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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            <s xml:id="echoid-s3836" xml:space="preserve">
              <pb o="21" file="0153" n="153" rhead="DE CENTRO GRAVIT. SOLID."/>
            diuidendo figura ſolida inſcripta ad dictam exceſſus par-
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            tem, ut τ e ad e ρ. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">& </s>
            <s xml:id="echoid-s3838" xml:space="preserve">quoniam à cono, ſeu coni portione,
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            cuius grauitatis centrum eſt e, aufertur figura inſcripta,
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            cuius centrum ρ: </s>
            <s xml:id="echoid-s3839" xml:space="preserve">reſiduæ magnitudinis compoſitæ ex par
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            te exceſſus, quæ intra coni, uel coni portionis ſuperficiem
              <lb/>
            continetur, centrum grauitatis erit in linea ζ e protracta,
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            atque in puncto τ. </s>
            <s xml:id="echoid-s3840" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">cõſtat ergo centrũ
              <lb/>
            grauitatis coni, uel coni portionis, eſſe in axe b d: </s>
            <s xml:id="echoid-s3842" xml:space="preserve">quod de
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            monſcrandum propoſuimus.</s>
            <s xml:id="echoid-s3843" xml:space="preserve"/>
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        <div xml:id="echoid-div234" type="section" level="1" n="80">
          <head xml:id="echoid-head87" xml:space="preserve">THE OREMA XI. PROPOSITIO XV.</head>
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            <s xml:id="echoid-s3844" xml:space="preserve">Cuiuslibet portionis ſphæræ uel ſphæroidis,
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            quæ dimidia maior non ſit: </s>
            <s xml:id="echoid-s3845" xml:space="preserve">itemq́; </s>
            <s xml:id="echoid-s3846" xml:space="preserve">cuiuslibet por
              <lb/>
            tionis conoidis, uel abſciſſæ plano ad axem recto,
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            uel non recto, centrum grauitatis in axe con-
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            ſiſtit.</s>
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            <s xml:id="echoid-s3848" xml:space="preserve">Demonſtratio ſimilis erit ei, quam ſupra in cono, uel co
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            ni portione attulimus, ne toties eadem fruſtra iterentur.</s>
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