Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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            <s xml:space="preserve">
              <pb file="0042" n="42" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">ſectionis diameter no: </s>
            <s xml:space="preserve">ſuperſiciei autem humidi ſectio
              <lb/>
            ſit is. </s>
            <s xml:space="preserve">Quoniam igitur axis non eſt ſecundum perpendicu
              <lb/>
            larem; </s>
            <s xml:space="preserve">ipſa no cum is non faciet angulos æquales. </s>
            <s xml:space="preserve">Du-
              <lb/>
            catur k ω contingens ſectionem apol in p; </s>
            <s xml:space="preserve">atque ipſi is
              <lb/>
            æquidiſtans: </s>
            <s xml:space="preserve">per p autem ducatur p f æquidiſtās ipſi n o:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumantur grauitatum centra: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius a p o l ſolidi
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            centrum r; </s>
            <s xml:space="preserve">eius quod extra humidum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta br
              <lb/>
            producatur adg,
              <lb/>
              <anchor type="figure" xlink:label="fig-0042-01a" xlink:href="fig-0042-01"/>
            quodſit centrum
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            grauitatis ſolidi ĩ
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            humido demerſi:
              <lb/>
            </s>
            <s xml:space="preserve">ſumatur præterea
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            r h æ qualis ei, quæ
              <lb/>
            uſque ad axẽ: </s>
            <s xml:space="preserve">o h
              <lb/>
            autem dupla ipſi-
              <lb/>
            us h m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia fiãt,
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            ſicuti ſuperius di-
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            ctum eſt. </s>
            <s xml:space="preserve">Itaque
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            cum portio ad hu
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            midum in grauita
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            te non maiorem
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            proportionem ha
              <lb/>
            bere ponatur, quã
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            exceſſus, quo quadratum n o excedit quadratum m o, ad
              <lb/>
            ipſum n o quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem in grauita
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            te portio habet ad humidum æqualis molis, eandem ha-
              <lb/>
            beat magnitudo portionis demerſa ad totam portio-
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            nem, quod demonſtratum eſt in prima propoſitione: </s>
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              <lb/>
            magnitudo demerſa non maiorem proportionem ha-
              <lb/>
              <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
            bebit ad totam portionem, quàm ſit dicta illa propor-
              <lb/>
            portio. </s>
            <s xml:space="preserve">quare non maiorem proportionem habet tota
              <lb/>
              <anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
            portio ad eam quæ eſt extra humidum, quàm quadratum
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            no ad quadratum m o. </s>
            <s xml:space="preserve">habet autem tota portio ad eam,
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              <anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
            quæ extra humidum proportionem eandem, quam qua-</s>
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