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 CENTRO GRAVIT. SOLID.
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        <div type="section" level="1" n="93">
          <p>
            <s xml:space="preserve">
              <pb o="41" file="0193" n="193" rhead="DE CENTRO GRAVIT. SOLID."/>
            noidis ad portiones reliquas, ita alia linea, quæ ſit 1
              <emph style="sc">K</emph>
            ad
              <lb/>
            k e: </s>
            <s xml:space="preserve">erit 1k maior, quam b k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ideo punctum l extra por-
              <lb/>
            tionem cadet. </s>
            <s xml:space="preserve">Quoniã
              <lb/>
              <anchor type="figure" xlink:label="fig-0193-01a" xlink:href="fig-0193-01"/>
            igitur à figura circum-
              <lb/>
            ſcripta, cuius grauitatis
              <lb/>
            centrum eſt k, aufertur
              <lb/>
            portio conoidis, cuius
              <lb/>
            centrum e. </s>
            <s xml:space="preserve">habetq; </s>
            <s xml:space="preserve">l K
              <lb/>
            ad K e eam proportio-
              <lb/>
            nem, quam portio co-
              <lb/>
            noidis ad reliquas por-
              <lb/>
            tiones; </s>
            <s xml:space="preserve">erit punctum l
              <lb/>
            extra portionem cadẽs,
              <lb/>
            centrum magnitudinis
              <lb/>
            ex reliquis portionibus compoſitæ. </s>
            <s xml:space="preserve">illud autem fieri nullo
              <lb/>
            modo poteſt. </s>
            <s xml:space="preserve">quare conſtat lineam k e ipſa g linea propoſi
              <lb/>
            ta minorem eſſe.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">8. quĭnti.</note>
            <note position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">29. quĭnti
              <lb/>
            ex tradi-
              <lb/>
            tione Cã-
              <lb/>
            ſàni.</note>
            <figure xlink:label="fig-0193-01" xlink:href="fig-0193-01a">
              <image file="0193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0193-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Rurfus inſcribatur portioni figura, uidelicet cylindr us
              <lb/>
            m n, ut ſit ipſius altitudo
              <lb/>
              <anchor type="figure" xlink:label="fig-0193-02a" xlink:href="fig-0193-02"/>
            æqualis dimidio axis b d:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem
              <lb/>
            habet b e ad g, habeat m n
              <lb/>
            cylindrus ad ſolidum o. </s>
            <s xml:space="preserve">
              <lb/>
            inſcrib itur deinde eidem
              <lb/>
            alia figura, ita ut portio-
              <lb/>
            nes reliquæ ſint ſolido o
              <lb/>
            minores: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrum gra
              <lb/>
            uitatis figuræ ſit p. </s>
            <s xml:space="preserve">Dico
              <lb/>
            lineam p e ipſa g minorẽ
              <lb/>
            eſſe. </s>
            <s xml:space="preserve">ſi enim non ſit mi-
              <lb/>
            nor, eodem, quo ſupra modo demonſtrabimus figuram in
              <lb/>
            ſcriptam ad reliquas portiones maiorem proportionem
              <lb/>
            habere, quàm b e ad e p. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi fiat alia linea l e ad e p, ut eſt
              <lb/>
            figura inſcripta ad reliquas portiones, pũctum l extra por</s>
          </p>
        </div>
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