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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="36" file="0083" n="83" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ad unum.</s>
            <s xml:space="preserve">] _Hoc nos proxime demonſtrauimus._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">Q</note>
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          <p>
            <s xml:space="preserve">Demonſtratum eſt enim ſuperius portionem cuius axis
              <lb/>
              <anchor type="note" xlink:label="note-0083-01a" xlink:href="note-0083-01"/>
            eſt maior, quàm ſeſquialter eius, quæ uſque ad axem, ſiad
              <lb/>
            humidum in grauitate non minorem proportionem ha-
              <lb/>
            beat &</s>
            <s xml:space="preserve">c.</s>
            <s xml:space="preserve">] _Illud uero demonſtrauit in quarta propoſitione buius_
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            _libri_.</s>
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          </p>
          <div type="float" level="2" n="5">
            <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">R</note>
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        <div type="section" level="1" n="48">
          <head xml:space="preserve">II.</head>
          <p>
            <s xml:space="preserve">Si portio ad humidum in grauitate minorem
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              <anchor type="note" xlink:label="note-0083-02a" xlink:href="note-0083-02"/>
            quidem proportionem habeat, quàm quadra-
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            tum ſ b ad quadratum b d; </s>
            <s xml:space="preserve">maiorem uero,
              <lb/>
            quàm quadratum x o ad quadratum b d; </s>
            <s xml:space="preserve">de-
              <lb/>
            miſſa in humidum, adeo inclinata, ut baſis ip-
              <lb/>
            ſius non contingat humidum, inclinata conſi-
              <lb/>
            ſtet; </s>
            <s xml:space="preserve">ita ut baſis ſuperficiem humidi nullo modo
              <lb/>
            contingat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cum humidi ſuperficie angu-
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            lum faciat maiorem angulo χ.</s>
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            <note position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">A</note>
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        <div type="section" level="1" n="49">
          <head xml:space="preserve">III.</head>
          <p>
            <s xml:space="preserve">Si portio ad humidum in grauitate, eam ha-
              <lb/>
            beat proportionem, quam quadratum x o ad
              <lb/>
            quadratum b d; </s>
            <s xml:space="preserve">demiſſa in humidum inclinata
              <lb/>
            adeo, ut baſis ipſius non contingat humidum;
              <lb/>
            </s>
            <s xml:space="preserve">conſiſtet, & </s>
            <s xml:space="preserve">manebit ita, ut baſis in uno pun-
              <lb/>
            cto humidi ſuperficiem contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cum
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            ſuperficie humidi angulũ faciat angulo χ æqualẽ. </s>
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              <lb/>
            Quòd ſi portio ad humidum in grauitate cam
              <lb/>
            proportionem habeat, quam quadratum p f ad</s>
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