Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            habeat circulus, uel ellipſis g h ad aliud ſpacium, in quo u:
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            <s xml:id="echoid-s3560" xml:space="preserve">& </s>
            <s xml:id="echoid-s3561" xml:space="preserve">in circulo, uel ellipſi plane deſcribatur rectilinea figura,
              <lb/>
            ita ut tãdem relinquãtur portiones minores ſpacio u, quæ
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            ſit o p g q r s h t: </s>
            <s xml:id="echoid-s3562" xml:space="preserve">deſcriptaq; </s>
            <s xml:id="echoid-s3563" xml:space="preserve">ſimili figura in oppoſitis pla-
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            nis c d, f e, per lineas ſibi ipſis reſpondentes plana ducãtur. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">
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            Itaque cylindrus, uel cylindri portio diuiditur in priſma,
              <lb/>
            cuius quidem baſis eſt figura rectilinea iam dicta, centrum
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            que grauitatis punctum K: </s>
            <s xml:id="echoid-s3565" xml:space="preserve">& </s>
            <s xml:id="echoid-s3566" xml:space="preserve">in multa ſolida, quæ pro baſi
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            bus habent relictas portiones, quas nos ſolidas portiones
              <lb/>
            appellabimus. </s>
            <s xml:id="echoid-s3567" xml:space="preserve">cum igitur portiones ſint minores ſpacio
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            u, circulus, uel ellipſis g h ad portiones maiorem propor-
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            tionem habebit, quàm linea m k ad K l. </s>
            <s xml:id="echoid-s3568" xml:space="preserve">fiat n k ad K l, ut
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            circulus uel ellipſis g h ad ipſas portiones. </s>
            <s xml:id="echoid-s3569" xml:space="preserve">Sed ut circulus
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            uel ellipſis g h ad figuram rectilineam in ipſa deſcri-
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            ptam, ita eſt cylindrus uel cylindri portio c e ad priſma,
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            quod rectilineam figuram pro baſi habet, & </s>
            <s xml:id="echoid-s3570" xml:space="preserve">altitudinem
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            æqualem; </s>
            <s xml:id="echoid-s3571" xml:space="preserve">id, quod infra demonſtrabitur, ergo per conuer
              <lb/>
            ſionem rationis, ut circulus, uel ellipſis g h ad portiones re
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            lictas, ita cylindrus, uel cylindri portio c e ad ſolidas por-
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            tiones, quare cylindrus uel cylindri portio ad ſolidas por-
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            tiones eandem proportionem habet, quam linea n k a d _k_
              <lb/>
            & </s>
            <s xml:id="echoid-s3572" xml:space="preserve">diuidendo priſma, cuius baſis eſt rectilinea figura ad ſo-
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            lidas portiones eandem proportionem habet, quam n lad
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            1 _k_. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">& </s>
            <s xml:id="echoid-s3574" xml:space="preserve">quoniam a cylindro uel cylindri portione, cuius gra-
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            uitatis centrum eſt l, aufertur priſma baſim habens rectili-
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            neam figurã, cuius centrũ grauitatis eſt _K_: </s>
            <s xml:id="echoid-s3575" xml:space="preserve">reſiduæ magnitu
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            dinis ex ſolidis portionibus cõpoſitæ grauitatis cẽtrũ erit
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            in linea k l protracta, & </s>
            <s xml:id="echoid-s3576" xml:space="preserve">in puncto n; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">quod eſt abſurdū. </s>
            <s xml:id="echoid-s3578" xml:space="preserve">relin
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            quitur ergo, ut cẽtrum grauitatis cylindri; </s>
            <s xml:id="echoid-s3579" xml:space="preserve">uel cylin dri por
              <lb/>
            tionis ſit punctũ k. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">quæ omnia demonſtrãda propoſuimus.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
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            <s xml:id="echoid-s3582" xml:space="preserve">At uero cylindrum, uel cylindri portionẽ ce
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            ad priſma, cuius baſis eſt rectilinea figura in ſpa-
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            cio g h deſcripta, & </s>
            <s xml:id="echoid-s3583" xml:space="preserve">altitudo æqualis; </s>
            <s xml:id="echoid-s3584" xml:space="preserve">eandem </s>
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