Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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FED. COMMANDINI
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              <pb file="0192" n="192" rhead="FED. COMMANDINI"/>
            grauitatis eſſe punctum m. </s>
            <s xml:space="preserve">patetigitur totius dodecahe-
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            dri, centrum grauitatis idẽ eſſe, quod & </s>
            <s xml:space="preserve">ſphæræ ipſum com
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            prehendentis centrum. </s>
            <s xml:space="preserve">quæ quidem omnia demonſtraſſe
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            oportebat.</s>
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          </p>
          <div type="float" level="2" n="5">
            <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a">
              <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0191-01"/>
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            <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">corol. pri
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            mæ ſphæ
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            ricorum
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            Theod.</note>
            <note position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">6. primi
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            phærico
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            rum.</note>
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        <div type="section" level="1" n="93">
          <head xml:space="preserve">PROBLEMA VI. PROPOSITIO XX VIII.</head>
          <p>
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              <emph style="sc">Data</emph>
            qualibet portione conoidis rectangu
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            li, abſciſſa plano ad axem recto, uel non recto; </s>
            <s xml:space="preserve">fie-
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            ri poteſt, ut portio ſolida inſcribatur, uel circum-
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            ſcribatur ex cylindris, uel cylindri portionibus,
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            æqualem habentibus altitudinem, ita ut recta li-
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            nea, quæ inter centrum grauitatis portionis, & </s>
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              <lb/>
            figuræ inſcriptæ, uel circumſcriptæ interiicitur,
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            ſit minor qualibet recta linea propoſita.</s>
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          </p>
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            <s xml:space="preserve">Sit portio conoidis rectanguli a b c, cuius axis b d, gra-
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            uitatisq; </s>
            <s xml:space="preserve">centrum e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fit g recta linea propoſita. </s>
            <s xml:space="preserve">quam ue
              <lb/>
            ro proportionem habet linea b e ad lineam g, eandem ha-
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            beat portio conoidis ad ſolidum h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">circumſcribatur por
              <lb/>
            tioni figura, ſicuti dictum eſt, ita ut portiones reliquæ ſint
              <lb/>
            ſolido h minores: </s>
            <s xml:space="preserve">cuius quidem figuræ centrum grauitatis
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            ſit punctum
              <emph style="sc">K</emph>
            . </s>
            <s xml:space="preserve">Dico lineã k e minorem eſſe linea g propo-
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            ſita. </s>
            <s xml:space="preserve">niſi enim ſit minor, uel æqualis, uel maior erit. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quo-
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            niam figura circumſcripta ad reliquas portiones maiorem
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              <anchor type="note" xlink:label="note-0192-01a" xlink:href="note-0192-01"/>
            proportionem habet, quàm portio conoidis ad ſolidum h;
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            </s>
            <s xml:space="preserve">hoc eſt maiorem, quàm b c ad g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b e ad g non minorem
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            habet proportionem, quàm ad _k_ e, propterea quod k e non
              <lb/>
            ponitur minor ipſa g: </s>
            <s xml:space="preserve">habebit figura circumſcripta ad por
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            tiones reliquas maiorem proportionem quàm b e ad e k: </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0192-02a" xlink:href="note-0192-02"/>
            & </s>
            <s xml:space="preserve">diuidendo portio conoidis ad reliquas portiones habe-
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            bit maiorem, quàm b
              <emph style="sc">K</emph>
            ad K e. </s>
            <s xml:space="preserve">quare ſi fiat ut portio co-</s>
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