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 GRA VIT. SOLID.
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              <pb o="12" file="0135" n="135" rhead="DE CENTRO GRA VIT. SOLID."/>
            Itaque ſolidi parallelepipedi y γ centrum grauitatis eſt in
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            linea δ: </s>
            <s xml:space="preserve">ſolidi u β centrum eſt in linea ε η: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidi s z in li
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            nea η m, quæ quidem lineæ axes ſunt, cum planorum oppo
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            ſitorum centra coniungant. </s>
            <s xml:space="preserve">ergo magnitudinis ex his ſoli
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            dis compoſitæ centrum grauitatis eſt in linea δ m, quod ſit
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            θ; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta θ o producatur: </s>
            <s xml:space="preserve">à puncto autem h ducatur h μ
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            ipſi m κ æquidiſtans, quæ cum θ o in μ conueniat. </s>
            <s xml:space="preserve">triangu
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            lum igitur g h κ ad omnia triangula g z r, r β t, t γ x, x δ k,
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            κ δ y, y u, u s, s α h eandem habet proportionem, quam h m
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            ad m q; </s>
            <s xml:space="preserve">hoc eſt, quam μ θ ad θ λ: </s>
            <s xml:space="preserve">nam ſi h m, μ θ produci in
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            telligantur, quouſque coeant; </s>
            <s xml:space="preserve">erit ob linearum q y, m k æ-
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            quidiſtantiam, ut h q ad q m, ita μ λ ad ad λ θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">componen
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            do, ut h m ad m q, ita μ θ ad θ λ. </s>
            <s xml:space="preserve">linea uero θ o maior eſt,
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            quàm θ λ: </s>
            <s xml:space="preserve">habebit igitur μ θ ad θ λ maiorem proportio-
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              <anchor type="note" xlink:label="note-0135-01a" xlink:href="note-0135-01"/>
            nem, quàm ad θ o. </s>
            <s xml:space="preserve">quare triangulum etiam g h k ad omnia
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            iam dicta triangula maiorem proportionẽ habebit, quàm
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            μ θ ad θ o. </s>
            <s xml:space="preserve">ſed ut triangulũ g h k ad omnia triangula, ita to-
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            tũ priſma a f ad omnia priſmata g z r, r β t, t γ x, x δ k, k δ y,
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            y u, u s, s α h: </s>
            <s xml:space="preserve">quoniam enim ſolida parallelepipeda æque al
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            ta, eandem inter ſe proportionem habent, quam baſes; </s>
            <s xml:space="preserve">ut
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            ex trigeſimaſecunda undecimi elementorum conſtat. </s>
            <s xml:space="preserve">ſunt
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              <anchor type="note" xlink:label="note-0135-02a" xlink:href="note-0135-02"/>
            autem ſolida parallelepipeda priſmatum triangulares ba-
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            ſes habentium dupla: </s>
            <s xml:space="preserve">ſequitur, ut etiam huiuſmodi priſ-
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              <anchor type="note" xlink:label="note-0135-03a" xlink:href="note-0135-03"/>
            matainter ſe ſint, ſicut eorum baſes. </s>
            <s xml:space="preserve">ergo totum priſma ad
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            omnia priſmata maiorem proportionem habet, quam μ θ
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            ad θ o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo ſolida parallelepipeda y γ, u β, s z ad o-
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              <anchor type="note" xlink:label="note-0135-04a" xlink:href="note-0135-04"/>
            mnia prifmata proportionem habent maiorem, quàm μ o
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            ad o θ. </s>
            <s xml:space="preserve">fiat @ o ad o θ, ut folida parallelepipeda y γ, u β, s z ad
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            omnia priſmata. </s>
            <s xml:space="preserve">Itaque cum à priſmate a f, cuius cẽtrum
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            grauitatis eſt o, auferatur magnitudo ex ſolidis parallelepi
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            pedis y γ, u β, s z conſtans: </s>
            <s xml:space="preserve">atque ipfius grauitatis centrum
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            ſit θ: </s>
            <s xml:space="preserve">reliquæ magnitudinis, quæ ex omnibus priſmatibus
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            conſtat, grauitatis centrum erit in linea θ o producta: </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            in puncto ν, ex o ctaua propoſitione eiuſdem libri Archi-</s>
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