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

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          <p>
            <s xml:id="echoid-s3890" xml:space="preserve">
              <pb o="164" file="0184" n="184" rhead="GEOMETRIÆ"/>
            mum, AE, ſimul cum figura, BCE, ſed, ne fiat confuſio, ſint ſub
              <lb/>
              <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">B. Def. 4.
                <lb/>
              lib. 1.</note>
            ampliori forma, & </s>
            <s xml:id="echoid-s3891" xml:space="preserve">inipſis tanquam in baſibus conſtituti intelligan-
              <lb/>
            tur duo cylindrici recti, FE, nempè in baſi, AE, &</s>
            <s xml:id="echoid-s3892" xml:space="preserve">, DGE, in baſi
              <lb/>
            figura, BCE, & </s>
            <s xml:id="echoid-s3893" xml:space="preserve">in eadem altitudine, quorum quod inſiſtit ipſi, A
              <lb/>
            E, eſt parallelepipedum, vt facilè oſtendetur, intelligatur nunc pa-
              <lb/>
            rallelepipedum, FE, ſecari vtcunque plano ipſi, GE, &</s>
            <s xml:id="echoid-s3894" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3895" xml:space="preserve">quidiſtante,
              <lb/>
            producetut ergo ex hac ſectione in ipſo parallelogrammum rectan-
              <lb/>
              <note position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">Coroll. 6.
                <lb/>
              lib. 1.</note>
            gulum, quod ſit, KO, eodem autem plano fiat in cylindrico, DG
              <lb/>
            E, rectangulum, LO, fiet autem & </s>
            <s xml:id="echoid-s3896" xml:space="preserve">in hoc cylindrico rectangulum,
              <lb/>
            quia dictum planum ducitur per latera baſi, BCE, rectè inſiſten-
              <lb/>
              <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a" number="107">
                <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0184-01"/>
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            tia, cum ducatur &</s>
            <s xml:id="echoid-s3897" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3898" xml:space="preserve">qui-
              <lb/>
            diſtanter ipſi, GE, quod
              <lb/>
            ducitur perlatera, GC,
              <lb/>
            SE, erit ergo rectange-
              <lb/>
            lum, KO, vnum ex ijs,
              <lb/>
            quę dicũtur omnia pla-
              <lb/>
            na parallelepipedi, FE,
              <lb/>
            regula, GE, & </s>
            <s xml:id="echoid-s3899" xml:space="preserve">rectan-
              <lb/>
            gulum, LO, erit vnum
              <lb/>
            ex ijs, quę dicuntur om-
              <lb/>
            nia plana cylindrici, G
              <lb/>
            DE, regula, GE, quę
              <lb/>
            rectangula erunt &</s>
            <s xml:id="echoid-s3900" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3901" xml:space="preserve">què
              <lb/>
            alta, ac rectangulum,
              <lb/>
            GE, omnia igitur pla-
              <lb/>
            na parallelepipedi, FE,
              <lb/>
            (regula, GE,) ſunt omnia rectangula &</s>
            <s xml:id="echoid-s3902" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3903" xml:space="preserve">què alta, ac, GE, ipſius pa-
              <lb/>
            rallelogrammi, AE, (regula, CE,) & </s>
            <s xml:id="echoid-s3904" xml:space="preserve">omnia plana cylindrici, G
              <lb/>
              <note position="left" xlink:label="note-0184-03" xlink:href="note-0184-03a" xml:space="preserve">E. Def. 8.
                <lb/>
              huius.</note>
            DE, ſunt omnia rectangula figuræ, BCE, &</s>
            <s xml:id="echoid-s3905" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3906" xml:space="preserve">quiangula, & </s>
            <s xml:id="echoid-s3907" xml:space="preserve">&</s>
            <s xml:id="echoid-s3908" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3909" xml:space="preserve">què
              <lb/>
            alta, ac ipſum, GE, regula eadem, CE: </s>
            <s xml:id="echoid-s3910" xml:space="preserve">Secentur nunc dicti cylin-
              <lb/>
            drici planis baſibus &</s>
            <s xml:id="echoid-s3911" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3912" xml:space="preserve">quidiſtantibus, fient ergo communes corum ſe-
              <lb/>
            ctiones ſimiles, & </s>
            <s xml:id="echoid-s3913" xml:space="preserve">&</s>
            <s xml:id="echoid-s3914" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3915" xml:space="preserve">quales baſibus, ſit in parallelepipedo, FE, pro-
              <lb/>
              <note position="left" xlink:label="note-0184-04" xlink:href="note-0184-04a" xml:space="preserve">Corol. 12.
                <lb/>
              lib. 1.</note>
            ducta, NP, & </s>
            <s xml:id="echoid-s3916" xml:space="preserve">in cylindrico, GDE, producta figura, HQP, erit
              <lb/>
            ergo vt, AE, ad figuram, BCE, ita, NP, ad figuram, HQP, & </s>
            <s xml:id="echoid-s3917" xml:space="preserve">
              <lb/>
            ita etiam quælibet alię figurę in ipſis per plana &</s>
            <s xml:id="echoid-s3918" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3919" xml:space="preserve">quidiſtanter baſibus
              <lb/>
            eoſdem ſecantia productæ, & </s>
            <s xml:id="echoid-s3920" xml:space="preserve">vt vna ad vnam, ſic omnes ad omnes
              <lb/>
              <note position="left" xlink:label="note-0184-05" xlink:href="note-0184-05a" xml:space="preserve">ExCorol.
                <lb/>
              A. huius.</note>
            .</s>
            <s xml:id="echoid-s3921" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3922" xml:space="preserve">vt, AE, ad figuram, CBE, ita omnia plana parallelepipedi, F
              <lb/>
            E, regula, AE, ad omnia plana cylindrici, GDE, regula eadem
              <lb/>
              <note position="left" xlink:label="note-0184-06" xlink:href="note-0184-06a" xml:space="preserve">ExCorol.
                <lb/>
              x. huius.</note>
            baſi, ſunt autem omnia plana parallelepipedi, FE, regula, AE, &</s>
            <s xml:id="echoid-s3923" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3924" xml:space="preserve">-
              <lb/>
            qualia omnibus eiuſdem planis, regula, GE, quæ ſunt omnia re-
              <lb/>
              <note position="left" xlink:label="note-0184-07" xlink:href="note-0184-07a" xml:space="preserve">E. Def. 8.
                <lb/>
              lib. 1.</note>
            ctangula ipſius, AE, regula, CE, &</s>
            <s xml:id="echoid-s3925" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3926" xml:space="preserve">què alta, acipſum, GF, & </s>
            <s xml:id="echoid-s3927" xml:space="preserve">
              <lb/>
            omnia plana cylindrici, GDE, regula baſi, CBE, ſunt &</s>
            <s xml:id="echoid-s3928" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3929" xml:space="preserve">qualia </s>
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