Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
[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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          <pb o="22" file="0155" n="155" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:id="echoid-s3876" xml:space="preserve">Ex demonſtratis perſpicue apparet, portioni
              <lb/>
            ſphæræ uel ſphæroidis, quæ dimidia maior eſt, cẽ
              <lb/>
            trum grauitatis in axe conſiſtere.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3878" xml:space="preserve">Data enim
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              <figure xlink:label="fig-0155-01" xlink:href="fig-0155-01a" number="108">
                <image file="0155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0155-01"/>
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            qualibet maio
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            ri portiõe, quo
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            niã totius ſphæ
              <lb/>
            ræ, uel ſphæroi
              <lb/>
            dis grauitatis
              <lb/>
            centrum eſt in
              <lb/>
            axe; </s>
            <s xml:id="echoid-s3879" xml:space="preserve">eſt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s3880" xml:space="preserve">in axe cen-
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            trum portio-
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            nis minoris:
              <lb/>
            </s>
            <s xml:id="echoid-s3881" xml:space="preserve">reliquæ portionis uidelicet maioris centrum in axe neceſ-
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            ſario conſiſtet.</s>
            <s xml:id="echoid-s3882" xml:space="preserve"/>
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        <div xml:id="echoid-div238" type="section" level="1" n="82">
          <head xml:id="echoid-head89" xml:space="preserve">THE OREMA XIII. PROPOSITIO XVII.</head>
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            <s xml:id="echoid-s3883" xml:space="preserve">Cuiuslibet pyramidis triã
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            gularem baſim habẽtis gra
              <lb/>
            uitatis centrum eſt in pun-
              <lb/>
            cto, in quo ipſius axes con-
              <lb/>
            ueniunt.</s>
            <s xml:id="echoid-s3884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3885" xml:space="preserve">Sit pyramis, cuius baſis trian
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            gulum a b c, axis d e: </s>
            <s xml:id="echoid-s3886" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s3887" xml:space="preserve">trian
              <lb/>
            guli b d c grauitatis centrum f:
              <lb/>
            </s>
            <s xml:id="echoid-s3888" xml:space="preserve">& </s>
            <s xml:id="echoid-s3889" xml:space="preserve">iungatur a f. </s>
            <s xml:id="echoid-s3890" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s3891" xml:space="preserve">a faxis eiuſ
              <lb/>
            dem pyramidis ex tertia diffini-
              <lb/>
            tione huius. </s>
            <s xml:id="echoid-s3892" xml:space="preserve">Itaque quoniam centrum grauitatis eſt in
              <lb/>
            axe d e; </s>
            <s xml:id="echoid-s3893" xml:space="preserve">eſt autem & </s>
            <s xml:id="echoid-s3894" xml:space="preserve">in axe a f; </s>
            <s xml:id="echoid-s3895" xml:space="preserve">quod proxime </s>
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