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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            medis. </s>
            <s xml:id="echoid-s3453" 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:id="echoid-s3454" xml:space="preserve">eſt enim ex diſſinitione centrum grauitatis ſolidæ figu
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            ræ intra ipſam poſitum, non extra. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">quare relinquitur, ut cẽ
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            trum grauitatis priſmatis ſit in linea K m. </s>
            <s xml:id="echoid-s3456" xml:space="preserve">Rurſus b c bifa-
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            riam in ξ diuidatur: </s>
            <s xml:id="echoid-s3457" xml:space="preserve">& </s>
            <s xml:id="echoid-s3458" xml:space="preserve">ducta a ξ, per ipſam, & </s>
            <s xml:id="echoid-s3459" xml:space="preserve">per lineam
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            a g d plan um ducatur; </s>
            <s xml:id="echoid-s3460" xml:space="preserve">quod priſma ſecet: </s>
            <s xml:id="echoid-s3461" xml:space="preserve">faciatq; </s>
            <s xml:id="echoid-s3462" 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:id="echoid-s3463" xml:space="preserve">& </s>
            <s xml:id="echoid-s3464" xml:space="preserve">erit p lani eius, & </s>
            <s xml:id="echoid-s3465" xml:space="preserve">trianguli g h K
              <lb/>
            communis ſectio g u; </s>
            <s xml:id="echoid-s3466" xml:space="preserve">quòd p ũctum u in inedio lineæ h K
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            poſitum ſi t. </s>
            <s xml:id="echoid-s3467" xml:space="preserve">Similiter demonſtrabimus centrum grauita-
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            tis priſm atis in ipſa g u ineſſe. </s>
            <s xml:id="echoid-s3468" 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:id="echoid-s3469" xml:space="preserve">ergo centrum
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            grauitatis pri ſmatis a f eſt punctum σ, centrum </s>
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