by help of
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              the contiguous
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              Air, they may
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              ſwim.</s>
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            <p type="main">
              <s>Let, therefore, for better illuſtration, D F N E be a Veſſell,
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              wherein the water is contained, and ſuppoſe a Plate or Board,
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              whoſe thickneſs is comprehended between the Lines I C and
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              O S, and let it be of Matter exceeding the water in Gravity, ſo that
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              being put upon the water, it dimergeth and abaſeth below the Levell
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              of the ſaid water, leaving the little Banks A I and B C, which are at
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              the greateſt height they can be, ſo that if the Plate I S ſhould but
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              deſcend any little ſpace farther, the little Banks or Ramparts would
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              no longer conſiſt, but expulſing the Air A I C B, they would
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              fuſe themſelves over the Superficies I C, and
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              would ſubmerge the Plate. </s>
              <s>The height AIBC
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              is therefore the greateſt profundity that the
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                <figure id="fig270" number="9"/>
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              little
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              B
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              anks of water admit of. </s>
              <s>Now I ſay,
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              that from this, and from the proportion in
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              vity, that the Matter of the Plate hath to the
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              water, we may eaſily ſinde of what thickneſs, at moſt, we may make
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              the ſaid Plates, to the end, they may be able to bear up above water:
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              for if the Matter of the Plate or
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              B
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              oard I S were, for Example, as
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              heavy again as the water, a
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              B
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              oard of that Matter ſhall be, at the moſt
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              of a thickneſs equall to the greateſt height of the
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              B
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              anks, that is, as
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              thick as A I is high: which we will thus demonſtrate. </s>
              <s>Lot the
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              lid I S be donble in Gravity to the water, and let it be a regular </s>
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          </chap>
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