Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[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.
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              <pb o="29" file="0069" n="69" rhead="DE IIS QVAE VEH. IN AQVA."/>
            interdũ quidem ita, ut baſis in humidum magis
              <lb/>
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">C</note>
            demergatur: </s>
            <s xml:id="echoid-s1669" xml:space="preserve">interdum uero ita, ut ſuperficiem
              <lb/>
              <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">D</note>
            humidi nullo modo contingat; </s>
            <s xml:id="echoid-s1670" xml:space="preserve">ſecundum pro-
              <lb/>
              <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">E</note>
            portionem, quam habet ad humidum in grauita-
              <lb/>
            te. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Eorum quæ dicta ſunt, ſingula inferius de-
              <lb/>
            monſtrabuntur.</s>
            <s xml:id="echoid-s1672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1673" xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:id="echoid-s1674" xml:space="preserve">& </s>
            <s xml:id="echoid-s1675" xml:space="preserve">ſecta ipſa plano per axẽ.
              <lb/>
            </s>
            <s xml:id="echoid-s1676" xml:space="preserve">recto ad ſuperficiem humidi, ſectio ſit a p o l rectanguli co
              <lb/>
            ni ſeccio: </s>
            <s xml:id="echoid-s1677" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s1678" xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:id="echoid-s1679" xml:space="preserve">ſece-
              <lb/>
            turq; </s>
            <s xml:id="echoid-s1680" xml:space="preserve">b d in puncto quidem _k_ ita, ut b k dupla ſitipſius
              <lb/>
            _k_ d: </s>
            <s xml:id="echoid-s1681" xml:space="preserve">in c uero ita, ut b d ad
              <emph style="sc">K C</emph>
            proportionẽ habeat ean-
              <lb/>
            dem, quam quindecim ad quatuor. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">conſtat igitur k c ma-
              <lb/>
              <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">F</note>
            iorem eſſe, quàm quæ uſque ad axem. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Sit ei quæ uſque ad
              <lb/>
              <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">G</note>
            axem æqualis k r: </s>
            <s xml:id="echoid-s1684" xml:space="preserve">& </s>
            <s xml:id="echoid-s1685" xml:space="preserve">ipſius k r ſeſquialtera d s. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">Eſt autem
              <lb/>
              <note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">H</note>
            & </s>
            <s xml:id="echoid-s1687" xml:space="preserve">s b ſeſquial-
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              <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a" number="43">
                <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0069-01"/>
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            tera ipſius b r.
              <lb/>
            </s>
            <s xml:id="echoid-s1688" xml:space="preserve">Itaque iũgatur
              <lb/>
            a b, & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">per c du
              <lb/>
            catur c e per-
              <lb/>
            pẽdicularis ad
              <lb/>
            b d, quæ lineã
              <lb/>
            a b in puncto
              <lb/>
            e ſecet: </s>
            <s xml:id="echoid-s1690" xml:space="preserve">& </s>
            <s xml:id="echoid-s1691" xml:space="preserve">per
              <lb/>
            e ducatur e z
              <lb/>
            æquidiſtãs b d. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">
              <lb/>
            Rurſus ipſa a b
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            bifariã in t di-
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            uiſa, ducatur t
              <lb/>
            h eidem b d æ-
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            quidiſtans: </s>
            <s xml:id="echoid-s1693" xml:space="preserve">& </s>
            <s xml:id="echoid-s1694" xml:space="preserve">
              <lb/>
            intelligantur rectanguli coni ſectiones deſcriptæ a e i </s>
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