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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/1047.jpg" pagenum="352"/>
                <emph type="italics"/>
              of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore
                <lb/>
              the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por­
                <lb/>
              tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre
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              of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be
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              in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid
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              Portions by the foreſaid 8 of
                <emph.end type="italics"/>
              Archimedis de Centro Gravitatis Planorum.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1158"/>
              A</s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>Truth is, that in ſome of theſe Figures C is put for X, and ſo it was in
                <lb/>
              the Greek Copy that I followed.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This Demoſtration is very difficult, to my thinking; but I believe that
                <lb/>
              it is becauſe I have not in memory the Propoſitions of that Book entituled
                <emph type="italics"/>
              De Cen­
                <lb/>
              tris Gravium.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>It is ſo.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>We will take a more convenient time to diſcourſe of that, and now return
                <lb/>
                <arrow.to.target n="marg1159"/>
                <lb/>
              to ſpeak of the two laſt Propoſitions. </s>
              <s>And I ſay that the Figures incerted in the
                <lb/>
              demonſtration would in my opinion, have been better and more intelligble unto
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              me, drawing the Axis according to its proper Poſition; that is in the half Arch of
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              theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe
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              that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it
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              were poſſible, did not ſtand according to the Perpendicular ſo often mentioned,
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              which doing, the Propoſition would be proved in the ſame manner as before:
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              and this way would be more naturall and clear.
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                <arrow.to.target n="marg1160"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1159"/>
              A</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1160"/>
              B</s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>You are in the right, but becauſe thus they were in the Greek Copy,
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              I thought not fit to alter them, although unto the better.</s>
            </p>
            <p type="main">
              <s>RIC. Companion, you have thorowly ſatisfied me in all that in the beginning
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              of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of
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              ſome other ingenious Novelties.</s>
            </p>
            <p type="head">
              <s>THE TRANSLATOR.</s>
            </p>
            <p type="main">
              <s>I ſay that the Figures, &c. </s>
              <s>would have been more intelligible to </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1161"/>
                <lb/>
              me, drawing the Axis Z T according to its proper Poſition, that
                <lb/>
              is in the half Arch of theſe Figures.]
                <emph type="italics"/>
              And in this conſideration I have followed
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              the Schemes of
                <emph.end type="italics"/>
              Commandine,
                <emph type="italics"/>
              who being the Reſtorer of the Demonſtrations of theſe two laſt
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              Propoſitions, hath well conſidered what
                <emph.end type="italics"/>
              Ricardo
                <emph type="italics"/>
              here propoſeth, and therefore hath drawn the
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              ſaid Axis (which in the Manuſcripts that he had by him is lettered F T, and not as in that of
                <emph.end type="italics"/>
                <lb/>
              Tartaylia
                <emph type="italics"/>
              Z T,) according to that its proper Poſition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1161"/>
              A</s>
            </p>
            <p type="main">
              <s>But becauſe thus they were in the Greek Copy, I thought not
                <lb/>
                <arrow.to.target n="marg1162"/>
                <lb/>
              fit to alter them although unto the better.]
                <emph type="italics"/>
              The Schemes of thoſe Manu-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.1047.1.jpg" xlink:href="040/01/1047/1.jpg" number="244"/>
                <lb/>
                <emph type="italics"/>
              ſcripts that
                <emph.end type="italics"/>
              Tartaylia
                <emph type="italics"/>
              had ſeen were more imperfect then thoſe
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              in Commandines Copies; but for variety ſake, take here one
                <lb/>
              of
                <emph.end type="italics"/>
              Tartaylia,
                <emph type="italics"/>
              it being that of the Portion of a Sphære, equall
                <lb/>
              to an Hemiſphære, with its Axis oblique, and its Baſe dimitted
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              into the Liquid, and Lettered as in this Edition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1162"/>
              B</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Now Courteous Readers, I hope that you may, amidſt the
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              great Obſcurity of the Originall in the Demonſtrations of theſe
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              two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our
                <lb/>
              more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the
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              Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand
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              erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the
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              Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes
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              oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall
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              return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards,
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              they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no
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              more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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