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-s3799" xml:space="preserve">
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            beat eam, quam χ τ ad τ f. </s>
            <s xml:id="echoid-s3800" xml:space="preserve">erit diuidendo ut χ f ad f τ, ita fi
              <lb/>
            gura ſolida inſcripta ad partem exceſſus, quæ eſtintra pyra
              <lb/>
            midem. </s>
            <s xml:id="echoid-s3801" xml:space="preserve">Cum ergo à pyramide, cuius grauitatis cẽtrum eſt
              <lb/>
            punctum f, ſolida figura inſcripta auferatur, cuius centrũ
              <lb/>
            τ: </s>
            <s xml:id="echoid-s3802" xml:space="preserve">reliquæ magnitudinis conſtantis ex parte exceſſus, quæ
              <lb/>
            eſtintra pyramidem, centrum grauitatis erit in linea τ f
              <lb/>
            producta, & </s>
            <s xml:id="echoid-s3803" xml:space="preserve">in puncto χ. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">quod fieri non poteſt. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">Sequitur
              <lb/>
            igitur, ut centrum grauitatis pyramidis in linea d e; </s>
            <s xml:id="echoid-s3806" xml:space="preserve">hoc
              <lb/>
            eſt in eius axe conſiſtat.</s>
            <s xml:id="echoid-s3807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3808" xml:space="preserve">Sit conus, uel coni portio, cuius axis b d: </s>
            <s xml:id="echoid-s3809" xml:space="preserve">& </s>
            <s xml:id="echoid-s3810" xml:space="preserve">ſecetur plano
              <lb/>
            per axem, ut ſectio ſit triangulum a b c. </s>
            <s xml:id="echoid-s3811" xml:space="preserve">Dico centrum gra
              <lb/>
            uitatis ipſius eſſe in linea b d. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Sit enim, ſi fieri poteſt, centrũ
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              <figure xlink:label="fig-0151-01" xlink:href="fig-0151-01a" number="104">
                <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0151-01"/>
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            e: </s>
            <s xml:id="echoid-s3813" xml:space="preserve">perq; </s>
            <s xml:id="echoid-s3814" xml:space="preserve">e ducatur e f axi æquidiſtans: </s>
            <s xml:id="echoid-s3815" xml:space="preserve">& </s>
            <s xml:id="echoid-s3816" xml:space="preserve">quam propor-
              <lb/>
            tionem habet c d ad d f, habeat conus, uel coni portio ad
              <lb/>
            ſolidum g. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">inſcribatur ergo in cono, uel coni portione </s>
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