Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[31. LEMMAI.]
[32. LEMMA II.]
[33. LEMMA III.]
[34. LEMMA IIII.]
[35. PROPOSITIO VII.]
[36. PROPOSITIO VIII.]
[37. COMMENTARIVS.]
[38. PROPOSITIO IX.]
[39. COMMENTARIVS.]
[40. PROPOSITIO X.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
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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>
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            <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>
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          <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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