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="25" file="0061" n="61" rhead="DE IIS QVAE VEH. IN AQVA."/>
            b ψ dupla ſit ψ d, erit d b ipſius b ψ ſeſquialtera. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam e b ſeſ
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            quialtera est b r, ſequitur reliquam c d ipſius ψ r, boc est eius, quæ
              <lb/>
              <anchor type="note" xlink:label="note-0061-01a" xlink:href="note-0061-01"/>
            uſque ad axem ſeſquialteram eſſe. </s>
            <s xml:space="preserve">quare b c erit exceſſus, quo axis
              <lb/>
            maior est, quàm ſeſquialter eius, quæ uſque ad axem.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0060-03" xlink:href="note-0060-03a" xml:space="preserve">A</note>
            <note position="right" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">12. quinti</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Quare f q minor éſtipſa b c.</s>
            <s xml:space="preserve">]_ Nam cum portio ad bumi-
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              <anchor type="note" xlink:label="note-0061-02a" xlink:href="note-0061-02"/>
            dum in grauitate proportionem habeat eandem, quàm quadratum
              <lb/>
            f q ad quadratum d b: </s>
            <s xml:space="preserve">habeatq, minorem proportionem, quàm qua
              <lb/>
            dratum factum ab exceſſu, quo axis maior eſt, quàm ſeſquialter eius,
              <lb/>
            quæ uſque ad axem, ad quadratum ab axe; </s>
            <s xml:space="preserve">boc eſt minorem, quàm
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            quadratum c b ad quadratum b d: </s>
            <s xml:space="preserve">ponitur enim linea b d æqualis
              <lb/>
            axi: </s>
            <s xml:space="preserve">quadratum f q ad quadratum d b proportionem minorem ha-
              <lb/>
            bebit, quàm quadratum c b ad idem b d quadratum. </s>
            <s xml:space="preserve">ergo quadra-
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              <anchor type="note" xlink:label="note-0061-03a" xlink:href="note-0061-03"/>
            tum f q minus erit quadrato c b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea linea f q ipſa b c
              <lb/>
            minor.</s>
            <s xml:space="preserve"/>
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          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">8. quinti.</note>
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          <p style="it">
            <s xml:space="preserve">_Etidcirco f minor ipſa b r.</s>
            <s xml:space="preserve">]_ Quoniam enim c b ſeſquial-
              <lb/>
              <anchor type="note" xlink:label="note-0061-04a" xlink:href="note-0061-04"/>
            tera eſt b r, & </s>
            <s xml:space="preserve">f q ipſius f ſeſquialtera: </s>
            <s xml:space="preserve">estq; </s>
            <s xml:space="preserve">f q minor b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">f
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              <anchor type="note" xlink:label="note-0061-05a" xlink:href="note-0061-05"/>
            ipſa b r minor erit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0061-05" xlink:href="note-0061-05a" xml:space="preserve">14. quin-
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            ti.</note>
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          <p style="it">
            <s xml:space="preserve">_Itaque quoniam ponitur axis portionis cum ſuperficie_
              <lb/>
              <anchor type="note" xlink:label="note-0061-06a" xlink:href="note-0061-06"/>
            _humidi facere angulum maiorem angulo b: </s>
            <s xml:space="preserve">erit angulus_
              <lb/>
            _p y i angulo b maior.</s>
            <s xml:space="preserve">]_ Nam cum linea p y ſuperficiei bumidi
              <lb/>
            æ quidistet; </s>
            <s xml:space="preserve">uidelicet ipſi x s: </s>
            <s xml:space="preserve">angulus p y i æqualis erit angulo, qui
              <lb/>
              <anchor type="note" xlink:label="note-0061-07a" xlink:href="note-0061-07"/>
            diametro portionis n o, & </s>
            <s xml:space="preserve">linea x s continetur. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">angulo
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            b maior erit.</s>
            <s xml:space="preserve"/>
          </p>
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            <note position="right" xlink:label="note-0061-06" xlink:href="note-0061-06a" xml:space="preserve">D</note>
            <note position="right" xlink:label="note-0061-07" xlink:href="note-0061-07a" xml:space="preserve">29. primi</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Maiorem igitur proportionem habet quadratum p i ad_
              <lb/>
              <anchor type="note" xlink:label="note-0061-08a" xlink:href="note-0061-08"/>
            _quadratum i y, quàm quadratum e ψ ad ψ b quadratu.</s>
            <s xml:space="preserve">]_
              <lb/>
            Deſcribantur ſeorſum triangula p i y, e ψ b. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum angulus p y i
              <lb/>
            maior ſit angulo e b ψ, ad lineam i y, atque ad punctum y in ea da-
              <lb/>
            tum fiat angulus u y i æqualis angulo e b ψ. </s>
            <s xml:space="preserve">est autem angulus ad
              <lb/>
            i rectus æqualis recto ad ψ. </s>
            <s xml:space="preserve">reliquus igitur y u i reliquo b c ψ est
              <lb/>
            æqualis. </s>
            <s xml:space="preserve">quare linea u i ad lineam i y eandem proportionem ha-
              <lb/>
              <anchor type="note" xlink:label="note-0061-09a" xlink:href="note-0061-09"/>
            bet, quam linea e ψ ad ψ b. </s>
            <s xml:space="preserve">Sed linea p i, quæ maior est ipſa u i ad
              <lb/>
              <anchor type="note" xlink:label="note-0061-10a" xlink:href="note-0061-10"/>
            lineam in maiorem habet proportionem quam u i ad eandem. </s>
            <s xml:space="preserve">ergo
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              <anchor type="note" xlink:label="note-0061-11a" xlink:href="note-0061-11"/>
            p i ad i y maiorem proportionem habebit, quàm e ψ ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            propterea quadratum p i ad quadratum i y maiorem habebit, quàm</s>
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