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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          <p>
            <s xml:space="preserve">
              <pb file="0132" n="132" rhead="FED. COMMANDINI"/>
            centrum z: </s>
            <s xml:space="preserve">parallelogram mi a d, θ: </s>
            <s xml:space="preserve">parallelogrammi f g, φ:
              <lb/>
            </s>
            <s xml:space="preserve">parallelogrammi d h, χ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="figure" xlink:label="fig-0132-01a" xlink:href="fig-0132-01"/>
            parallelogrammi c g centrũ
              <lb/>
            ψ: </s>
            <s xml:space="preserve">atque erit ω punctum me
              <lb/>
            dium uniuſcuiuſque axis, ui
              <lb/>
            delicet eius lineæ, quæ oppo
              <lb/>
            ſitorum planorũ centra con
              <lb/>
            iungit. </s>
            <s xml:space="preserve">Dico ω centrum effe
              <lb/>
            grauitatis ipſius ſolidi. </s>
            <s xml:space="preserve">eſt
              <lb/>
            enim, ut demonſtrauimus,
              <lb/>
              <anchor type="note" xlink:label="note-0132-01a" xlink:href="note-0132-01"/>
            ſolidi a f centrum grauitatis
              <lb/>
            in plano K n; </s>
            <s xml:space="preserve">quod oppoſi-
              <lb/>
            tis planis a d, g f æ quidiſtans
              <lb/>
            reliquorum planorum late-
              <lb/>
            ra biſariam diuidit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fimili
              <lb/>
            rationeidem centrum eſt in plano o r, æ quidiſtante planis
              <lb/>
            a e, b f oppo ſitis. </s>
            <s xml:space="preserve">ergo in communi ipſorum fectione: </s>
            <s xml:space="preserve">ui-
              <lb/>
            delicet in linea y z. </s>
            <s xml:space="preserve">Sed eſt etiam in plano t u, quod quidẽ
              <lb/>
            y z ſecat in ω. </s>
            <s xml:space="preserve">Conſtat igitur centrum grauitatis ſolidi eſſe
              <lb/>
            punctum ω, medium ſcilicet axium, hoc eſt linearum, quæ
              <lb/>
            planorum oppoſitorum centra coniungunt.</s>
            <s xml:space="preserve"/>
          </p>
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            <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a">
              <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0132-01"/>
            </figure>
            <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">6. huius</note>
          </div>
          <p>
            <s xml:space="preserve">Sit aliud prima a f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in eo plana, quæ opponuntur, tri-
              <lb/>
            angula a b c, d e f: </s>
            <s xml:space="preserve">diuiſisq; </s>
            <s xml:space="preserve">bifariam parallelogrammorum
              <lb/>
            lateribus a d, b e, c f in punctis g h κ, per diuiſiones planũ
              <lb/>
            ducatur, quod oppoſitis planis æ quidiſtans faciet ſe ctionẽ
              <lb/>
            triangulum g h k æ quale, & </s>
            <s xml:space="preserve">ſimile ipſis a b c, d e f. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
            diuidatur a b bifariam in l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta c l per ipſam, & </s>
            <s xml:space="preserve">per
              <lb/>
            c _K_ f planum ducatur priſma ſecans, cuius, & </s>
            <s xml:space="preserve">parallelogrã
              <lb/>
            mi a e communis ſcctio ſit l m n. </s>
            <s xml:space="preserve">diuidet pun ctum m li-
              <lb/>
            neam g h bifariam; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita n diuidet lineam d e: </s>
            <s xml:space="preserve">quoniam
              <lb/>
            triangula a c l, g k m, d f n æ qualia ſunt, & </s>
            <s xml:space="preserve">ſimilia, ut ſu pra
              <lb/>
              <anchor type="note" xlink:label="note-0132-02a" xlink:href="note-0132-02"/>
            demonſtrauimus. </s>
            <s xml:space="preserve">Iam ex iis, quæ tradita ſunt, conſtat cen
              <lb/>
            trum greuitatis priſmatis in plano g h k contineri. </s>
            <s xml:space="preserve">Dico
              <lb/>
            ipſum eſſe in linea k m. </s>
            <s xml:space="preserve">Si enim fieri poteſt, ſit o centrum;</s>
            <s xml:space="preserve"/>
          </p>
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