Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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          <p>
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              <pb file="0058" n="58" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">quam proportionem habet quadratum e ψ ad quadra-
              <lb/>
              <anchor type="note" xlink:label="note-0058-01a" xlink:href="note-0058-01"/>
            tum ψ b, eandem habet dimidium lineæ _k_ r ad lineã ψ b.
              <lb/>
            </s>
            <s xml:space="preserve">quare maiorem babet proportionem _k_ r ad i y, quàm di-
              <lb/>
              <anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
            midium k r ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco i y minor eſt, quàm dupla
              <lb/>
              <anchor type="note" xlink:label="note-0058-03a" xlink:href="note-0058-03"/>
            ψ b. </s>
            <s xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:space="preserve">ergo o i minor eſt, quàm
              <lb/>
            ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">i ω maior, quàm ψ r. </s>
            <s xml:space="preserve">ſed ψ r eſt æqualis ipſi f. </s>
            <s xml:space="preserve">maior
              <lb/>
              <anchor type="note" xlink:label="note-0058-04a" xlink:href="note-0058-04"/>
            igitur eſt i ω, quàm f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portio ad humidum in
              <lb/>
            grauitate eam ponitur habere proportionem, quam qua-
              <lb/>
            dratum f q ad quadratum b d: </s>
            <s xml:space="preserve">quam uero proportionem
              <lb/>
            habet portio ad humidum in grauitate, eam habet pars ip
              <lb/>
            ſius demerſa ad totam portionem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam pars ipſius de-
              <lb/>
            merſa habet ad totam, eandem habet quadratum p m ad
              <lb/>
            quadratnm o n: </s>
            <s xml:space="preserve">ſequitur quadratum p m ad quadratum
              <lb/>
            o n eam proportionem habere, quam quadratum f q ad
              <lb/>
            b d quadratum.
              <lb/>
            </s>
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              <anchor type="figure" xlink:label="fig-0058-01a" xlink:href="fig-0058-01"/>
            atque ideo ſ q æ-
              <lb/>
              <anchor type="note" xlink:label="note-0058-05a" xlink:href="note-0058-05"/>
            qualis eſt ipſi p m.
              <lb/>
            </s>
            <s xml:space="preserve">demõſtrata eſt au
              <lb/>
              <anchor type="note" xlink:label="note-0058-06a" xlink:href="note-0058-06"/>
            tem p h maior,
              <lb/>
            quàm f. </s>
            <s xml:space="preserve">cõſtat igi
              <lb/>
            tur p m minorem
              <lb/>
            eſſe, quàm ſeſqui-
              <lb/>
            alterã ipſius p h:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco p h ma
              <lb/>
            iorem, quàm du-
              <lb/>
            plam h m. </s>
            <s xml:space="preserve">Sit p z
              <lb/>
            ipſius z m dupla. </s>
            <s xml:space="preserve">
              <lb/>
            erit t quidem cẽ-
              <lb/>
            trũ grauitatis to-
              <lb/>
            tius ſolidi: </s>
            <s xml:space="preserve">centrũ
              <lb/>
            eius partis, quæ intra humidum, punctumz: </s>
            <s xml:space="preserve">reliquæ uero
              <lb/>
            partis centrum erit in linea z t producta uſque ad g. </s>
            <s xml:space="preserve">Eodẽ
              <lb/>
              <anchor type="note" xlink:label="note-0058-07a" xlink:href="note-0058-07"/>
            modo demonſtrabitur linea th perpendicularis ad ſuper-
              <lb/>
            ficiem humidi. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio demerſa in humido ſeretur extra</s>
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