Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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              <pb o="23" file="0057" n="57" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ipſa b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco f minor ipſa b r. </s>
            <s xml:space="preserve">ſit ipſi f æqualis r ψ:
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            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/>
            ducaturq; </s>
            <s xml:space="preserve">ad b d perpendicularis ψ e, quæ posſit dimidiũ
              <lb/>
            eius, quod lineis _k_ r, ψ b continetur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur b c. </s>
            <s xml:space="preserve">De-
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            monſtrandum eſt portionem in humidum demiſſam, ſicu-
              <lb/>
            ti dictum eſt, conſiſtere inclinatam ita, ut axis cum ſuperſi-
              <lb/>
            cie humidi angulum faciat angulo c b ψ æqualem. </s>
            <s xml:space="preserve">demit-
              <lb/>
            tatur enim aliqua portio in humidum, ut baſis ipſius hu-
              <lb/>
            midi ſuperficiem non contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi fieri poteſt, axis cum
              <lb/>
            ſuperficie humidi non faciat angulum æqualem angulo
              <lb/>
            e b ψ; </s>
            <s xml:space="preserve">ſed primo maiorem. </s>
            <s xml:space="preserve">ſecta autẽ portione plano per
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            axem, recto ad ſu-
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              <anchor type="figure" xlink:label="fig-0057-01a" xlink:href="fig-0057-01"/>
            perficiem humi-
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            di, ſit ſectio a p o l
              <lb/>
            rectanguli coni ſe
              <lb/>
            ctio: </s>
            <s xml:space="preserve">ſuperficiei
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            humidi ſectio x s:
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            </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">axis portio-
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            nis, & </s>
            <s xml:space="preserve">ſectiõis dia
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            meter n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">du-
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            catur p y quidem
              <lb/>
            ipſi x s æquidi-
              <lb/>
            ſtans, quæ ſectio-
              <lb/>
            nem a p o l contin
              <lb/>
            gat in p: </s>
            <s xml:space="preserve">p m ue-
              <lb/>
            ro æquidiſtans ip-
              <lb/>
            ſi n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p i ad
              <lb/>
            n o perpendicularis. </s>
            <s xml:space="preserve">ſit præterea b r æqualis o ω. </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0057-02a" xlink:href="note-0057-02"/>
            r k ipſi t _a_ & </s>
            <s xml:space="preserve">ω h perpendicularis ad axem. </s>
            <s xml:space="preserve">Itaque quo-
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            niam ponitut axis portionis cum ſuperficie humidi facere
              <lb/>
            angulum maiorem angulo b: </s>
            <s xml:space="preserve">erit angulus p y i angulo b
              <lb/>
              <anchor type="note" xlink:label="note-0057-03a" xlink:href="note-0057-03"/>
            maior. </s>
            <s xml:space="preserve">maiorem ergo proportionem habet quadratum
              <lb/>
            p i ad quadratum y i, quam quadratum e ψ ad ψ b qua-
              <lb/>
              <anchor type="note" xlink:label="note-0057-04a" xlink:href="note-0057-04"/>
            dratum. </s>
            <s xml:space="preserve">Sed quam proportionem habet quadratum p i
              <lb/>
            ad quadratum i y, eandem linea k r habet ad lineam i y:</s>
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