Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[Figure 151]
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        <div xml:id="echoid-div111" type="section" level="1" n="38">
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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
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            portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
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            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
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            monſtratis apparere poteſt. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Quòd ſi axis cum ſuperficie
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            humidi fecerit angulum minorem angulo b, ſimiliter de-
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              <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
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            utique axis cum ſuperficie humidi faciat angulum angulo
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            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>
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            <s xml:id="echoid-s1618" xml:space="preserve">QVARE quadratum b d magis excedit quadratum
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              <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,
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            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_
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            _quadratum b d excedit quadratum b c ad quadratum b d minorem_
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            _proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
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            _dratum f q, ad idem quadratum: </s>
            <s xml:id="echoid-s1624" xml:space="preserve">erit ex octaua quinti exceſſus, quo_
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            _quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
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            _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">
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            _propterea linea f q minor linea b c. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Sed f q ad f eandem proportionẽ_
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            _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_
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              <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
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              <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_
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            _dratum ſ y
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            : </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_
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            _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_
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              <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-
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              <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
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            dratum f q.</s>
            <s xml:id="echoid-s1645" xml:space="preserve">] _Cum pars demerſa ad totam portionem ita ſit, ut_
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            _exceſſus, quo quadratum b d excedit quadratum f q ad b d quadratu
              <unsure/>
            :_</s>
            <s xml:id="echoid-s1646" xml:space="preserve"/>
          </p>
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