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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          <head xml:space="preserve">THEOREMA X. PROPOSITIO XIIII.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet pyramidis, & </s>
            <s xml:space="preserve">cuiuslibet coni, uel
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            coni portionis, centrum grauitatis in axe cõſiſtit.</s>
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          <p>
            <s xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis d e.
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            </s>
            <s xml:space="preserve">Dico in linea d e ipſius grauitatis centrum ineſſe. </s>
            <s xml:space="preserve">Si enim
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            fieri poteſt, ſit centrum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab f ducatur ad baſim pyrami
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            dis linea f g, axi æquidiſtans: </s>
            <s xml:space="preserve">iunctaq; </s>
            <s xml:space="preserve">e g ad latera trian-
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            guli a b c producatur in h. </s>
            <s xml:space="preserve">quam uero proportionem ha-
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            bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
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            quo K: </s>
            <s xml:space="preserve">inſcribaturq; </s>
            <s xml:space="preserve">in pyramide ſolida figura, & </s>
            <s xml:space="preserve">altera cir
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            cumſcribatur ex priſmatibus æqualem habentibus altitu-
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            dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
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            dine, quæ ſolido _k_ ſit minor. </s>
            <s xml:space="preserve">Et quoniam in pyramide pla
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            num baſi æquidiſtans ductum ſectionem facit figuram ſi-
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            milem ei, quæ eſt baſis; </s>
            <s xml:space="preserve">centrumq; </s>
            <s xml:space="preserve">grauitatis in axe haben
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            tem: </s>
            <s xml:space="preserve">erit priſmatis s t grauitatis centrũ in linear q; </s>
            <s xml:space="preserve">priſ-
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            matis u x centrum in linea q p; </s>
            <s xml:space="preserve">priſmatis y z in linea p o; </s>
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              <lb/>
            priſmatis η θ in l_i_nea o n; </s>
            <s xml:space="preserve">priſmatis λ μ in linea n m; </s>
            <s xml:space="preserve">priſ-
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            matis ν π in m l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">denique priſmatis ρ σ in l e. </s>
            <s xml:space="preserve">quare to-</s>
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