Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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            <s xml:id="echoid-s10372" xml:space="preserve">
              <pb o="400" file="0420" n="420" rhead="GEOMETRIÆ"/>
            quatuor rationes primò dictam rationem componentes .</s>
            <s xml:id="echoid-s10373" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10374" xml:space="preserve">ratione
              <lb/>
            rectanguli, AOZ, bis, cum {2/3}. </s>
            <s xml:id="echoid-s10375" xml:space="preserve">quadrati, VZ, ad rectangulum, AZ
              <lb/>
            O, rationem, ZO, ad OS, rationem rectanguli, AZV, ad rectan-
              <lb/>
            gulum, ASV, & </s>
            <s xml:id="echoid-s10376" xml:space="preserve">tandem rationem rectanguli, ASO, ad rectangu-
              <lb/>
            lum, AOS, bis cum {2/3}. </s>
            <s xml:id="echoid-s10377" xml:space="preserve">quadrati, SV, harum autem rationum illa,
              <lb/>
              <figure xlink:label="fig-0420-01" xlink:href="fig-0420-01a" number="285">
                <image file="0420-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0420-01"/>
              </figure>
            quam habet rectangulum, AZV, adrectã,
              <lb/>
            gulum, ASV, componitur ex ratione, Z
              <lb/>
            V, ad, VS, & </s>
            <s xml:id="echoid-s10378" xml:space="preserve">ex ratione, ZA, ad, AS, ha-
              <lb/>
            bemus ergo quinque rationes componen-
              <lb/>
            tes rationem primò dictam, ſitigitur pri-
              <lb/>
            mo loco diſpoſita ratio, quam habet re-
              <lb/>
            ctangulum bis ſub, AOZ, cum {2/3} quadra-
              <lb/>
            ti, ZV, ad rectangulum, AZO; </s>
            <s xml:id="echoid-s10379" xml:space="preserve">ſi rurlus
              <lb/>
            aſſumamus ex cæteris quatuor rationibus
              <lb/>
            eam, quam habet, ZA, ad, AS, vel (rum
              <lb/>
            pta, ZO, communi altitudine) quam ha
              <lb/>
            bet rectangulum, AZO, ad rectangulu
              <lb/>
            ſub, ZO, AS, quæ habeatur ſecundo roco;
              <lb/>
            </s>
            <s xml:id="echoid-s10380" xml:space="preserve">& </s>
            <s xml:id="echoid-s10381" xml:space="preserve">inſuper ſiex cæteris tribus ratiombus
              <lb/>
            ſumamus, quam habet, ZO, ad, OS, vel
              <lb/>
            (ſumpta, AS, communi altitudine) quam
              <lb/>
            habet rectangulum ſub, ZO, AS, ad rectangulum, ASO, quæ ſit
              <lb/>
            poſita tertio loco, & </s>
            <s xml:id="echoid-s10382" xml:space="preserve">tandem ſiteneamus quartò loco eam, quam
              <lb/>
            habet rectangulum, ASO, ad rectangulum ſub, AOS, bis, {2/3}. </s>
            <s xml:id="echoid-s10383" xml:space="preserve">qua-
              <lb/>
            drati, SV, habebimus has quatuor hoc ordine diſpoſitas conſequẽ-
              <lb/>
            ter rationes .</s>
            <s xml:id="echoid-s10384" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10385" xml:space="preserve">rationem rectanguli ſub, AOZ, bis cum {2/3}, quadra-
              <lb/>
            ti, ZV, ad rectangulum, AZO, rationem huius ad rectangulum
              <lb/>
            ſub, AS, OZ, rationem huius ad rectangulum, ASO, & </s>
            <s xml:id="echoid-s10386" xml:space="preserve">tandem
              <lb/>
            rationem huius ad rectangulum, AOS, bis, vna cum {2/3}. </s>
            <s xml:id="echoid-s10387" xml:space="preserve">quadrati,
              <lb/>
            SV, quæ component rationem primæ ad vitimam .</s>
            <s xml:id="echoid-s10388" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10389" xml:space="preserve">eam, quam
              <lb/>
              <note position="left" xlink:label="note-0420-01" xlink:href="note-0420-01a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            habet rectangulum, AOZ, bis vna cum {2/3}. </s>
            <s xml:id="echoid-s10390" xml:space="preserve">quadrati, ZV, ad rectã-
              <lb/>
            gulum, AOS, bis, vna cum {2/3}. </s>
            <s xml:id="echoid-s10391" xml:space="preserve">quadrati, SV, vel quam habent ho-
              <lb/>
            rum dimidia .</s>
            <s xml:id="echoid-s10392" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10393" xml:space="preserve">rectangulum, AOZ, cum {1/3}. </s>
            <s xml:id="echoid-s10394" xml:space="preserve">quadrat V, Z, ad rectã-
              <lb/>
            gulum, AOS, cum {1/3}. </s>
            <s xml:id="echoid-s10395" xml:space="preserve">quadrati, SV, @llas ergo quatuor rationes in
              <lb/>
            ſolam hane redegimus; </s>
            <s xml:id="echoid-s10396" xml:space="preserve">huicſi iungamus eam, quam habet, ZV,
              <lb/>
            ad, VS, quæ erat quinta ratio, quæreſidua erat, componetur ex
              <lb/>
            dictis quinque rationibus hæcſola .</s>
            <s xml:id="echoid-s10397" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10398" xml:space="preserve">quam habet parallelepipedũ
              <lb/>
            ſub altitudine, ZV, baſi rectangulo, AOZ, vel, VOZ, cum {1/3}. </s>
            <s xml:id="echoid-s10399" xml:space="preserve">qua-
              <lb/>
            drati, ZV, ad parallelepipedum ſub altitudine, SV, baſi rectangu-
              <lb/>
            lo, AOS, vel, VOS, cum {1/3}. </s>
            <s xml:id="echoid-s10400" xml:space="preserve">quadrati, SV, quę erit ea, quam habe-
              <lb/>
            bunt omnia quadrata, FC, demptis omnibus quadratis </s>
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