Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[81. THE OREMA XII. PROPOSITIO XVI.]
[82. THE OREMA XIII. PROPOSITIO XVII.]
[83. THEOREMA XIIII. PROPOSITIO XVIII.]
[84. THEOREMA XV. PROPOSITIO XIX.]
[85. THE OREMA XVI. PROPOSITIO XX.]
[86. THEOREMA XVII. PROPOSITIO XXI.]
[87. THE OREMA XVIII. PROPOSITIO XXII.]
[88. THEOREMA XIX. PROPOSITIO XXIII.]
[89. PROBLEMA V. PROPOSITIO XXIIII.]
[90. THEOREMA XX. PROPOSITIO XXV.]
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DE IIS QVAE VEH. IN AQVA.
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              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
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            n t æqualem eſſe ipſi u i: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portiones a u q, a n z inter
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            ſe ſe æquales.
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            Itaque quoniã
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            ĩ portionibus
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            æqualibus, & </s>
            <s xml:space="preserve">ſi
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            milibus a u q l,
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            a n z g ductæ
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            sũt a q, a z, por
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            tiones æqua-
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            les auferentes;
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            </s>
            <s xml:space="preserve">cum diametris
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            portionum æ-
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            quales angu-
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            los cõtinebũt. </s>
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              <lb/>
            ergo triangulo
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            rum n l s, u ω c
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            anguli, qui cõ-
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            ſiſtũt ad l ω pũ-
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            cta, æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:space="preserve">ſ r ipſi cr,
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            n χ ipſi u h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ tipſi h i. </s>
            <s xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
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            erit n χ maior, quàm dupla χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t du
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            pla. </s>
            <s xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
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            tionem; </s>
            <s xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:space="preserve">ponebatur autem portio
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            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:space="preserve">ergo ne-
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            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
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            <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a">
              <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0097-01"/>
            </figure>
            <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a">
              <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0098-01"/>
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              <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0099-01"/>
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        <div type="section" level="1" n="57">
          <head xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT denique portio ad humidum in grauitate
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            minorem proportionem, quàm quadratum f p ad quadra-
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            tum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad humidũ
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            in grauitate, eandem quadratum, quod fit à linea ψ habeat
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            ad quadratum b d. </s>
            <s xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:space="preserve">Rurſus aptetur</s>
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