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>
            <s xml:id="echoid-s1342" xml:space="preserve">quam proportionem habet quadratum e ψ ad quadra-
              <lb/>
              <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">G</note>
            tum ψ b, eandem habet dimidium lineæ _k_ r ad lineã ψ b.
              <lb/>
            </s>
            <s xml:id="echoid-s1343" xml:space="preserve">quare maiorem babet proportionem _k_ r ad i y, quàm di-
              <lb/>
              <note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">13. quin-
                <lb/>
              ti.</note>
            midium k r ad ψ b: </s>
            <s xml:id="echoid-s1344" xml:space="preserve">& </s>
            <s xml:id="echoid-s1345" xml:space="preserve">idcirco i y minor eſt, quàm dupla
              <lb/>
              <note position="left" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve">H</note>
            ψ b. </s>
            <s xml:id="echoid-s1346" xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:id="echoid-s1347" xml:space="preserve">ergo o i minor eſt, quàm
              <lb/>
            ψ b: </s>
            <s xml:id="echoid-s1348" xml:space="preserve">& </s>
            <s xml:id="echoid-s1349" xml:space="preserve">i ω maior, quàm ψ r. </s>
            <s xml:id="echoid-s1350" xml:space="preserve">ſed ψ r eſt æqualis ipſi f. </s>
            <s xml:id="echoid-s1351" xml:space="preserve">maior
              <lb/>
              <note position="left" xlink:label="note-0058-04" xlink:href="note-0058-04a" xml:space="preserve">K</note>
            igitur eſt i ω, quàm f. </s>
            <s xml:id="echoid-s1352" xml:space="preserve">& </s>
            <s xml:id="echoid-s1353" xml:space="preserve">quoniam portio ad humidum in
              <lb/>
            grauitate eam ponitur habere proportionem, quam qua-
              <lb/>
            dratum f q ad quadratum b d: </s>
            <s xml:id="echoid-s1354" xml:space="preserve">quam uero proportionem
              <lb/>
            habet portio ad humidum in grauitate, eam habet pars ip
              <lb/>
            ſius demerſa ad totam portionem: </s>
            <s xml:id="echoid-s1355" xml:space="preserve">& </s>
            <s xml:id="echoid-s1356" xml:space="preserve">quam pars ipſius de-
              <lb/>
            merſa habet ad totam, eandem habet quadratum p m ad
              <lb/>
            quadratnm o n: </s>
            <s xml:id="echoid-s1357" xml:space="preserve">ſequitur quadratum p m ad quadratum
              <lb/>
            o n eam proportionem habere, quam quadratum f q ad
              <lb/>
            b d quadratum.
              <lb/>
            </s>
            <s xml:id="echoid-s1358" xml:space="preserve">
              <figure xlink:label="fig-0058-01" xlink:href="fig-0058-01a" number="37">
                <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0058-01"/>
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            atque ideo ſ q æ-
              <lb/>
              <note position="left" xlink:label="note-0058-05" xlink:href="note-0058-05a" xml:space="preserve">L</note>
            qualis eſt ipſi p m.
              <lb/>
            </s>
            <s xml:id="echoid-s1359" xml:space="preserve">demõſtrata eſt au
              <lb/>
              <note position="left" xlink:label="note-0058-06" xlink:href="note-0058-06a" xml:space="preserve">M</note>
            tem p h maior,
              <lb/>
            quàm f. </s>
            <s xml:id="echoid-s1360" xml:space="preserve">cõſtat igi
              <lb/>
            tur p m minorem
              <lb/>
            eſſe, quàm ſeſqui-
              <lb/>
            alterã ipſius p h:
              <lb/>
            </s>
            <s xml:id="echoid-s1361" xml:space="preserve">& </s>
            <s xml:id="echoid-s1362" xml:space="preserve">idcirco p h ma
              <lb/>
            iorem, quàm du-
              <lb/>
            plam h m. </s>
            <s xml:id="echoid-s1363" xml:space="preserve">Sit p z
              <lb/>
            ipſius z m dupla. </s>
            <s xml:id="echoid-s1364" xml:space="preserve">
              <lb/>
            erit t quidem cẽ-
              <lb/>
            trũ grauitatis to-
              <lb/>
            tius ſolidi: </s>
            <s xml:id="echoid-s1365" xml:space="preserve">centrũ
              <lb/>
            eius partis, quæ intra humidum, punctumz: </s>
            <s xml:id="echoid-s1366" xml:space="preserve">reliquæ uero
              <lb/>
            partis centrum erit in linea z t producta uſque ad g. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">Eodẽ
              <lb/>
              <note position="left" xlink:label="note-0058-07" xlink:href="note-0058-07a" xml:space="preserve">N</note>
            modo demonſtrabitur linea th perpendicularis ad ſuper-
              <lb/>
            ficiem humidi. </s>
            <s xml:id="echoid-s1368" xml:space="preserve">& </s>
            <s xml:id="echoid-s1369" xml:space="preserve">portio demerſa in humido ſeretur </s>
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