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="2" file="0115" n="115" rhead="DE CENTRO GRAVIT. SOLID."/>
            tur, centrum grauitatis eſt idem, quod circuli cen
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            trum.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit primo triangulum æquilaterum a b c in circulo de-
              <lb/>
            ſcriptum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuiſa a c bifariam in d, ducatur b d. </s>
            <s xml:space="preserve">erit in li-
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            nea b d centrum grauitatis triãguli a b c, ex tertia decima
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            primi libri Archimedis de centro grauitatis planorum. </s>
            <s xml:space="preserve">Et
              <lb/>
            quoniam linea a b eſt æqualis
              <lb/>
              <anchor type="figure" xlink:label="fig-0115-01a" xlink:href="fig-0115-01"/>
            lineæ b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a d ipſi d c; </s>
            <s xml:space="preserve">eſtq́;
              <lb/>
            </s>
            <s xml:space="preserve">b d utrique communis: </s>
            <s xml:space="preserve">trian-
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            gulum a b d æquale erit trian
              <lb/>
              <anchor type="note" xlink:label="note-0115-01a" xlink:href="note-0115-01"/>
            gulo c b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli angulis æ-
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            quales, qui æqualibus lateri-
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            bus ſubtenduntur. </s>
            <s xml:space="preserve">ergo angu
              <lb/>
              <anchor type="note" xlink:label="note-0115-02a" xlink:href="note-0115-02"/>
            li ad d utriq; </s>
            <s xml:space="preserve">recti ſunt. </s>
            <s xml:space="preserve">quòd
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            cum linea b d ſecet a c biſa-
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            riam, & </s>
            <s xml:space="preserve">ad angulos rectos; </s>
            <s xml:space="preserve">in
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              <anchor type="note" xlink:label="note-0115-03a" xlink:href="note-0115-03"/>
            ipſa b d eſt centrum circuli.
              <lb/>
            </s>
            <s xml:space="preserve">quare in eadem b d linea erit
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            centrum grauitatis trianguli, & </s>
            <s xml:space="preserve">circuli centrum. </s>
            <s xml:space="preserve">Similiter
              <lb/>
            diuiſa a b bifariam in e, & </s>
            <s xml:space="preserve">ducta c e, oſtendetur in ipſa utrũ
              <lb/>
            que centrum contineri. </s>
            <s xml:space="preserve">ergo ea erunt in puncto, in quo li-
              <lb/>
            neæ b d, c e conueniunt. </s>
            <s xml:space="preserve">trianguli igitur a b c centrum gra
              <lb/>
            uitatis eſt idem, quod circuli centrum.</s>
            <s xml:space="preserve"/>
          </p>
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            <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a">
              <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-01"/>
            </figure>
            <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">8. primi.</note>
            <note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">13. primi.</note>
            <note position="right" xlink:label="note-0115-03" xlink:href="note-0115-03a" xml:space="preserve">corol. p@@
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            mæ tertii</note>
          </div>
          <p>
            <s xml:space="preserve">Sit quadratum a b c d in cir-
              <lb/>
              <anchor type="figure" xlink:label="fig-0115-02a" xlink:href="fig-0115-02"/>
            culo deſcriptum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducantur
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            a c, b d, quæ conueniant in e. </s>
            <s xml:space="preserve">er-
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            go punctum e eſt centrum gra
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            uitatis quadrati, ex decima eiuſ
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            dem libri Archimedis. </s>
            <s xml:space="preserve">Sed cum
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            omnes anguli ad a b c d recti
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            ſint; </s>
            <s xml:space="preserve">erit a b c femicirculus:
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            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0115-04a" xlink:href="note-0115-04"/>
            itemq́; </s>
            <s xml:space="preserve">b c d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea li-
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            neæ a c, b d diametri circuli:</s>
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          </p>
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