Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
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ARCHIMEDIS
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            <s xml:space="preserve">
              <pb file="0042" n="42" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">ſectionis diameter no: </s>
            <s xml:space="preserve">ſuperſiciei autem humidi ſectio
              <lb/>
            ſit is. </s>
            <s xml:space="preserve">Quoniam igitur axis non eſt ſecundum perpendicu
              <lb/>
            larem; </s>
            <s xml:space="preserve">ipſa no cum is non faciet angulos æquales. </s>
            <s xml:space="preserve">Du-
              <lb/>
            catur k ω contingens ſectionem apol in p; </s>
            <s xml:space="preserve">atque ipſi is
              <lb/>
            æquidiſtans: </s>
            <s xml:space="preserve">per p autem ducatur p f æquidiſtās ipſi n o:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumantur grauitatum centra: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius a p o l ſolidi
              <lb/>
            centrum r; </s>
            <s xml:space="preserve">eius quod extra humidum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta br
              <lb/>
            producatur adg,
              <lb/>
              <anchor type="figure" xlink:label="fig-0042-01a" xlink:href="fig-0042-01"/>
            quodſit centrum
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            grauitatis ſolidi ĩ
              <lb/>
            humido demerſi:
              <lb/>
            </s>
            <s xml:space="preserve">ſumatur præterea
              <lb/>
            r h æ qualis ei, quæ
              <lb/>
            uſque ad axẽ: </s>
            <s xml:space="preserve">o h
              <lb/>
            autem dupla ipſi-
              <lb/>
            us h m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia fiãt,
              <lb/>
            ſicuti ſuperius di-
              <lb/>
            ctum eſt. </s>
            <s xml:space="preserve">Itaque
              <lb/>
            cum portio ad hu
              <lb/>
            midum in grauita
              <lb/>
            te non maiorem
              <lb/>
            proportionem ha
              <lb/>
            bere ponatur, quã
              <lb/>
            exceſſus, quo quadratum n o excedit quadratum m o, ad
              <lb/>
            ipſum n o quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem in grauita
              <lb/>
            te portio habet ad humidum æqualis molis, eandem ha-
              <lb/>
            beat magnitudo portionis demerſa ad totam portio-
              <lb/>
            nem, quod demonſtratum eſt in prima propoſitione: </s>
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              <lb/>
            magnitudo demerſa non maiorem proportionem ha-
              <lb/>
              <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
            bebit ad totam portionem, quàm ſit dicta illa propor-
              <lb/>
            portio. </s>
            <s xml:space="preserve">quare non maiorem proportionem habet tota
              <lb/>
              <anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
            portio ad eam quæ eſt extra humidum, quàm quadratum
              <lb/>
            no ad quadratum m o. </s>
            <s xml:space="preserve">habet autem tota portio ad eam,
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              <anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
            quæ extra humidum proportionem eandem, quam qua-</s>
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