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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            <s xml:id="echoid-s706" xml:space="preserve">
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            angulus b n f œqualis angulo o g f: </s>
            <s xml:id="echoid-s707" xml:space="preserve">quòd cum ſit g o perpendi-
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">29, primi</note>
            cularis ad e f, & </s>
            <s xml:id="echoid-s708" xml:space="preserve">h n ad eandem perpendicularis erit. </s>
            <s xml:id="echoid-s709" xml:space="preserve">quod de-
              <lb/>
            monstrare oportebat.</s>
            <s xml:id="echoid-s710" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s711" xml:space="preserve">Et quod in humido eſt ſurſum ſeretur ſecundum per-
              <lb/>
              <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">G</note>
            pendicularem, quæ per b ducta eſtipſi rt æquidiſtans.</s>
            <s xml:id="echoid-s712" xml:space="preserve">]
              <lb/>
            _Cur hoc quidem ſurſum, illud uero deorſum per lineam perpen-_
              <lb/>
            _dicularem feratur, diximus ſupra in octauam primi libri buius. </s>
            <s xml:id="echoid-s713" xml:space="preserve">qua_
              <lb/>
            _re neque in hac, neque in alijs, quæ ſequuntur, eadem iterare neceſſa_
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            _rium exiſtimauimus._</s>
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        <div xml:id="echoid-div53" type="section" level="1" n="24">
          <head xml:id="echoid-head29" xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s715" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli quando
              <lb/>
            axem habuerit minorem, quam ſeſquialterum
              <lb/>
            eius, quæ uſque ad axem, quamcunque propor-
              <lb/>
            tionem habens ad humidum in grauitate; </s>
            <s xml:id="echoid-s716" xml:space="preserve">demiſ-
              <lb/>
            ſa in humidum, ita ut baſis ipſius tota ſit in humi
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            do; </s>
            <s xml:id="echoid-s717" xml:space="preserve">& </s>
            <s xml:id="echoid-s718" xml:space="preserve">poſita inclinata, non manebit inclinata, ſed
              <lb/>
            ita reſtituetur, ut axis ipſius ſecundum perpendi
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            cularem fiat.</s>
            <s xml:id="echoid-s719" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s720" xml:space="preserve">DEMITTATVR enim aliqua portio in humidum,
              <lb/>
            qualis dicca eſt: </s>
            <s xml:id="echoid-s721" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s722" xml:space="preserve">ipſius baſis in humido: </s>
            <s xml:id="echoid-s723" xml:space="preserve">& </s>
            <s xml:id="echoid-s724" xml:space="preserve">ſecta ipſa
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            plano per axẽ, recto ad ſuperficiẽ humidi, ſit ſectio a p ol
              <lb/>
            rectanguli coniſectio: </s>
            <s xml:id="echoid-s725" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s726" xml:space="preserve">ſectionis diame-
              <lb/>
            ter p f: </s>
            <s xml:id="echoid-s727" xml:space="preserve">ſuperficiei autem humidi ſectio ſit is. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Quòd ſi incli
              <lb/>
            nata iaceat portio, non erit axis ſecundum perpendicula-
              <lb/>
            rem. </s>
            <s xml:id="echoid-s729" xml:space="preserve">ergo p f cum is angulos rectos non faciet. </s>
            <s xml:id="echoid-s730" xml:space="preserve">Itaque
              <lb/>
            ducatur linea quædã k ω æquidiſtans ipſi is; </s>
            <s xml:id="echoid-s731" xml:space="preserve">contingensq;
              <lb/>
            </s>
            <s xml:id="echoid-s732" xml:space="preserve">ſectionẽ ap ol in o: </s>
            <s xml:id="echoid-s733" xml:space="preserve">& </s>
            <s xml:id="echoid-s734" xml:space="preserve">ſolidæ quidẽ magnitudinis a p o l
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            ſit r grauitatis centrum: </s>
            <s xml:id="echoid-s735" xml:space="preserve">ipſius autem i p o s centrum </s>
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