Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo
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              <pb o="16" file="0043" n="43" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dratum n o ad quadratum p f. </s>
            <s xml:id="echoid-s903" xml:space="preserve">quadratum igitur n o ad
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            quadratum p f non maiorem proportionem habet, quàm
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            ad quadratum m o. </s>
            <s xml:id="echoid-s904" xml:space="preserve">ex quo eſſicitur, ut p f non ſit minor
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              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">C</note>
            ipſa o m; </s>
            <s xml:id="echoid-s905" xml:space="preserve">neque p b ipſa o h. </s>
            <s xml:id="echoid-s906" xml:space="preserve">quæ ergo ab h ducitur ad
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">D</note>
            rectos angulos ipſi n o, coibit cum b p inter p & </s>
            <s xml:id="echoid-s907" xml:space="preserve">b. </s>
            <s xml:id="echoid-s908" xml:space="preserve">co-
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            eatin t. </s>
            <s xml:id="echoid-s909" xml:space="preserve">& </s>
            <s xml:id="echoid-s910" xml:space="preserve">quoniam in rectanguli coniſectione p f eſt æqui
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            diſtans diametro n o; </s>
            <s xml:id="echoid-s911" xml:space="preserve">h t autem ad diametrum perpẽ-
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            dicularis: </s>
            <s xml:id="echoid-s912" xml:space="preserve">& </s>
            <s xml:id="echoid-s913" xml:space="preserve">r h æqualis ei, quæ uſque ad axem: </s>
            <s xml:id="echoid-s914" xml:space="preserve">conſtat r t
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            productam ſacere angulos rectos cum ipſa k p ω. </s>
            <s xml:id="echoid-s915" xml:space="preserve">quare
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            & </s>
            <s xml:id="echoid-s916" xml:space="preserve">cum is. </s>
            <s xml:id="echoid-s917" xml:space="preserve">ergo rt perpendicularis eſt ad ſuperſiciem hu
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            midi. </s>
            <s xml:id="echoid-s918" xml:space="preserve">et ſi per b g puncta ducantur æquidiſtantes ipſirt,
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            ad ſuperſiciem humidi perpendicular es erunt. </s>
            <s xml:id="echoid-s919" xml:space="preserve">portio igi
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            tur, qnæ eſt extra humidum, deorſum in humidum feretur
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            ſecundum perpendicularem per b ductam; </s>
            <s xml:id="echoid-s920" xml:space="preserve">quæ uero in-
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            tra humidum ſecundum perpendicularem per g ſurſum
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            feretur: </s>
            <s xml:id="echoid-s921" xml:space="preserve">& </s>
            <s xml:id="echoid-s922" xml:space="preserve">non manebit ſolida portio a p o l, ſedintra hu
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            midum mouebitur, donecutique ipſa n o ſecundum per-
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            pendicularem ſiat.</s>
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        <div xml:id="echoid-div67" type="section" level="1" n="28">
          <head xml:id="echoid-head33" xml:space="preserve">COMMENTARIVS.</head>
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            <s xml:id="echoid-s924" xml:space="preserve">_Quare non maiorem proportionem habet tota portio_
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              <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">A</note>
            _ad eam, quæ eſt extra humidum, quam quadratum n o ad_
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            _quadratum m o]_ cum enim magnitudo portionis in bumidum
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            demerſa ad totam portionem non maiorem proportionem babeat,
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            quàm exceſſus, quo quadratum n o excedit quadratum m o, ad ip-
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            ſum no quadratum: </s>
            <s xml:id="echoid-s925" xml:space="preserve">conuertendo per uigeſimáſextam quinti ele-
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            mentorum ex traditione Campani, tota portio ad magnitudinem de
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            merſam non minorem proportionem babebit, quàm quadratum n o
              <lb/>
            ad exceſſum, quo ipſum quadratum no excedit quadratum m o. </s>
            <s xml:id="echoid-s926" xml:space="preserve">In
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            telligatur portio, quæ extra bumidum, magnitudo prima: </s>
            <s xml:id="echoid-s927" xml:space="preserve">quæ in bu
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            mido demerſa est, ſecunda: </s>
            <s xml:id="echoid-s928" xml:space="preserve">tertia autem magnitudo ſit quadratum
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            mo: </s>
            <s xml:id="echoid-s929" xml:space="preserve">& </s>
            <s xml:id="echoid-s930" xml:space="preserve">exceſſus, quo quadratum n o excedit quadratum m o ſit
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            quarta. </s>
            <s xml:id="echoid-s931" xml:space="preserve">ex his igitur magnitudinibus, primæ & </s>
            <s xml:id="echoid-s932" xml:space="preserve">ſecundæ ad </s>
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Impressum