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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              <pb file="0024" n="24" rhead="ARCHIMEDIS"/>
            in linea ft. </s>
            <s xml:space="preserve">nam ſit primum figura maior dimidia ſphære:
              <lb/>
            </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">in dimidia ſphæra ſphæræ centrum t; </s>
            <s xml:space="preserve">in minori por-
              <lb/>
            tioneſit centrum p; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in maiori _k_: </s>
            <s xml:space="preserve">per _k_ uero, & </s>
            <s xml:space="preserve">terræ cen
              <lb/>
            trum l ducatur _k_ l ſecans circunferentiam e f h in pun-
              <lb/>
            cto n. </s>
            <s xml:space="preserve">Quoniam igitur unaquæque ſphæræportio axem
              <lb/>
              <anchor type="note" xlink:label="note-0024-01a" xlink:href="note-0024-01"/>
            habet in linea, quæ à cẽtro ſphæræ ad cius baſim perpen-
              <lb/>
            dicularis ducitur: </s>
            <s xml:space="preserve">habetq; </s>
            <s xml:space="preserve">in axe grauitatis centrum:
              <lb/>
            </s>
            <s xml:space="preserve">portionis in humido demerſæ, quæ ex duabus ſphæræ
              <lb/>
            portionibus conſtat, axis erit in perpendiculari per _k_ du-
              <lb/>
            cta. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco centrum grauitatis ipſius erit in linea n _k_,
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            quod ſit r. </s>
            <s xml:space="preserve">ſed totius portionis grauitatis centrum eſt in li
              <lb/>
              <anchor type="note" xlink:label="note-0024-02a" xlink:href="note-0024-02"/>
            nea f t inter _k_, & </s>
            <s xml:space="preserve">f, quod ſit x. </s>
            <s xml:space="preserve">reliquæ ergo figuræ, quæ eſt
              <lb/>
              <anchor type="note" xlink:label="note-0024-03a" xlink:href="note-0024-03"/>
            extra humidum, centrum erit in linea r x producta ad par
              <lb/>
            tes x; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">aſſumpta ex ea, linea quadam, quæ ad r x eandem
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            proportionem habeat, quam grauitas portionis in humi-
              <lb/>
            do demerſæ habet ad grauitatem figuræ, quæ eſt extra hu-
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            midum. </s>
            <s xml:space="preserve">Sit autem s centrum dictæ figuræ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per s duca-
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            tur perpendicularis l s. </s>
            <s xml:space="preserve">Feretur ergo grauitas figuræ qui-
              <lb/>
              <anchor type="note" xlink:label="note-0024-04a" xlink:href="note-0024-04"/>
            dem, quæ extra humidum per rectam s l deorſum; </s>
            <s xml:space="preserve">portio
              <lb/>
            nis autem, quæ in humido, ſurſum per rectam r l. </s>
            <s xml:space="preserve">quare
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            non manebit figura: </s>
            <s xml:space="preserve">ſed partes eius, quæ ſunt ad e, deor-
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            ſum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ ad h ſurſum ſerẽtur: </s>
            <s xml:space="preserve">idq; </s>
            <s xml:space="preserve">cõtinenter fiet, quoad
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            ſ t ſit ſecundum perpendicularem. </s>
            <s xml:space="preserve">Eodem modo in aliis
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            portionibus idem demonſtrabitur.</s>
            <s xml:space="preserve">]</s>
          </p>
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            <note position="right" xlink:label="note-0023-03" xlink:href="note-0023-03a" xml:space="preserve">Suppleta
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            a Federi-
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            co Cõm.</note>
            <figure xlink:label="fig-0023-01" xlink:href="fig-0023-01a">
              <image file="0023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0023-01"/>
            </figure>
            <note position="left" xlink:label="note-0024-01" xlink:href="note-0024-01a" xml:space="preserve">C</note>
            <note position="left" xlink:label="note-0024-02" xlink:href="note-0024-02a" xml:space="preserve">D</note>
            <note position="left" xlink:label="note-0024-03" xlink:href="note-0024-03a" xml:space="preserve">E</note>
            <note position="left" xlink:label="note-0024-04" xlink:href="note-0024-04a" xml:space="preserve">F</note>
          </div>
          <figure>
            <image file="0024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0024-01"/>
          </figure>
        </div>
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