Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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            <s xml:id="echoid-s197" xml:space="preserve">
              <pb o="3" file="0017" n="17" rhead="DE IIS QVAE VEH. IN AQVA."/>
            iuncta, & </s>
            <s xml:id="echoid-s198" xml:space="preserve">continuata: </s>
            <s xml:id="echoid-s199" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s200" xml:space="preserve">ſectio planorũ ipſius K m K n:
              <lb/>
            </s>
            <s xml:id="echoid-s201" xml:space="preserve">& </s>
            <s xml:id="echoid-s202" xml:space="preserve">in humido intelligatur quædam magnitudo r s q y ex ip
              <lb/>
            ſo humido conſtans, æqualis, & </s>
            <s xml:id="echoid-s203" xml:space="preserve">ſimilis ſolidæ b h t c, quæ
              <lb/>
            quidem pars eſt ſolidæ magnitudinis in humido demerſa. </s>
            <s xml:id="echoid-s204" xml:space="preserve">
              <lb/>
            partes igitur humidi, quæ ſcilicet in prima pyramide ſuper
              <lb/>
            ficie x o continetur, & </s>
            <s xml:id="echoid-s205" xml:space="preserve">quæ in altera continetur p o, æquali
              <lb/>
            ter ſunt poſitæ, & </s>
            <s xml:id="echoid-s206" xml:space="preserve">continuatæ ſed non ſimiliter premun-
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            tur. </s>
            <s xml:id="echoid-s207" xml:space="preserve">nam contenta quidem x o, premitur ſolido e h t f, & </s>
            <s xml:id="echoid-s208" xml:space="preserve">
              <lb/>
            humido interiecto inter ſuperficies x o, l m, & </s>
            <s xml:id="echoid-s209" xml:space="preserve">plana pyra-
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            midis; </s>
            <s xml:id="echoid-s210" xml:space="preserve">contenta uero p o premitur ſolido r s q y, & </s>
            <s xml:id="echoid-s211" xml:space="preserve">humi-
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            do inter ſuperficies o p, m n, & </s>
            <s xml:id="echoid-s212" xml:space="preserve">pyramidis plana interiecto. </s>
            <s xml:id="echoid-s213" xml:space="preserve">
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            minor autem eſt grauitas humidi, quod eſt inter m n, o p,
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            quàm eius, quod inter l m, x o. </s>
            <s xml:id="echoid-s214" xml:space="preserve">ſolidum enim r s q y eſt mi
              <lb/>
            nus ſolido e h t f: </s>
            <s xml:id="echoid-s215" xml:space="preserve">cum ſit æquale ipſi b h t c; </s>
            <s xml:id="echoid-s216" xml:space="preserve">quia magnitu
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            dine æquale, & </s>
            <s xml:id="echoid-s217" xml:space="preserve">æque graue ponitur ſolidum, atque humi-
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            dum: </s>
            <s xml:id="echoid-s218" xml:space="preserve">reliquum autem reliquo inæquale eſt. </s>
            <s xml:id="echoid-s219" xml:space="preserve">conſtatigitur
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            partem contentã ſuperficie o p, expelli ab ea, quæ ipſa x o
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            continetur: </s>
            <s xml:id="echoid-s220" xml:space="preserve">& </s>
            <s xml:id="echoid-s221" xml:space="preserve">non conſiſtere humidum. </s>
            <s xml:id="echoid-s222" xml:space="preserve">ponebatur au-
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            tem conſiſtens, & </s>
            <s xml:id="echoid-s223" xml:space="preserve">manens: </s>
            <s xml:id="echoid-s224" xml:space="preserve">non ergo ex ſuperficie humidi
              <lb/>
            extat aliquid ſolidæ magnitudinis. </s>
            <s xml:id="echoid-s225" xml:space="preserve">ſed neque demerſum
              <lb/>
            ſolidum ad inferiora feretur. </s>
            <s xml:id="echoid-s226" xml:space="preserve">Similiter enim prementur
              <lb/>
            omnes partes humidi æqualiter poſitæ, cum ſolidum ſit æ-
              <lb/>
            que graue, atque humidum.</s>
            <s xml:id="echoid-s227" xml:space="preserve"/>
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          <head xml:id="echoid-head14" xml:space="preserve">PROPOSITIO IIII.</head>
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              <emph style="sc">Solidarvm</emph>
            magnitudinum, quæcunque
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            leuior humido fuerit, demiſſa in humidum non
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            demergetur tota, ſed aliqua pars ipſius ex humi-
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            di ſuperficie extabit.</s>
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            <s xml:id="echoid-s230" xml:space="preserve">SIT magnitudo ſolida humido leuior; </s>
            <s xml:id="echoid-s231" xml:space="preserve">& </s>
            <s xml:id="echoid-s232" xml:space="preserve">demiſſa in hu
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            midum demergatur tota, ſi fieri poteſt, ut nulla pars </s>
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