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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DE CENTRO GRAVIT. SOLID.
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              <pb o="3" file="0117" n="117" rhead="DE CENTRO GRAVIT. SOLID."/>
            cta b d in g puncto, ducatur c g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">protrahatur ad circuli
              <lb/>
            uſque circumferentiam; </s>
            <s xml:space="preserve">quæ ſecet a e in h. </s>
            <s xml:space="preserve">Similiter conclu
              <lb/>
            demus c g per centrum circuli tranſire: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſecare
              <lb/>
            lineam a e; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">lineas b d, a e inter ſe æquidiſtantes eſſe.
              <lb/>
            </s>
            <s xml:space="preserve">Cumigitur c g per centrum circuli tranſeat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad punctũ
              <lb/>
            f perueniat neceſſe eſt: </s>
            <s xml:space="preserve">quòd c d e f ſit dimidium circumfe
              <lb/>
            rentiæ circuli. </s>
            <s xml:space="preserve">Quare in eadem
              <lb/>
              <anchor type="figure" xlink:label="fig-0117-01a" xlink:href="fig-0117-01"/>
            diametro c f erunt centra gra
              <lb/>
              <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/>
            uitatis triangulorum b c d,
              <lb/>
            a f e, & </s>
            <s xml:space="preserve">quadrilateri a b d e, ex
              <lb/>
              <anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/>
            quibus conſtat hexagonum a b
              <lb/>
            c d e f. </s>
            <s xml:space="preserve">perſpicuum eſt igitur in
              <lb/>
            ipſa c f eſſe circuli centrum, & </s>
            <s xml:space="preserve">
              <lb/>
            centrum grauitatis hexagoni.
              <lb/>
            </s>
            <s xml:space="preserve">Rurſus ducta altera diametro
              <lb/>
            a d, eiſdem rationibus oſtende-
              <lb/>
            mus in ipſa utrumque cẽtrum
              <lb/>
            ineſſe. </s>
            <s xml:space="preserve">Centrum ergo grauita-
              <lb/>
            tis hexagoni, & </s>
            <s xml:space="preserve">centrum circuli idem erit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <figure xlink:label="fig-0117-01" xlink:href="fig-0117-01a">
              <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0117-01"/>
            </figure>
            <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">13. Archi
              <lb/>
            medis.</note>
            <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">9. @iuſdé.</note>
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          <p>
            <s xml:space="preserve">Sit heptagonum a b c d e f g æquilaterum atque æquian
              <lb/>
            gulum in circulo deſcriptum:
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0117-02a" xlink:href="fig-0117-02"/>
            & </s>
            <s xml:space="preserve">iungantur c e, b f, a g: </s>
            <s xml:space="preserve">di-
              <lb/>
            uiſa autem c e bifariam in pũ
              <lb/>
            cto h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta d h produca-
              <lb/>
            tur in k. </s>
            <s xml:space="preserve">non aliter demon-
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            ſtrabimus in linea d k eſſe cen
              <lb/>
            trum circuli, & </s>
            <s xml:space="preserve">centrum gra-
              <lb/>
            uitatis trianguli c d e, & </s>
            <s xml:space="preserve">tra-
              <lb/>
            peziorum b c e f, a b f g, hoc
              <lb/>
            eſt centrum totius heptago-
              <lb/>
            ni: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus eadem centra in
              <lb/>
            alia diametro cl ſimiliter du-
              <lb/>
            cta contineri. </s>
            <s xml:space="preserve">Quare & </s>
            <s xml:space="preserve">centrum grauitatis heptagoni, & </s>
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              <lb/>
            centrum circuli in idem punctum conucniunt. </s>
            <s xml:space="preserve">Eodem mo</s>
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