Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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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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        <div xml:id="echoid-div190" type="section" level="1" n="62">
          <head xml:id="echoid-head69" xml:space="preserve">FEDERICI COMMANDINI
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          VRBINATIS LIBER DE CENTRO
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          GRAVITATIS SOLIDORVM.
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          DIFFINITIONES.</head>
          <p>
            <s xml:id="echoid-s2808" xml:space="preserve">
              <emph style="sc">CEntrvm</emph>
            grauitatis, Pappus
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            Alexandrinus in octauo ma-
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            thematicarum collectionum
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            libro ita diffiniuit.</s>
            <s xml:id="echoid-s2809" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2810" xml:space="preserve">λέγομεν δἐ κἐντρον βάρ
              <unsure/>
            ους ἑκά στου σἀ
              <unsure/>
              <lb/>
            ματος {εἶ}ναι σημ\~ειον τικείμενον ἑντὸς, ἀφ
              <unsure/>
              <lb/>
            οὖ κα\’τ ἐποίνιαν ἀρτηθέν τό βάρ
              <unsure/>
            ος ἡμερ{εἶ}
              <lb/>
            φερ
              <unsure/>
            όμενον, καὶ φυλὰσσει τήν ἐξἀρχ\~νςθἐ-
              <lb/>
            σιν, οὐ μὴ περιτρ
              <unsure/>
            επ ὸμενον ἐντῆ φορ
              <unsure/>
            ᾶ. </s>
            <s xml:id="echoid-s2811" xml:space="preserve">hoc eſt,</s>
          </p>
          <p>
            <s xml:id="echoid-s2812" xml:space="preserve">Dicimus autem centrum grauitatis uniuſcu-
              <lb/>
            inſque corporis punctum quoddam intra poſi-
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            cum, à quo ſi graue appenſum mente concipia-
              <lb/>
            tur, dum fertur quieſcit; </s>
            <s xml:id="echoid-s2813" xml:space="preserve">& </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ſeruat eam, quam in
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            principio habebat poſitionem: </s>
            <s xml:id="echoid-s2815" xml:space="preserve">neque in ipſa la-
              <lb/>
            tione circumuertitur.</s>
            <s xml:id="echoid-s2816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2817" xml:space="preserve">Poſſumus etiam hoc modo diffinire.</s>
            <s xml:id="echoid-s2818" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2819" xml:space="preserve">Centrum grauitatis uniuſcuiuſque ſolidæ figu
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            ræ eſt punctum illud intra poſitum, circa quod
              <lb/>
            undique partes æqualium momentorum conſi-
              <lb/>
            ſtunt. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">ſi enim per tale centrum ducatur planum
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            figuram quomodocunque ſecans ſemper in </s>
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