Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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            <s xml:id="echoid-s3931" xml:space="preserve">
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            ut altitudo ad altitudinem & </s>
            <s xml:id="echoid-s3932" xml:space="preserve">componendo conuertendo
              <lb/>
            que ſolidum a b g h, hoc eſt ſolidum a b c d ipſi æquale, ad
              <lb/>
              <note position="left" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">7. quinti.</note>
            ſolidum a b e f, ut altitudo ſolidi a b c d ad ſolidi a b e f al-
              <lb/>
            titudinem.</s>
            <s xml:id="echoid-s3933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3934" xml:space="preserve">Sint ſolida parallelepipeda a b, c d in æqualibus baſibus
              <lb/>
            conſtituta: </s>
            <s xml:id="echoid-s3935" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s3936" xml:space="preserve">b e altitudo ſolidi a b: </s>
            <s xml:id="echoid-s3937" xml:space="preserve">& </s>
            <s xml:id="echoid-s3938" xml:space="preserve">ſolidi c d altitudo
              <lb/>
            d f; </s>
            <s xml:id="echoid-s3939" xml:space="preserve">quæ quidem maior ſit, quàm b e. </s>
            <s xml:id="echoid-s3940" xml:space="preserve">Dico ſolidum a b ad
              <lb/>
            ſolidum c d eandem habere proportionem, quam be ad
              <lb/>
            d f. </s>
            <s xml:id="echoid-s3941" xml:space="preserve">abſcindatur enim à linea d f æqualis ipſi b e, quæ ſit g f:
              <lb/>
            </s>
            <s xml:id="echoid-s3942" xml:space="preserve">& </s>
            <s xml:id="echoid-s3943" xml:space="preserve">per g ducatur planum ſecans ſolidum c d; </s>
            <s xml:id="echoid-s3944" xml:space="preserve">quod baſibus
              <lb/>
            æquidiſtet, faciatq; </s>
            <s xml:id="echoid-s3945" xml:space="preserve">ſectionẽ h K. </s>
            <s xml:id="echoid-s3946" xml:space="preserve">erunt ſolida a b, c k æque
              <lb/>
              <note position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">31. unde
                <lb/>
              cimi</note>
            alta inter
              <lb/>
              <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a" number="112">
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            ſe æqualia
              <lb/>
            cũ æqua-
              <lb/>
            les baſes
              <lb/>
            habeant.
              <lb/>
            </s>
            <s xml:id="echoid-s3947" xml:space="preserve">Sed ſolidũ
              <lb/>
              <note position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">18. huius</note>
            h d ad ſoli
              <lb/>
            dum c _K_
              <lb/>
            eſt, ut alti
              <lb/>
            tudo d g
              <lb/>
            ad g f alti-
              <lb/>
            tudinẽ ſe
              <lb/>
            catur enim ſolidum c d plano baſi
              <lb/>
              <figure xlink:label="fig-0158-02" xlink:href="fig-0158-02a" number="113">
                <image file="0158-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0158-02"/>
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            bus æquidiſtante: </s>
            <s xml:id="echoid-s3948" xml:space="preserve">& </s>
            <s xml:id="echoid-s3949" xml:space="preserve">rurſus cõpo-
              <lb/>
            nendo, conuertendoq; </s>
            <s xml:id="echoid-s3950" xml:space="preserve">ſolidũ c _k_
              <lb/>
            ad ſolidum c d, ut g f ad fd. </s>
            <s xml:id="echoid-s3951" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">7. quinti.</note>
            ſolidum a b, quod eſt æquale ipſi
              <lb/>
            c k ad ſolidum c d eam proportio
              <lb/>
            nem habet, quam altitudo g f, hoc
              <lb/>
            eſt b e ad d f altitudinem.</s>
            <s xml:id="echoid-s3952" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3953" xml:space="preserve">Sint deinde ſolida parallelepipe
              <lb/>
            da a b, a c in eadem baſi; </s>
            <s xml:id="echoid-s3954" xml:space="preserve">quorum
              <lb/>
            axes d e, ſ e cum ipſa æquales </s>
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