Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s439" xml:space="preserve">
              <pb file="0026" n="26" rhead="ARCHIMEDIS"/>
            @e centro grauitatis ſolidorum demonstrauimus: </s>
            <s xml:id="echoid-s440" xml:space="preserve">erit magnitudi-
              <lb/>
            nis ex utriſque portionibus b n c, b g c conſtantis; </s>
            <s xml:id="echoid-s441" xml:space="preserve">hoc eſt portionis
              <lb/>
            in humido demerſa grauitatis centrum in linea n g, quæ ipſarum
              <lb/>
            ſphæræ portionum centra graui-
              <lb/>
              <figure xlink:label="fig-0026-01" xlink:href="fig-0026-01a" number="14">
                <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0026-01"/>
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            tatis coniungit. </s>
            <s xml:id="echoid-s442" xml:space="preserve">ſi enim fieri po-
              <lb/>
            teſt, ſit extra lineam n g, ut in
              <lb/>
            q: </s>
            <s xml:id="echoid-s443" xml:space="preserve">sîtq; </s>
            <s xml:id="echoid-s444" xml:space="preserve">portionis b n c centrum
              <lb/>
            grauitatis u; </s>
            <s xml:id="echoid-s445" xml:space="preserve">& </s>
            <s xml:id="echoid-s446" xml:space="preserve">ducatur u q.</s>
            <s xml:id="echoid-s447" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s448" xml:space="preserve">Quoniam igitur à portione in bu-
              <lb/>
            mido demerſa aufertur ſphæræ
              <lb/>
            portio b n c, non habens idem cen
              <lb/>
            trum grauitatis: </s>
            <s xml:id="echoid-s449" xml:space="preserve">erit ex octaua
              <lb/>
            primi libri Archimcdis de centro
              <lb/>
            grauitatis planorum, reliquæ por
              <lb/>
            tionis b g c centrum in linea u q
              <lb/>
            producta. </s>
            <s xml:id="echoid-s450" xml:space="preserve">quod fieri non potest; </s>
            <s xml:id="echoid-s451" xml:space="preserve">eſt enim in axe ipſius mg. </s>
            <s xml:id="echoid-s452" xml:space="preserve">sequi-
              <lb/>
            tur ergo ut portionis in humido demerſæ centrum grauitatis ſit in li
              <lb/>
            nean k. </s>
            <s xml:id="echoid-s453" xml:space="preserve">quod oſtendendum propoſuimus.</s>
            <s xml:id="echoid-s454" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s455" xml:space="preserve">_Sed totius portionis grauitatis centrum eſt in linea ft, in-_
              <lb/>
              <note position="left" xlink:label="note-0026-01" xlink:href="note-0026-01a" xml:space="preserve">D</note>
            _ter_ k, _& </s>
            <s xml:id="echoid-s456" xml:space="preserve">f, quod ſit x.</s>
            <s xml:id="echoid-s457" xml:space="preserve">]_ Compleatur ſphæra, ut ſit portionis additæ
              <lb/>
            axis t y; </s>
            <s xml:id="echoid-s458" xml:space="preserve">& </s>
            <s xml:id="echoid-s459" xml:space="preserve">centrú grauitatis z. </s>
            <s xml:id="echoid-s460" xml:space="preserve">Itaque quoniá à tota ſphæra, cuius
              <lb/>
            grauitatis cétrum eſt k, ut etiam in eodem libro demóſtrauimus, au
              <lb/>
              <note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve">8. primi
                <lb/>
              Archime
                <lb/>
              dis.</note>
            fertur portio e y h centrú grauitatis habens z: </s>
            <s xml:id="echoid-s461" xml:space="preserve">erit reliquæ portionis
              <lb/>
            e f h cétrú in linea z k producta. </s>
            <s xml:id="echoid-s462" xml:space="preserve">quare inter k. </s>
            <s xml:id="echoid-s463" xml:space="preserve">& </s>
            <s xml:id="echoid-s464" xml:space="preserve">f neceſſario cadet.</s>
            <s xml:id="echoid-s465" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s466" xml:space="preserve">Reliquæ ergo figuræ, quæ eſt extra humidum, centrum erit
              <lb/>
              <note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve">E</note>
            in linea r x producta.</s>
            <s xml:id="echoid-s467" xml:space="preserve">] _Ex eadem octaua primi libri Archime-_
              <lb/>
            _dis de centro grauitatis planorum._</s>
            <s xml:id="echoid-s468" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s469" xml:space="preserve">_Feretur ergo grauitas, figuræ quidem quæ extra humi_-
              <lb/>
              <note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve">F</note>
            _dum per rectam s l deorſum; </s>
            <s xml:id="echoid-s470" xml:space="preserve">portionis autem, quæ in_
              <lb/>
            _humido ſurſum per rectam r l.</s>
            <s xml:id="echoid-s471" xml:space="preserve">]_ Ex antecedenti poſitio-
              <lb/>
            ne. </s>
            <s xml:id="echoid-s472" xml:space="preserve">magnitudo @enim, quæ in humido demerſa est, tanta ui per li-
              <lb/>
            neam r l ſurſum@fertur, quanta quæ extra humidum per li-
              <lb/>
            neam s l, deorſum: </s>
            <s xml:id="echoid-s473" xml:space="preserve">id quod ex propoſitione ſexta huius li-
              <lb/>
            briconſtare poteſt. </s>
            <s xml:id="echoid-s474" xml:space="preserve">& </s>
            <s xml:id="echoid-s475" xml:space="preserve">quoniam feruntur per alias, atque alias </s>
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