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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FED. COMMANDINI
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            At cum e f ſit ſexta pars axis
              <lb/>
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            ſphæræ, crit d e tripla e f. </s>
            <s xml:space="preserve">ergo
              <lb/>
            punctum e eſt grauitatis cen-
              <lb/>
            trum ipſius pyramidis: </s>
            <s xml:space="preserve">quod
              <lb/>
            in uigeſima ſecunda huius de-
              <lb/>
            monſtratum fuit. </s>
            <s xml:space="preserve">Sed e eſt cen
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            trum ſphæræ. </s>
            <s xml:space="preserve">Sequitur igitur,
              <lb/>
            ut centrum grauitatis pyrami-
              <lb/>
            dis in ſphæra deſcriptæ idem
              <lb/>
            ſit, quod ipſius ſphæræ cen-
              <lb/>
            trum.</s>
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            <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a">
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          <p>
            <s xml:space="preserve">Sit cubus in ſphæra deſcriptus a b, & </s>
            <s xml:space="preserve">oppoſitorum pla-
              <lb/>
            norum lateribus bifariam diuiſis, per puncta diuiſionum
              <lb/>
            plana ducantur, ut communis ipſorum ſectio ſit recta li-
              <lb/>
            nea c d. </s>
            <s xml:space="preserve">Itaque ſi ducatur a b, ſolidi ſcilicet diameter, lineæ
              <lb/>
            a b, c d ex trigeſimanona undecimi ſeſe bifariam ſecabunt.
              <lb/>
            </s>
            <s xml:space="preserve">ſecent autem in puncto e. </s>
            <s xml:space="preserve">erit
              <lb/>
              <anchor type="figure" xlink:label="fig-0188-02a" xlink:href="fig-0188-02"/>
            e centrũ grauitatis ſolidi a b,
              <lb/>
            id quod demonſtratum eſt in
              <lb/>
            octaua huius. </s>
            <s xml:space="preserve">Sed quoniam ab
              <lb/>
            eſt ſphæræ diametro æqualis,
              <lb/>
            ut in decima quinta propoſi-
              <lb/>
            tione tertii decimi libri elemẽ
              <lb/>
            torum oſtenditur: </s>
            <s xml:space="preserve">punctum e
              <lb/>
            ſphæræ quoque centrum erit.
              <lb/>
            </s>
            <s xml:space="preserve">Cubi igitur in ſphæra deſcri-
              <lb/>
            pti grauitatis centrum idem
              <lb/>
            eſt, quod centrum ipſius ſphæræ.</s>
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            <figure xlink:label="fig-0188-02" xlink:href="fig-0188-02a">
              <image file="0188-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0188-02"/>
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            <s xml:space="preserve">Sit octahedrum a b c d e f, in ſphæra deſcriptum, cuius
              <lb/>
            ſphæræ centrum ſit g. </s>
            <s xml:space="preserve">Dico punctum g ipſius octahedri
              <lb/>
            grauitatis centrum eſſe. </s>
            <s xml:space="preserve">Conſtat enim ex iis, quæ demon-
              <lb/>
            ſtrata ſunt à Campano in quinto decimo libro elemento-
              <lb/>
            rum, propoſitione ſextadecima eiuſimodi ſolidum diuidi
              <lb/>
            in duas pyramides æquales, & </s>
            <s xml:space="preserve">ſimiles; </s>
            <s xml:space="preserve">uidelicetin pyrami-</s>
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