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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              <pb o="5" file="0121" n="121" rhead="DE CENTRO GRAVIT. SOLID."/>
            quo ſcilicet ln, om conueniunt. </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Poſtremo in figura
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            a p l q b r m s c t n u d x o y centrum grauitatis trian
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            guli pay, & </s>
            <s xml:id="echoid-s3080" xml:space="preserve">trapezii ploy eſtin linea a z: </s>
            <s xml:id="echoid-s3081" xml:space="preserve">trapeziorum
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            uero lqxo, q b d x centrum eſtin linea z k: </s>
            <s xml:id="echoid-s3082" xml:space="preserve">& </s>
            <s xml:id="echoid-s3083" xml:space="preserve">trapeziorũ
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            b r u d, r m n u in k φ: </s>
            <s xml:id="echoid-s3084" xml:space="preserve">& </s>
            <s xml:id="echoid-s3085" xml:space="preserve">denique trapezii m s t n; </s>
            <s xml:id="echoid-s3086" xml:space="preserve">& </s>
            <s xml:id="echoid-s3087" xml:space="preserve">triangu
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            li s c t in φ c. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">quare magnitudinis ex his compoſitæ centrū
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            in linea a c conſiſtit. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">Rurſus trianguli q b r, & </s>
            <s xml:id="echoid-s3090" xml:space="preserve">trapezii q l
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            m r centrum eſt in linea b χ: </s>
            <s xml:id="echoid-s3091" xml:space="preserve">trapeziorum l p s m, p a c s,
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            a y t c, y o n t in linea χ φ: </s>
            <s xml:id="echoid-s3092" xml:space="preserve">trapeziiq; </s>
            <s xml:id="echoid-s3093" xml:space="preserve">o x u n, & </s>
            <s xml:id="echoid-s3094" xml:space="preserve">trianguli
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            x d u centrum in ψ d. </s>
            <s xml:id="echoid-s3095" xml:space="preserve">totius ergo magnitudinis centrum
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            eſtin linea b d. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">ex quo ſequitur, centrum grauitatis figuræ
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            a p l q b r m s c t n u d x o y eſſe punctū _K_, lineis ſcilicet a c,
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            b d commune, quæ omnia demonſtrare oportebat.</s>
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          <head xml:id="echoid-head73" xml:space="preserve">THE OREMA III. PROPOSITIO III.</head>
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            <s xml:id="echoid-s3098" xml:space="preserve">Cuiuslibet portio-
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            nis circuli, & </s>
            <s xml:id="echoid-s3099" xml:space="preserve">ellipſis,
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            quæ dimidia non ſit
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            maior, centrum graui
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            tatis in portionis dia-
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            metro conſiſtit.</s>
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            <s xml:id="echoid-s3101" xml:space="preserve">HOC eodem prorſus
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            modo demonſtrabitur,
              <lb/>
            quo in libro de centro gra
              <lb/>
            uitatis planorum ab Ar-
              <lb/>
            chimede demonſtratũ eſt,
              <lb/>
            in portione cõtenta recta
              <lb/>
            linea, & </s>
            <s xml:id="echoid-s3102" xml:space="preserve">rectanguli coni ſe
              <lb/>
            ctione grauitatis cẽtrum
              <lb/>
            eſſe in diametro portio-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">Etita demonſtrari po
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