Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[1. None]
[2. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBRI DVO. A FEDERICO COMMANDINO VRBINATE IN PRISTINVM NITOREM RESTITVTI, ET COMMENTARIIS ILLVSTRATI.]
[3. CVM PRIVILEGIO IN ANNOS X. BONONIAE,]
[4. M D LXV.]
[5. RANVTIO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[6. Federicus Commandinus.]
[7. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER PRIMVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. POSITIO.]
[8. PROPOSITIO I.]
[9. PROPOSITIO II.]
[10. PROPOSITIO III.]
[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
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ARCHIMEDIS
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        <div type="section" level="1" n="18">
          <p style="it">
            <s xml:space="preserve">
              <pb file="0026" n="26" rhead="ARCHIMEDIS"/>
            @e centro grauitatis ſolidorum demonstrauimus: </s>
            <s xml:space="preserve">erit magnitudi-
              <lb/>
            nis ex utriſque portionibus b n c, b g c conſtantis; </s>
            <s xml:space="preserve">hoc eſt portionis
              <lb/>
            in humido demerſa grauitatis centrum in linea n g, quæ ipſarum
              <lb/>
            ſphæræ portionum centra graui-
              <lb/>
              <anchor type="figure" xlink:label="fig-0026-01a" xlink:href="fig-0026-01"/>
            tatis coniungit. </s>
            <s xml:space="preserve">ſi enim fieri po-
              <lb/>
            teſt, ſit extra lineam n g, ut in
              <lb/>
            q: </s>
            <s xml:space="preserve">sîtq; </s>
            <s xml:space="preserve">portionis b n c centrum
              <lb/>
            grauitatis u; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur u q.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0025-03" xlink:href="note-0025-03a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0025-04" xlink:href="note-0025-04a" xml:space="preserve">29. primi</note>
            <note position="right" xlink:label="note-0025-05" xlink:href="note-0025-05a" xml:space="preserve">3. tertii.</note>
            <figure xlink:label="fig-0026-01" xlink:href="fig-0026-01a">
              <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0026-01"/>
            </figure>
          </div>
          <p style="it">
            <s 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: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:space="preserve">quod fieri non potest; </s>
            <s xml:space="preserve">eſt enim in axe ipſius mg. </s>
            <s xml:space="preserve">sequi-
              <lb/>
            tur ergo ut portionis in humido demerſæ centrum grauitatis ſit in li
              <lb/>
            nean k. </s>
            <s xml:space="preserve">quod oſtendendum propoſuimus.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">_Sed totius portionis grauitatis centrum eſt in linea ft, in-_
              <lb/>
              <anchor type="note" xlink:label="note-0026-01a" xlink:href="note-0026-01"/>
            _ter_ k, _& </s>
            <s xml:space="preserve">f, quod ſit x.</s>
            <s xml:space="preserve">]_ Compleatur ſphæra, ut ſit portionis additæ
              <lb/>
            axis t y; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrú grauitatis z. </s>
            <s xml:space="preserve">Itaque quoniá à tota ſphæra, cuius
              <lb/>
            grauitatis cétrum eſt k, ut etiam in eodem libro demóſtrauimus, au
              <lb/>
              <anchor type="note" xlink:label="note-0026-02a" xlink:href="note-0026-02"/>
            fertur portio e y h centrú grauitatis habens z: </s>
            <s xml:space="preserve">erit reliquæ portionis
              <lb/>
            e f h cétrú in linea z k producta. </s>
            <s xml:space="preserve">quare inter k. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">f neceſſario cadet.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0026-01" xlink:href="note-0026-01a" xml:space="preserve">D</note>
            <note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve">8. primi
              <lb/>
            Archime
              <lb/>
            dis.</note>
          </div>
          <p>
            <s xml:space="preserve">Reliquæ ergo figuræ, quæ eſt extra humidum, centrum erit
              <lb/>
              <anchor type="note" xlink:label="note-0026-03a" xlink:href="note-0026-03"/>
            in linea r x producta.</s>
            <s xml:space="preserve">] _Ex eadem octaua primi libri Archime-_
              <lb/>
            _dis de centro grauitatis planorum._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve">E</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Feretur ergo grauitas, figuræ quidem quæ extra humi_-
              <lb/>
              <anchor type="note" xlink:label="note-0026-04a" xlink:href="note-0026-04"/>
            _dum per rectam s l deorſum; </s>
            <s xml:space="preserve">portionis autem, quæ in_
              <lb/>
            _humido ſurſum per rectam r l.</s>
            <s xml:space="preserve">]_ Ex antecedenti poſitio-
              <lb/>
            ne. </s>
            <s 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:space="preserve">id quod ex propoſitione ſexta huius li-
              <lb/>
            briconſtare poteſt. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam feruntur per alias, atque alias li-</s>
          </p>
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