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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DE CENTRO GRAVIT. SOLID.
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              <pb o="18" file="0147" n="147" rhead="DE CENTRO GRAVIT. SOLID."/>
            tione quarta Apollonius demonſtrauit. </s>
            <s xml:space="preserve">Si igitur à ſingu-
              <lb/>
            lis horum circulorum, duo cylindri fiant; </s>
            <s xml:space="preserve">unus quidem ad
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            baſis partes; </s>
            <s xml:space="preserve">alter ad partes uerticis: </s>
            <s xml:space="preserve">inſcripta erit in co-
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            no ſolida quædam figura, & </s>
            <s xml:space="preserve">altera circumſcripta ex cylin-
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            dris æqualem altitudinem habentibus conſtans; </s>
            <s xml:space="preserve">quorum
              <lb/>
            unuſquiſque, qui in
              <lb/>
              <anchor type="figure" xlink:label="fig-0147-01a" xlink:href="fig-0147-01"/>
            figura inſcripta con-
              <lb/>
            tinetur æqualis eſt ei,
              <lb/>
            qui ab eodem fit cir-
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            culo in figura circũ-
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            ſcripta. </s>
            <s xml:space="preserve">Itaque cylin
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            drus o p æqualis eſt
              <lb/>
            cylindro o n; </s>
            <s xml:space="preserve">cylin-
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            drus r s cylĩdro r q;
              <lb/>
            </s>
            <s xml:space="preserve">cylindrus u x cylin-
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            dro u t cſt æqualis; </s>
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              <lb/>
            & </s>
            <s xml:space="preserve">alii aliis ſimiliter. </s>
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              <lb/>
            quare conſtat circũ-
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            ſcriptam figuram ſu-
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            perare inſcriptam cy
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            lindro, cuius baſis eſt
              <lb/>
            circulus circa diametrum a c, & </s>
            <s xml:space="preserve">axis d e. </s>
            <s xml:space="preserve">atque hic eſtmi-
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            nor ſolida magnitudine propoſita.</s>
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            <figure xlink:label="fig-0147-01" xlink:href="fig-0147-01a">
              <image file="0147-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0147-01"/>
            </figure>
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        <div type="section" level="1" n="77">
          <head xml:space="preserve">PROBLEMA III. PROPOSITIO XII.</head>
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              <emph style="sc">Data</emph>
            coni portione, poteſt ſolida quædam
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            figura inſcribi, & </s>
            <s xml:space="preserve">altera circumſcribi ex cylindri
              <lb/>
            portionibus æqualem altitudinem habentibus;
              <lb/>
            </s>
            <s xml:space="preserve">ita ut circumſcripta inſcriptam exuperet, magni
              <lb/>
            tudine, quæ minor ſit ſolida magnitudine pro-
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            poſita.</s>
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