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="14" file="0139" n="139" rhead="DE CENTRO GRAVIT. SOLID."/>
            ſimiliter demonſtrabitur totius priſmatis a _K_ grauitatis eſ
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            ſe centrum. </s>
            <s xml:space="preserve">Simili ratione & </s>
            <s xml:space="preserve">in aliis priſinatibus illud
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            idem ſacile demonſtrabitur. </s>
            <s xml:space="preserve">Quo autem pacto in omni
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            figura rectilinea centrum grauitatis inueniatur, do cuimus
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            in commentariis in ſextam propoſitionem Archimedis de
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            quadratura parabolæ.</s>
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            <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a">
              <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0138-01"/>
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            <s xml:space="preserve">Sit cylindrus, uel cylindri portio c e cuius axis a b: </s>
            <s xml:space="preserve">ſece-
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            turq, plano per axem ducto; </s>
            <s xml:space="preserve">quod ſectionem faciat paral-
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            lelo grammum c d e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuiſis c f, d e bifariam in punctis
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              <anchor type="figure" xlink:label="fig-0139-01a" xlink:href="fig-0139-01"/>
            g h, per ea ducatur planum baſi æquidiſtans. </s>
            <s xml:space="preserve">erit ſectio g h
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            circulus, uel ellipſis, centrum habens in axe; </s>
            <s xml:space="preserve">quod ſit K: </s>
            <s xml:space="preserve">at-
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              <anchor type="note" xlink:label="note-0139-01a" xlink:href="note-0139-01"/>
            que erunt ex iis, quæ demonſtrauimus, centra grauitatis
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            planorum oppoſitorum puncta a b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">plani g h ipſum _k_. </s>
            <s xml:space="preserve">in
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            quo quidem plano eſt centrum grauitatis cylindri, uel cy-
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            lindri portionis. </s>
            <s xml:space="preserve">Dico punctum K cylindri quoque, uel cy
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            lindri portionis grauitatis centrum eſſe. </s>
            <s xml:space="preserve">Si enim fieri po-
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            teſt, ſitl centrum: </s>
            <s xml:space="preserve">ducaturq; </s>
            <s xml:space="preserve">k l, & </s>
            <s xml:space="preserve">extra figuram in m pro-
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            ducatur. </s>
            <s xml:space="preserve">quam uero proportionem habet linea m K ad _k_ l</s>
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