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="13" file="0037" n="37" rhead="DE IIS QVAE VEH. IN AQVA."/>
            b: </s>
            <s xml:id="echoid-s736" xml:space="preserve">iunctaq; </s>
            <s xml:id="echoid-s737" xml:space="preserve">br producatur: </s>
            <s xml:id="echoid-s738" xml:space="preserve">& </s>
            <s xml:id="echoid-s739" xml:space="preserve">ſit g centrum grauitatis
              <lb/>
            reliquæ figuræ isla. </s>
            <s xml:id="echoid-s740" xml:space="preserve">ſimiliter demonſtrabitur angulum
              <lb/>
            rok acutu eſ-
              <lb/>
              <figure xlink:label="fig-0037-01" xlink:href="fig-0037-01a" number="22">
                <image file="0037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0037-01"/>
              </figure>
            ſe: </s>
            <s xml:id="echoid-s741" xml:space="preserve">& </s>
            <s xml:id="echoid-s742" xml:space="preserve">perpendi
              <lb/>
            culare ab r ad
              <lb/>
            k ω ductam ca
              <lb/>
            dereinter k & </s>
            <s xml:id="echoid-s743" xml:space="preserve">
              <lb/>
            o, quæ ſit rt.
              <lb/>
            </s>
            <s xml:id="echoid-s744" xml:space="preserve">ſi autem à pun
              <lb/>
            ctis g b ducan
              <lb/>
            tur ipſi r t æqui
              <lb/>
            diſtantes; </s>
            <s xml:id="echoid-s745" xml:space="preserve">pars
              <lb/>
            quidem ſolidæ
              <lb/>
            magnitudinis,
              <lb/>
            quæ in humido eſt, ſurſum feretur ſecundum perpendicu-
              <lb/>
            larem per g ductam: </s>
            <s xml:id="echoid-s746" xml:space="preserve">quæ autem extra humidum ſecundũ
              <lb/>
            perpendicularem per b deorſum feretur: </s>
            <s xml:id="echoid-s747" xml:space="preserve">& </s>
            <s xml:id="echoid-s748" xml:space="preserve">non manebit
              <lb/>
            ſolidum a p o l ſic habens in humido: </s>
            <s xml:id="echoid-s749" xml:space="preserve">ſed quod quidem
              <lb/>
            eſt ad a feretur ſurſum: </s>
            <s xml:id="echoid-s750" xml:space="preserve">quod autem ad l deorſum, donec
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            p f fiat ſecundum perpendicularem.</s>
            <s xml:id="echoid-s751" xml:space="preserve"/>
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          <head xml:id="echoid-head30" xml:space="preserve">PROPOSITIO IIII.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            fuerit humido leuior, & </s>
            <s xml:id="echoid-s753" xml:space="preserve">axem habuerit maiorẽ,
              <lb/>
            qnàm ſeſquialterum eius, quæ uſque ad axem: </s>
            <s xml:id="echoid-s754" xml:space="preserve">ſi
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            in grauitate ad humidum æqualis molis non mi-
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            norem proportionem habeat ea, quàm quadra-
              <lb/>
            tũ, quod fit ab exceſſu, quo axis maior eſt, quàm
              <lb/>
            ſeſquialter eius, quæ uſque ad axẽ, habet ad qua-
              <lb/>
            dratum, quod ab axe; </s>
            <s xml:id="echoid-s755" xml:space="preserve">demiſſa in humidum, </s>
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