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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        <div type="section" level="1" n="23">
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            angulus b n f œqualis angulo o g f: </s>
            <s xml:space="preserve">quòd cum ſit g o perpendi-
              <lb/>
              <anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/>
            cularis ad e f, & </s>
            <s xml:space="preserve">h n ad eandem perpendicularis erit. </s>
            <s xml:space="preserve">quod de-
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            monstrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
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            <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">cor. 8. ſe-
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            xti.</note>
            <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a">
              <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0035-01"/>
            </figure>
            <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">17. ſextĩ.</note>
            <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">14. ſexti.</note>
            <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">32. primi</note>
            <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">4. primi.</note>
            <note position="right" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">28</note>
            <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">29, primi</note>
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          <p>
            <s xml:space="preserve">Et quod in humido eſt ſurſum ſeretur ſecundum per-
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              <anchor type="note" xlink:label="note-0036-02a" xlink:href="note-0036-02"/>
            pendicularem, quæ per b ducta eſtipſi rt æquidiſtans.</s>
            <s xml:space="preserve">]
              <lb/>
            _Cur hoc quidem ſurſum, illud uero deorſum per lineam perpen-_
              <lb/>
            _dicularem feratur, diximus ſupra in octauam primi libri buius. </s>
            <s xml:space="preserve">qua_
              <lb/>
            _re neque in hac, neque in alijs, quæ ſequuntur, eadem iterare neceſſa_
              <lb/>
            _rium exiſtimauimus._</s>
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            <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">G</note>
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        </div>
        <div type="section" level="1" n="24">
          <head xml:space="preserve">PROPOSITIO III.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli quando
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            axem habuerit minorem, quam ſeſquialterum
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            eius, quæ uſque ad axem, quamcunque propor-
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            tionem habens ad humidum in grauitate; </s>
            <s xml:space="preserve">demiſ-
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            ſa in humidum, ita ut baſis ipſius tota ſit in humi
              <lb/>
            do; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poſita inclinata, non manebit inclinata, ſed
              <lb/>
            ita reſtituetur, ut axis ipſius ſecundum perpendi
              <lb/>
            cularem fiat.</s>
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          </p>
          <p>
            <s xml:space="preserve">DEMITTATVR enim aliqua portio in humidum,
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            qualis dicca eſt: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius baſis in humido: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa
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            plano per axẽ, recto ad ſuperficiẽ humidi, ſit ſectio a p ol
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            rectanguli coniſectio: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis diame-
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            ter p f: </s>
            <s xml:space="preserve">ſuperficiei autem humidi ſectio ſit is. </s>
            <s xml:space="preserve">Quòd ſi incli
              <lb/>
            nata iaceat portio, non erit axis ſecundum perpendicula-
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            rem. </s>
            <s xml:space="preserve">ergo p f cum is angulos rectos non faciet. </s>
            <s xml:space="preserve">Itaque
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            ducatur linea quædã k ω æquidiſtans ipſi is; </s>
            <s xml:space="preserve">contingensq;
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            </s>
            <s xml:space="preserve">ſectionẽ ap ol in o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidæ quidẽ magnitudinis a p o l
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            ſit r grauitatis centrum: </s>
            <s xml:space="preserve">ipſius autem i p o s centrum ſit</s>
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