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="19" file="0149" n="149" rhead="DE CENTRO GRAVIT. SOLID."/>
          <figure>
            <image file="0149-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0149-01"/>
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        <div type="section" level="1" n="79">
          <head xml:space="preserve">THEOREMA X. PROPOSITIO XIIII.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet pyramidis, & </s>
            <s xml:space="preserve">cuiuslibet coni, uel
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            coni portionis, centrum grauitatis in axe cõſiſtit.</s>
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          </p>
          <p>
            <s xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:space="preserve">Dico in linea d e ipſius grauitatis centrum ineſſe. </s>
            <s xml:space="preserve">Si enim
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            fieri poteſt, ſit centrum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab f ducatur ad baſim pyrami
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            dis linea f g, axi æquidiſtans: </s>
            <s xml:space="preserve">iunctaq; </s>
            <s xml:space="preserve">e g ad latera trian-
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            guli a b c producatur in h. </s>
            <s xml:space="preserve">quam uero proportionem ha-
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            bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
              <lb/>
            quo K: </s>
            <s xml:space="preserve">inſcribaturq; </s>
            <s xml:space="preserve">in pyramide ſolida figura, & </s>
            <s xml:space="preserve">altera cir
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            cumſcribatur ex priſmatibus æqualem habentibus altitu-
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            dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
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            dine, quæ ſolido _k_ ſit minor. </s>
            <s xml:space="preserve">Et quoniam in pyramide pla
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            num baſi æquidiſtans ductum ſectionem facit figuram ſi-
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            milem ei, quæ eſt baſis; </s>
            <s xml:space="preserve">centrumq; </s>
            <s xml:space="preserve">grauitatis in axe haben
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            tem: </s>
            <s xml:space="preserve">erit priſmatis s t grauitatis centrũ in linear q; </s>
            <s xml:space="preserve">priſ-
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            matis u x centrum in linea q p; </s>
            <s xml:space="preserve">priſmatis y z in linea p o; </s>
            <s xml:space="preserve">
              <lb/>
            priſmatis η θ in l_i_nea o n; </s>
            <s xml:space="preserve">priſmatis λ μ in linea n m; </s>
            <s xml:space="preserve">priſ-
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            matis ν π in m l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">denique priſmatis ρ σ in l e. </s>
            <s xml:space="preserve">quare to-</s>
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