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="14" file="0039" n="39" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ſeſquialter eius, quæ uſque ad axem, quanta eſt linea m o.
              <lb/>
            </s>
            <s xml:space="preserve">Ponebatur autem portio ad humidum æqualis molis non
              <lb/>
            minorem in grauitate proportionem habere, quam qua-
              <lb/>
            dratum, quod fit ab exceſſu, quo axis eſt maior, quam ſeſ-
              <lb/>
            quialter eius, quæ uſque ad axem, ad quadratum, quod ab
              <lb/>
            axe. </s>
            <s xml:space="preserve">quare conſtat portionem ad humidum in grauitate
              <lb/>
            non minorem proportionem habere, quàm quadratum li
              <lb/>
            neæ m o ad quadratum ipſius n o. </s>
            <s xml:space="preserve">Sed quam proportio-
              <lb/>
            nem habet portio ad humidum in grauitate, eandem por-
              <lb/>
            tio ipſius demerla habet ad totam portionem: </s>
            <s xml:space="preserve">hoc enim
              <lb/>
              <anchor type="note" xlink:label="note-0039-01a" xlink:href="note-0039-01"/>
            ſupra demonſtratum eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet de
              <lb/>
              <anchor type="note" xlink:label="note-0039-02a" xlink:href="note-0039-02"/>
            merſa portio ad totam, eam quadratum p f habet ad n o
              <lb/>
            quadratum: </s>
            <s xml:space="preserve">cum demonſtratum ſit in iis, quæ de conoidi
              <lb/>
            bus, & </s>
            <s xml:space="preserve">ſphæroidibus, ſi à rectangulo conoide duæ portio-
              <lb/>
            nes planis quomodocunque ductis abſcindantur, portio-
              <lb/>
            nes inter ſe eandem habere proportionem, qnàm quadra-
              <lb/>
            ta, quæ ab ipſorum axibus conſtituuntur. </s>
            <s xml:space="preserve">non minorem
              <lb/>
            ergo proportionẽ habet quadratum pf ad quadratũ n o,
              <lb/>
            quàm quadratum m o ad idem n o quadratum. </s>
            <s xml:space="preserve">quare
              <lb/>
              <anchor type="note" xlink:label="note-0039-03a" xlink:href="note-0039-03"/>
            p f non eſt minor ipſa m o; </s>
            <s xml:space="preserve">nec b p item minor h o. </s>
            <s xml:space="preserve">Si
              <lb/>
              <anchor type="note" xlink:label="note-0039-04a" xlink:href="note-0039-04"/>
            igitur ab h ducatur linea ad rectos angulos ipſi n o, coi-
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              <anchor type="note" xlink:label="note-0039-05a" xlink:href="note-0039-05"/>
            bit cum b p, atque inter b, & </s>
            <s xml:space="preserve">p cadet. </s>
            <s xml:space="preserve">coeat in t. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quo
              <lb/>
              <anchor type="note" xlink:label="note-0039-06a" xlink:href="note-0039-06"/>
            niam p f quidem æquidiſtans eſt diametro, h t autem ad
              <lb/>
            diametrum perpendicularis; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">r h æqualis ei, quæ uſque
              <lb/>
            ad axem: </s>
            <s xml:space="preserve">ducta linea ab r ad t & </s>
            <s xml:space="preserve">producta angulos rectos
              <lb/>
            faciet cum linea ſectionem in puncto p contingente. </s>
            <s xml:space="preserve">qua-
              <lb/>
            re & </s>
            <s xml:space="preserve">cum is, & </s>
            <s xml:space="preserve">cum humidi ſuperficie, quæ per is tran-
              <lb/>
            ſit. </s>
            <s xml:space="preserve">Itaque ſi per b g puncta lineæ ipſi r t æquidiſtantes du
              <lb/>
            cantur, angulos rectos facient cum ſuperficie humidi: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            quod quidem in humido eſt ſolidum conoidis feretur ſur-
              <lb/>
            ſum ſecundum eam, quæ per b ducta fuerit ipſi r t æquidi
              <lb/>
            ſtans: </s>
            <s xml:space="preserve">quod autem extra humidum, ſecundum eam, quæ
              <lb/>
            per g deorſum feretur. </s>
            <s xml:space="preserve">atque hoc tandiu fiet, quoad co-
              <lb/>
            noides rectum conſtituatur.</s>
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            <figure xlink:label="fig-0038-01" xlink:href="fig-0038-01a">
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            <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">10. quinti</note>
            <note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0038-04" xlink:href="note-0038-04a" xml:space="preserve">19. quinti</note>
            <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">D</note>
            <note position="right" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">E</note>
            <note position="right" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">F</note>
            <note position="right" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">G</note>
            <note position="right" xlink:label="note-0039-06" xlink:href="note-0039-06a" xml:space="preserve">H</note>
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