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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/1035.jpg" pagenum="340"/>
              contained between the Sphærical Superficies that proceed accord­
                <lb/>
              ing to P O and M N and the Planes of the Pyramid; and the Gra­
                <lb/>
              vity of the Liquid, which is according to M N O P, ſhall be leſſer
                <lb/>
              than that which is according to L M X O; becauſe that Solid of
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              Liquor which proceeds according to R S C Y is leſs than the Solid
                <lb/>
              E Z H T (having been ſuppoſed to be equal in quantity to only
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              the part H B G T of that:) And the ſaid Solid E Z H T hath been
                <lb/>
              ſuppoſed to be equally grave with the Liquid: Therefore the Gra­
                <lb/>
              vity of the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid compriſed betwixt the two Sphærical Superfi­
                <lb/>
              cies L M and
                <emph type="italics"/>
              X
                <emph.end type="italics"/>
              O, and betwixt the ſides L
                <emph type="italics"/>
              X
                <emph.end type="italics"/>
              and M O of the
                <lb/>
                <figure id="id.040.01.1035.1.jpg" xlink:href="040/01/1035/1.jpg" number="231"/>
                <lb/>
              Pyramid, together with
                <lb/>
              the whole Solid EZHT,
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              ſhall exceed the Gravity
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              of the Liquid compri­
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              ſed betwixt the other
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              two Sphærical Superfi­
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              cies M N and O P, and
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              the Sides M O and N P
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              of the Pyramid, toge­
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              ther with the Solid of Liquor R S C Y by the quantity of the Gra­
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              vity of the part E B Z G, ſuppoſed to remain above the Surface of
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              the Liquid: And therefore it is manifeſt that the part which pro­
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              ceedeth according to the Circumference O P is preſſed, driven, and
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              repulſed, according to the
                <emph type="italics"/>
              Suppoſition,
                <emph.end type="italics"/>
              by that which proceeds ac­
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              cording to the Circumference X O, by which means the Liquid
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              would not be ſetled and ſtill: But we did preſuppoſe that it was
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              ſetled, namely ſo, as to be without motion: It followeth, therefore,
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              that the ſaid Solid cannot in any part of it exceed or lie above the
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              Superficies of the Liquid: And alſo that being dimerged in the Li­
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              quid it cannot deſcend to the Bottom, for that all the parts of the
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              Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe
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              the Solid is equally grave with the Liquid, by what we preſuppoſed.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I do underſtand your Argumentation, but I underſtand not that Phraſe
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                <emph type="italics"/>
              Solid Magnitudes.
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              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>I will declare this Term unto you.
                <emph type="italics"/>
              Magnitude
                <emph.end type="italics"/>
              is a general Word that
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              reſpecteth all the Species of Continual Quantity; and the Species of Continual
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              Quantity are three, that is, the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ine, the Superficies, and the Body; which Body
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              is alſo called a Solid, as having in it ſelf
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ength, Breadth, and Thickneſs, or Depth:
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              and therefore that none might equivocate or take that Term
                <emph type="italics"/>
              Magnitudes
                <emph.end type="italics"/>
              to be
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              meant of
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              ines, or Superficies, but only of Solid
                <emph type="italics"/>
              Magnitudes,
                <emph.end type="italics"/>
              that is, Bodies, he
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              did ſpecifie it by that manner of expreſſion, as was ſaid. </s>
              <s>The truth is, that he
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              might have expreſt that
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              in this manner:
                <emph type="italics"/>
              Solids (or Bodies) which being
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              of equal Gravity with an equal Maſs of the Liquid,
                <emph.end type="italics"/>
              &c. </s>
              <s>And this
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              would have
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              been more cleer and intelligible, for it is as ſignificant to ſay, a
                <emph type="italics"/>
              Solid,
                <emph.end type="italics"/>
              or, a
                <emph type="italics"/>
              Body,
                <emph.end type="italics"/>
              as
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              to ſay, a
                <emph type="italics"/>
              Solid Magnitude:
                <emph.end type="italics"/>
              therefore wonder not if for the future I uſe theſe three
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              kinds of words indifferently.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>You have ſufficiently ſatisfied me, wherefore that we may loſe no time
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              let us go forwards to the fourth
                <emph type="italics"/>
              Propoſition.
                <emph.end type="italics"/>
              </s>
            </p>
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