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>
            <s xml:space="preserve">quam proportionem habet quadratum e ψ ad quadra-
              <lb/>
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            tum ψ b, eandem habet dimidium lineæ _k_ r ad lineã ψ b.
              <lb/>
            </s>
            <s xml:space="preserve">quare maiorem babet proportionem _k_ r ad i y, quàm di-
              <lb/>
              <anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
            midium k r ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco i y minor eſt, quàm dupla
              <lb/>
              <anchor type="note" xlink:label="note-0058-03a" xlink:href="note-0058-03"/>
            ψ b. </s>
            <s xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:space="preserve">ergo o i minor eſt, quàm
              <lb/>
            ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">i ω maior, quàm ψ r. </s>
            <s xml:space="preserve">ſed ψ r eſt æqualis ipſi f. </s>
            <s xml:space="preserve">maior
              <lb/>
              <anchor type="note" xlink:label="note-0058-04a" xlink:href="note-0058-04"/>
            igitur eſt i ω, quàm f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portio ad humidum in
              <lb/>
            grauitate eam ponitur habere proportionem, quam qua-
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            dratum f q ad quadratum b d: </s>
            <s xml:space="preserve">quam uero proportionem
              <lb/>
            habet portio ad humidum in grauitate, eam habet pars ip
              <lb/>
            ſius demerſa ad totam portionem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam pars ipſius de-
              <lb/>
            merſa habet ad totam, eandem habet quadratum p m ad
              <lb/>
            quadratnm o n: </s>
            <s xml:space="preserve">ſequitur quadratum p m ad quadratum
              <lb/>
            o n eam proportionem habere, quam quadratum f q ad
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            b d quadratum.
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            </s>
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            atque ideo ſ q æ-
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            qualis eſt ipſi p m.
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            </s>
            <s xml:space="preserve">demõſtrata eſt au
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            tem p h maior,
              <lb/>
            quàm f. </s>
            <s xml:space="preserve">cõſtat igi
              <lb/>
            tur p m minorem
              <lb/>
            eſſe, quàm ſeſqui-
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            alterã ipſius p h:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco p h ma
              <lb/>
            iorem, quàm du-
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            plam h m. </s>
            <s xml:space="preserve">Sit p z
              <lb/>
            ipſius z m dupla. </s>
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              <lb/>
            erit t quidem cẽ-
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            trũ grauitatis to-
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            tius ſolidi: </s>
            <s xml:space="preserve">centrũ
              <lb/>
            eius partis, quæ intra humidum, punctumz: </s>
            <s xml:space="preserve">reliquæ uero
              <lb/>
            partis centrum erit in linea z t producta uſque ad g. </s>
            <s xml:space="preserve">Eodẽ
              <lb/>
              <anchor type="note" xlink:label="note-0058-07a" xlink:href="note-0058-07"/>
            modo demonſtrabitur linea th perpendicularis ad ſuper-
              <lb/>
            ficiem humidi. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio demerſa in humido ſeretur extra</s>
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