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

Table of figures

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            <pb xlink:href="040/01/1042.jpg" pagenum="347"/>
            <p type="margin">
              <s>
                <margin.target id="marg1138"/>
              B</s>
            </p>
            <p type="main">
              <s>For the declaration of this
                <emph type="italics"/>
              Propoſition,
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              let a Solid Magnitude
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              that hath the Figure of a portion of a Sphære, as hath been ſaid,
                <lb/>
              be imagined to be de­
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                <figure id="id.040.01.1042.1.jpg" xlink:href="040/01/1042/1.jpg" number="236"/>
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              mitted into the Liquid; and
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              alſo, let a Plain be ſuppoſed
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              to be produced thorow the
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              Axis of that portion, and
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              thorow the Center of the
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              Earth: and let the Section
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              of the Surface of the Liquid
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              be the Circumference A B
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              C D, and of the Figure, the
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              Circumference E F H, & let
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              E H be a right line, and F T
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              the Axis of the Portion. </s>
              <s>If now
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              it were poſſible, for ſatisfact­
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              ion of the Adverſary, Let
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              it be ſuppoſed that the ſaid Axis were not according to the
                <emph type="italics"/>
              (a)
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              Per­
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                <arrow.to.target n="marg1139"/>
                <lb/>
              pendicular; we are then to demonſtrate, that the Figure will not
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              continue as it was conſtituted by the Adverſary, but that it will re­
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              turn, as hath been ſaid, unto its former poſition, that is, that the
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              Axis F T ſhall be according to the Perpendicular. </s>
              <s>It is manifeſt, by
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              the
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              Corollary
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              of the 1. of 3.
                <emph type="italics"/>
              Euclide,
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              that the Center of the Sphære
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              is in the Line F T, foraſmuch as that is the Axis of that Figure.
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              </s>
              <s>And in regard that the Por­
                <lb/>
                <figure id="id.040.01.1042.2.jpg" xlink:href="040/01/1042/2.jpg" number="237"/>
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              tion of a Sphære, may be
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              greater or leſſer than an He­
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              miſphære, and may alſo be
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              an Hemiſphære, let the Cen­
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              tre of the Sphære, in the He­
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              miſphære, be the Point T,
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              and in the leſſer Portion the
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              Point P, and in the greater,
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              the Point K, and let the Cen­
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              tre of the Earth be the Point
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              L. </s>
              <s>And ſpeaking, firſt, of
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              that greater Portion which
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              hath its Baſe out of, or a­
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              bove, the Liquid, thorew the Points K and L, draw the Line KL
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              cutting the Circumference E F H in the Point N, Now, becauſe
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                <arrow.to.target n="marg1140"/>
                <lb/>
              every Portion of a Sphære, hath its Axis in the Line, that from the
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              Centre of the Sphære is drawn perpendicular unto its Baſe, and hath
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              its Centre of Gravity in the Axis; therefore that Portion of the Fi­
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              gure which is within the Liquid, which is compounded of two </s>
            </p>
          </chap>
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