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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          <p>
            <s xml:id="echoid-s1271" xml:space="preserve">
              <pb o="22" file="0055" n="55" rhead="DE IIS QVAE VEH. IN AQVA."/>
            & </s>
            <s xml:id="echoid-s1272" xml:space="preserve">c o quidẽ
              <lb/>
              <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a" number="34">
                <image file="0055-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0055-01"/>
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            ducatur con
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            tingẽs ſectio
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            nẽin o, quæ
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            ipſi s l æqui-
              <lb/>
            diſtet; </s>
            <s xml:id="echoid-s1273" xml:space="preserve">n o au
              <lb/>
            tem æquidi-
              <lb/>
              <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">10. quinti</note>
            ſtet p f: </s>
            <s xml:id="echoid-s1274" xml:space="preserve">& </s>
            <s xml:id="echoid-s1275" xml:space="preserve">pri
              <lb/>
            mum ipſam
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            k ω ſecet, at-
              <lb/>
            quein pũcto
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            i ſimiliter ut
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            in ſuperiori-
              <lb/>
            bus demonſtrabitur no, uel ſeſquialtera ipſius oi, uel
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            maior, quàm ſeſquialtera. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Sit autem o i minor, quam du-
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            pla ipſius in: </s>
            <s xml:id="echoid-s1277" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s1278" xml:space="preserve">o b dupla b n: </s>
            <s xml:id="echoid-s1279" xml:space="preserve">& </s>
            <s xml:id="echoid-s1280" xml:space="preserve">diſponantur eadem,
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            quæſupra. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">Similiter demonſtrabimus, ſi ducatur linea r t,
              <lb/>
            facere eam angulos rectos cum linea c o, & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">cum ſuperficie
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            humidi. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">quare à punctis b g lineæ ductæipſi r t æquidiſtã
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            tes, etiã ad humidi ſuperfi-
              <lb/>
              <figure xlink:label="fig-0055-02" xlink:href="fig-0055-02a" number="35">
                <image file="0055-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0055-02"/>
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            ciẽ perpẽdiculares erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s1284" xml:space="preserve">portio igitur quæ eſt extra
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            humidũ deorſum feretur
              <lb/>
            ſecundum eam perpendi-
              <lb/>
            cularem, quæ per b tran-
              <lb/>
            ſit; </s>
            <s xml:id="echoid-s1285" xml:space="preserve">quæ uero intra humi-
              <lb/>
            dum ſecundum eam, quæ
              <lb/>
            per g ſurſum ſeretur. </s>
            <s xml:id="echoid-s1286" xml:space="preserve">ex
              <lb/>
            quibus conſtat reuolui ſo-
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            lidum, ita ut baſis ipſius
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            nullo modo humidi ſuper
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            ficiem contingat: </s>
            <s xml:id="echoid-s1287" xml:space="preserve">quo-
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            niam nuncin uno puncto
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            contingens deorſum </s>
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