Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s991" xml:space="preserve">
              <pb file="0046" n="46" rhead="ARCHIMEDIS"/>
            pla eſt, aut minor, quàm dupla. </s>
            <s xml:id="echoid-s992" xml:space="preserve">Sit autem p t dupla t i. </s>
            <s xml:id="echoid-s993" xml:space="preserve">erit
              <lb/>
            centrum grauitatis eius, quod eſt in humido, punctum t.
              <lb/>
            </s>
            <s xml:id="echoid-s994" xml:space="preserve">Itaque iuncta t f producatur; </s>
            <s xml:id="echoid-s995" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s996" xml:space="preserve">eius, quod extra humi
              <lb/>
            dum grauitatis centrum g: </s>
            <s xml:id="echoid-s997" xml:space="preserve">& </s>
            <s xml:id="echoid-s998" xml:space="preserve">à puncto b ad rectos angu-
              <lb/>
            los ipſi n o ducatur b r. </s>
            <s xml:id="echoid-s999" xml:space="preserve">Quòd cum p i quidem ſit æqui-
              <lb/>
            diſtans diametro n o: </s>
            <s xml:id="echoid-s1000" xml:space="preserve">br autem ad diametrum perpendi
              <lb/>
            cularis. </s>
            <s xml:id="echoid-s1001" xml:space="preserve">& </s>
            <s xml:id="echoid-s1002" xml:space="preserve">f b æqualis ei, quæ uſque ad axem: </s>
            <s xml:id="echoid-s1003" xml:space="preserve">perſpicuum
              <lb/>
            eſt f r productam æquales facere angulos cum ea, quæ ſe-
              <lb/>
            ctionem a p o l in puncto p contingit. </s>
            <s xml:id="echoid-s1004" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s1005" xml:space="preserve">cum a s: </s>
            <s xml:id="echoid-s1006" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s1007" xml:space="preserve">cum ſuperficie humidi. </s>
            <s xml:id="echoid-s1008" xml:space="preserve">lineæ autem ductæ per tg æqui-
              <lb/>
            diſtantes ipſi f r, erunt & </s>
            <s xml:id="echoid-s1009" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a" number="27">
                <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0046-01"/>
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            ad humidi ſuperficiẽ per-
              <lb/>
            pendiculares: </s>
            <s xml:id="echoid-s1010" xml:space="preserve">& </s>
            <s xml:id="echoid-s1011" xml:space="preserve">ſolidi
              <lb/>
            a p o l magnitudo, quæ ẽ
              <lb/>
            intra humidum ſurſum fe
              <lb/>
            retur ſecundum perpen-
              <lb/>
            dicularem per t ductam;
              <lb/>
            </s>
            <s xml:id="echoid-s1012" xml:space="preserve">quæ uero extra humidum
              <lb/>
            ſecundum eam, quæ per g
              <lb/>
            deorſum feretur. </s>
            <s xml:id="echoid-s1013" xml:space="preserve">reuolue
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">E</note>
            tur ergo ſolidum a p o l:
              <lb/>
            </s>
            <s xml:id="echoid-s1014" xml:space="preserve">& </s>
            <s xml:id="echoid-s1015" xml:space="preserve">baſis ipſius nullo modo
              <lb/>
            humidi ſuperficiem con-
              <lb/>
            tinget. </s>
            <s xml:id="echoid-s1016" xml:space="preserve">At ſi pi lineam k ω
              <lb/>
            non ſecet, ut in ſecunda
              <lb/>
            figura; </s>
            <s xml:id="echoid-s1017" xml:space="preserve">manifeſtum eſt punctum t, quod eſt centrum gra-
              <lb/>
            uitatis demerſæ portionis, cadere inter p & </s>
            <s xml:id="echoid-s1018" xml:space="preserve">i: </s>
            <s xml:id="echoid-s1019" xml:space="preserve">& </s>
            <s xml:id="echoid-s1020" xml:space="preserve">reliqua
              <lb/>
            ſimiliter demonſtrabuntur.</s>
            <s xml:id="echoid-s1021" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div74" type="section" level="1" n="30">
          <head xml:id="echoid-head35" xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:id="echoid-s1022" xml:space="preserve">Demonſtrandum eſt non manere ipſam portionem, ſed
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">A</note>
            reuolui ita, ut baſis nullo modo ſuperficiem humidi con-
              <lb/>
            tingat.</s>
            <s xml:id="echoid-s1023" xml:space="preserve">] _Hæcnos addidimus tanquam ab interprete omiſſa_.</s>
            <s xml:id="echoid-s1024" xml:space="preserve"/>
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