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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ARCHIMEDIS
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          <pb file="0034" n="34" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:space="preserve">_Erit r o minor, quàm, quæ uſque ad axem]_ Ex decima
              <lb/>
              <anchor type="note" xlink:label="note-0034-01a" xlink:href="note-0034-01"/>
            propoſitione quinti libri elementorum. </s>
            <s xml:space="preserve">Linea, quæ uſque ad axem
              <lb/>
            apud Archimedem, eſt dimidia eius, iuxta quam poſſunt, quæ à ſe-
              <lb/>
            ctione ducuntur; </s>
            <s xml:space="preserve">ut ex quarta propoſitione libri de conoidibus, & </s>
            <s xml:space="preserve">
              <lb/>
            ſphæroidibus apparet. </s>
            <s xml:space="preserve">cur uero ita appellata ſit, nos in commentarijs
              <lb/>
            in eam editis tradidimus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">E</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Quare angulus r p ω acutus erit]_ producatur linea n o ad
              <lb/>
              <anchor type="note" xlink:label="note-0034-02a" xlink:href="note-0034-02"/>
            h, ut ſit r h æqualis ei, quæ uſque ad axem. </s>
            <s xml:space="preserve">ſi igitur à puncto h du-
              <lb/>
            catur linea ad rectos angulos ipſi n h, conueniet cum f p extra ſe-
              <lb/>
            ctionem: </s>
            <s xml:space="preserve">ducta enim per o ipſi a l æquidiſtans, extra ſectionem ca
              <lb/>
            dit ex decima ſepti-
              <lb/>
              <anchor type="figure" xlink:label="fig-0034-01a" xlink:href="fig-0034-01"/>
            ma primi libri coni-
              <lb/>
            corum. </s>
            <s xml:space="preserve">Itaque con-
              <lb/>
            ueniat in u. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quo
              <lb/>
            niam f p est æqui-
              <lb/>
            distans diametro;
              <lb/>
            </s>
            <s xml:space="preserve">h u uero ad diame-
              <lb/>
            trum perpendicula-
              <lb/>
            ris; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">r h æqualis
              <lb/>
            ei, quæ uſq; </s>
            <s xml:space="preserve">ad axẽ,
              <lb/>
            linea à puncto r ad
              <lb/>
            u ducta angulos re-
              <lb/>
            ctos faciet cum ea, quæ ſectionem in puncto p contingit, hoc eſt cum
              <lb/>
            k ω, ut mox demonstrabitur. </s>
            <s xml:space="preserve">quare perpendicularis r t inter p & </s>
            <s xml:space="preserve">
              <lb/>
            ω cadet; </s>
            <s xml:space="preserve">erítque r p ω angulus acutus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">F</note>
            <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a">
              <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0034-01"/>
            </figure>
          </div>
          <p style="it">
            <s xml:space="preserve">Sit rectanguli coni ſectio, ſeu parabole a b c, cuius
              <lb/>
            diameter b d: </s>
            <s xml:space="preserve">atque ipſam contingat linea e f in pun-
              <lb/>
            cto g: </s>
            <s xml:space="preserve">ſumatur autem in diametro b d linea h k æqua-
              <lb/>
            lis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per g ducta g l, diame-
              <lb/>
            tro æquidistante, à puncto _k_ ad rectos angulos ipſi b d
              <lb/>
            ducatur _k_ m, ſecans g l in m. </s>
            <s xml:space="preserve">Dico lineam ab h ad</s>
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