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-s1612" xml:space="preserve">
              <pb o="22" file="0067" n="67" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dum eam, quæ per g ſurſum eleuabitur. </s>
            <s xml:id="echoid-s1613" xml:space="preserve">non igitur manebit
              <lb/>
            portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
              <lb/>
            ciem humidi ſit perpendicularis: </s>
            <s xml:id="echoid-s1614" xml:space="preserve">quoniam quæ ex parte 1
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">F</note>
            deorſum; </s>
            <s xml:id="echoid-s1615" xml:space="preserve">quæ uero ex parte a ſurſum ferentur, ut ex iam de
              <lb/>
            monſtratis apparere poteſt. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Quòd ſi axis cum ſuperficie
              <lb/>
            humidi fecerit angulum minorem angulo b, ſimiliter de-
              <lb/>
              <note position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">G</note>
            monſtrabitur, nõ manere portionem, ſed inclinari, donec
              <lb/>
            utique axis cum ſuperficie humidi faciat angulum angulo
              <lb/>
            b æqualem.</s>
            <s xml:id="echoid-s1617" xml:space="preserve"/>
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        <div xml:id="echoid-div113" type="section" level="1" n="39">
          <head xml:id="echoid-head44" xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:id="echoid-s1618" xml:space="preserve">QVARE quadratum b d magis excedit quadratum
              <lb/>
              <note position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">A</note>
            f q, quàm b c quadratum: </s>
            <s xml:id="echoid-s1619" xml:space="preserve">& </s>
            <s xml:id="echoid-s1620" xml:space="preserve">idcirco linea f q minor eſt,
              <lb/>
            quàm b c: </s>
            <s xml:id="echoid-s1621" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s1622" xml:space="preserve">f minor quam b r.</s>
            <s xml:id="echoid-s1623" xml:space="preserve">] _Quoniani exceſſus, quo_
              <lb/>
            _quadratum b d excedit quadratum b c ad quadratum b d minorem_
              <lb/>
            _proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
              <lb/>
            _dratum f q, ad idem quadratum: </s>
            <s xml:id="echoid-s1624" xml:space="preserve">erit ex octaua quinti exceſſus, quo_
              <lb/>
            _quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
              <lb/>
            _cedit quadratum f q. </s>
            <s xml:id="echoid-s1625" xml:space="preserve">ergo quadratum f q minus est quadrato b c: </s>
            <s xml:id="echoid-s1626" xml:space="preserve">&_</s>
            <s xml:id="echoid-s1627" xml:space="preserve">
              <lb/>
            _propterea linea f q minor linea b c. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Sed f q ad f eandem proportionẽ_
              <lb/>
            _habet, quam b c ad b r; </s>
            <s xml:id="echoid-s1629" xml:space="preserve">utraque enim utriuſque ſeſquialtera est. </s>
            <s xml:id="echoid-s1630" xml:space="preserve">cum_
              <lb/>
              <note position="right" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">14. quinti</note>
            _igitur f q ſit minor b c, & </s>
            <s xml:id="echoid-s1631" xml:space="preserve">f ipſa b r minor erit_.</s>
            <s xml:id="echoid-s1632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1633" xml:space="preserve">Et propterea k r ad ſ y maiorem habet, quàm dimidium
              <lb/>
              <note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">B</note>
            ipſius k r ad ψ b.</s>
            <s xml:id="echoid-s1634" xml:space="preserve">] _Est enim k r ad ſ y, ut quadratum p s ad qua_
              <lb/>
            _dratum ſ y
              <unsure/>
            : </s>
            <s xml:id="echoid-s1635" xml:space="preserve">& </s>
            <s xml:id="echoid-s1636" xml:space="preserve">dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
              <lb/>
            _ad quadratum ψ b_.</s>
            <s xml:id="echoid-s1637" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1638" xml:space="preserve">Et s o minor quàm ψ b] _Est enim ſ y dupla ipſius ſ o._</s>
            <s xml:id="echoid-s1639" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">C</note>
          <p>
            <s xml:id="echoid-s1640" xml:space="preserve">Et p h maior, quàm f.</s>
            <s xml:id="echoid-s1641" xml:space="preserve">] _Nam p h eſt æqualis ſ ω, & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">r ψ_
              <lb/>
              <note position="right" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">D</note>
            _ipſi f_.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">Habebit ergo tota portio ad eam, quæ eſt extra humi-
              <lb/>
              <note position="right" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">E</note>
            dum proportionem eandem, quam quadratum b d ad qua
              <lb/>
            dratum f q.</s>
            <s xml:id="echoid-s1645" xml:space="preserve">] _Cum pars demerſa ad totam portionem ita ſit, ut_
              <lb/>
            _exceſſus, quo quadratum b d excedit quadratum f q ad b d quadratu
              <unsure/>
            :_</s>
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