Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
[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.]
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FED. COMMANDINI
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            medis. </s>
            <s xml:space="preserve">ergo punctum v extra p riſima a f poſitum, centrũ
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            erit magnitudinis cõpoſitæ e x omnibus priſmatibus g z r,
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            r β t, t γ x, x δ k, k δ y, y u, u s, s α h, quod fieri nullo modo po
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            teſt. </s>
            <s xml:space="preserve">eſt enim ex diſſinitione centrum grauitatis ſolidæ figu
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            ræ intra ipſam poſitum, non extra. </s>
            <s xml:space="preserve">quare relinquitur, ut cẽ
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            trum grauitatis priſmatis ſit in linea K m. </s>
            <s xml:space="preserve">Rurſus b c bifa-
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            riam in ξ diuidatur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducta a ξ, per ipſam, & </s>
            <s xml:space="preserve">per lineam
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            a g d plan um ducatur; </s>
            <s xml:space="preserve">quod priſma ſecet: </s>
            <s xml:space="preserve">faciatq; </s>
            <s xml:space="preserve">in paral
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            lelogrammo b f ſectionem ξ π di uidet punctum π lineam
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            quoque c f bifariam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">erit p lani eius, & </s>
            <s xml:space="preserve">trianguli g h K
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            communis ſectio g u; </s>
            <s xml:space="preserve">quòd p ũctum u in inedio lineæ h K
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              <anchor type="figure" xlink:label="fig-0136-01a" xlink:href="fig-0136-01"/>
            poſitum ſi t. </s>
            <s xml:space="preserve">Similiter demonſtrabimus centrum grauita-
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            tis priſm atis in ipſa g u ineſſe. </s>
            <s xml:space="preserve">ſit autem planorum c f n l,
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            a d π ξ communis ſectio linea ρ ο τ quæ quidem priſmatis
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            axis erit, cum tranſeat per centra grauitatis triangulorum
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            a b c, g h k, d e f, ex quartadecima eiuſdem. </s>
            <s xml:space="preserve">ergo centrum
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            grauitatis pri ſmatis a f eſt punctum σ, centrum ſcilicet</s>
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