Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[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.
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            mus: </s>
            <s xml:id="echoid-s3896" xml:space="preserve">erit utique grauitatis centrum pyramidis punctum
              <lb/>
            g: </s>
            <s xml:id="echoid-s3897" xml:space="preserve">in quo ſcilicet ipſi axes conueniunt.</s>
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        <div xml:id="echoid-div240" type="section" level="1" n="83">
          <head xml:id="echoid-head90" xml:space="preserve">THEOREMA XIIII. PROPOSITIO XVIII.</head>
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            <s xml:id="echoid-s3899" xml:space="preserve">
              <emph style="sc">Si</emph>
            ſolidum parallelepipedum ſecetur plano
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            baſibus æquidiſtante; </s>
            <s xml:id="echoid-s3900" xml:space="preserve">erit ſolidum ad ſolidum,
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            ſicut altitudo ad altitudinem, uel ſicut axisad
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            axem.</s>
            <s xml:id="echoid-s3901" xml:space="preserve"/>
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            <s xml:id="echoid-s3902" xml:space="preserve">Sit ſolidum parallelepipe
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            dum a b c d e f g h, cuius axis
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            k 1: </s>
            <s xml:id="echoid-s3903" xml:space="preserve">ſeceturq; </s>
            <s xml:id="echoid-s3904" xml:space="preserve">plano baſibus
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            æquidiſtante, quod faciat
              <lb/>
            fectionem m n o p; </s>
            <s xml:id="echoid-s3905" xml:space="preserve">& </s>
            <s xml:id="echoid-s3906" xml:space="preserve">axi in
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            puncto q occurrat. </s>
            <s xml:id="echoid-s3907" xml:space="preserve">Dico
              <lb/>
            ſolidum g m ad ſolidum m c
              <lb/>
            eam proportionem habere,
              <lb/>
            quam altitudo ſolidi g m ha-
              <lb/>
            betad ſolidi m c altitudi-
              <lb/>
            nem; </s>
            <s xml:id="echoid-s3908" xml:space="preserve">uel quam axis k q ad
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            axem q l. </s>
            <s xml:id="echoid-s3909" xml:space="preserve">Sienim axis K l ad
              <lb/>
            baſis planum ſit perpendicu
              <lb/>
            laris, & </s>
            <s xml:id="echoid-s3910" xml:space="preserve">linea g c, quæ ex quin
              <lb/>
            ta huius ipſi k l æquidiſtat,
              <lb/>
            perpendicularis erit ad idẽ
              <lb/>
            planum, & </s>
            <s xml:id="echoid-s3911" xml:space="preserve">ſolidi altitudi-
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            nem dimetietur. </s>
            <s xml:id="echoid-s3912" xml:space="preserve">Itaqueſo-
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              <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">2. undeci
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              mi.</note>
            lidum g m ad ſolidum m c
              <lb/>
            eam proportionem habet,
              <lb/>
            quam parallelogrammũ g n
              <lb/>
            ad parallelogrammum n c,
              <lb/>
            hoc eſt quam linea g o, quæ
              <lb/>
              <note position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">i. ſexti.</note>
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