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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DE CENTRO GRAVIT. SOLID.
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              <pb o="24" file="0159" n="159" rhead="DE CENTRO GRAVIT. SOLID."/>
            los contineant. </s>
            <s xml:space="preserve">Dico ſolidum a b ad ſolidum a c eãdem ha
              <lb/>
            bere proportionem, quam axis d e ad axem e f. </s>
            <s xml:space="preserve">Sienim
              <lb/>
            axes in eadem recta linea fuerint conſtituti, hæc duo ſoli-
              <lb/>
            da, in unum, atque i @m ſolidum conuenient. </s>
            <s xml:space="preserve">quare ex
              <lb/>
            iis, quæ proxime tradita ſunt, habebit ſolidum a b ad ſo-
              <lb/>
            lidum a c eandem proportionem, quam axis d e ad e f
              <lb/>
            axem. </s>
            <s xml:space="preserve">Siuero axes non ſint in eadem recta linea, demittan
              <lb/>
            tur a punctis d, f perpendiculares ad baſis planum, d g, fh:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur e g, e h. </s>
            <s xml:space="preserve">Quoniam igitur axes cum baſibus
              <lb/>
            æquales angulos eontinent, erit d e g angulus æqualis an-
              <lb/>
            gulo f e h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="figure" xlink:label="fig-0159-01a" xlink:href="fig-0159-01"/>
            anguli ad g h re-
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            cti, quare & </s>
            <s xml:space="preserve">re-
              <lb/>
            liquus e d g æqua
              <lb/>
            lis erit reliquo
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            e fh: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
              <lb/>
            lum d e g triãgu-
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            lo f e h ſimile. </s>
            <s xml:space="preserve">er-
              <lb/>
            go g d ad d e eſt,
              <lb/>
            ut h f ad f e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            mutando g d ad
              <lb/>
            h f, ut d e ad e f.
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            </s>
            <s xml:space="preserve">Sed ſolidum a b
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            ad ſolidum a c
              <lb/>
            eandem propor-
              <lb/>
            tionem habet,
              <lb/>
            quam d g altitu-
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            do ad altitudinẽ
              <lb/>
            f h. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ean-
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            dẽ habebit, quã
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            axis d e a l e f axẽ</s>
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            <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a">
              <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0159-01"/>
            </figure>
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          <p>
            <s xml:space="preserve">Poſtremo ſint
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            ſolida parallelepi
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            peda a b, c d in</s>
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