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

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            <s xml:id="echoid-s13327" xml:space="preserve">
              <pb o="515" file="0535" n="535" rhead="LIBER VII."/>
            φ8, æqualem, CD, ſimiliter, & </s>
            <s xml:id="echoid-s13328" xml:space="preserve">Δ, VΩ, X℟, deinceps æquales ipſis,
              <lb/>
            FH, kM, SO, ſicut etiam, ΣΛ, ΠΛ, NO, deinceps æqualesipſis,
              <lb/>
            GH, LM, NO, & </s>
            <s xml:id="echoid-s13329" xml:space="preserve">in ſuperficie, DΖΓΟ, ipſas, DZ, H9, Μβ, CΓ,
              <lb/>
            deinceps æquales eiſdem, BD, FH, KM, SO, & </s>
            <s xml:id="echoid-s13330" xml:space="preserve">cætera plana pa-
              <lb/>
            rallela ſimiliter ſe habuerint (ipſę autem ſuperficies, BO, DΓ, T℟,
              <lb/>
            inter ſe, vti etiam, CO, φO, inter ſe, erunt homologæ, regula quo-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s13331" xml:space="preserve">dictorum eaſdem ſecantium planorum inter ſe æquidiſtan-
              <lb/>
            tium.) </s>
            <s xml:id="echoid-s13332" xml:space="preserve">Dicimus ergo ſolidum rectangulum, AO, nedum contine-
              <lb/>
            ri ex. </s>
            <s xml:id="echoid-s13333" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13334" xml:space="preserve">ſub ſuperficiebus, BDOS, CDON, in quibus iacent latera
              <lb/>
            præfata rectangula continentia, ſed etiam ſub ſuperficiebus, T℟,
              <lb/>
            CO, vel, T℟, φO, vel ſub ſuperficiebus, ΓΖDΟ, ODCN, vel ſub,
              <lb/>
            ΓΖDΟ, φΝΟΛ8, in his enim plana parallela produxerunt latera
              <lb/>
            ijs æqualia, ſub quibus parallelogramma rectangula, AD, EH, I
              <lb/>
            M, RO, & </s>
            <s xml:id="echoid-s13335" xml:space="preserve">cætera huiuſmodi continentur, vt dictum fuit, in quo
              <lb/>
            non nihil à modo loquendi in planis diſcedere videmur, dicitur. </s>
            <s xml:id="echoid-s13336" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s13337" xml:space="preserve">ex. </s>
            <s xml:id="echoid-s13338" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13339" xml:space="preserve">rectangulum planum, AD, contineri ſub, BD, DC, quæ re-
              <lb/>
            ctum angulum conſtituunt, & </s>
            <s xml:id="echoid-s13340" xml:space="preserve">non ſub, TY, φ8, quæ ipſius rectũ
              <lb/>
              <note position="right" xlink:label="note-0535-01" xlink:href="note-0535-01a" xml:space="preserve">Pri. Def.
                <lb/>
              Sec. Elem.</note>
            angulum non conſtituunt, hoc tamen loquendimodo vſus ſum,
              <lb/>
            potius ſoliditatis deterrninationẽ reſpiciens, quam continentiam,
              <lb/>
            quæ fit à ſuperficiebus in ambitu contentorum ſolidorum exiſten-
              <lb/>
            tibus, cum enim cernerem non omnes ſuperficies ſolidum rectan-
              <lb/>
            gulum vt ſic continentes poſſe in ipſius contenti ſolidi ambitu re-
              <lb/>
            periri (vt ex. </s>
            <s xml:id="echoid-s13341" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13342" xml:space="preserve">cum contineretur duabus ſuperficiebus planis in il-
              <lb/>
            lius ambitu exiſtentibus, aliæ autem illis homologæ eſſent curuæ)
              <lb/>
            & </s>
            <s xml:id="echoid-s13343" xml:space="preserve">tamen latera ‘in his concepta viderem adæquari lateribus rectā-
              <lb/>
            gula plana continentibus, & </s>
            <s xml:id="echoid-s13344" xml:space="preserve">conſequenter eorundem areæ quan-
              <lb/>
            titatem præſcribere, vnde & </s>
            <s xml:id="echoid-s13345" xml:space="preserve">iſtæ prædictis homologæ ſuperficies
              <lb/>
            viderentur ipſius contenti ſoliditatẽ determinare (quęcumq; </s>
            <s xml:id="echoid-s13346" xml:space="preserve">enim
              <lb/>
            ſolida ſub ip ſius contineantur inter ſe erunt æqualia, vt infra oſtẽ-
              <lb/>
            demus) ideò volui præfata ſolida rectangula dici ſub omnibus his
              <lb/>
            ſuper ficiebus homologis ſecundum eandem regulam contineri.
              <lb/>
            </s>
            <s xml:id="echoid-s13347" xml:space="preserve">Quemadmodum ſi quis aliter ab Euclide diceret parallelogrammũ
              <lb/>
            rectangulum nedum ſub lateribus ipſius angulum rectum conſti-
              <lb/>
            tuentibus, ſed etiam ſub quibuſcunq; </s>
            <s xml:id="echoid-s13348" xml:space="preserve">alijs lateribus prædictis æ-
              <lb/>
            qualibus contineri, ſubintelligendo non hoc parallelogrammũ
              <lb/>
            in ipſius ambitu neceſlariò ipſa latera continentia habere, ſed per
              <lb/>
            ea ſiue ſint in ambitu, ſiue non, ipſius areæ quantitatem determi-
              <lb/>
            nari, patallelogrammum enim rectangulum contentum ſub duo-
              <lb/>
            bus lateribus, iuxta modum loquendi Euclidianum, æquatur cui-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s13349" xml:space="preserve">parallelogrammo rectangulo ſub alijs duobus prædictis æ-
              <lb/>
            qualibus contento. </s>
            <s xml:id="echoid-s13350" xml:space="preserve">Quod ſi quis attendat demonſtrationes ſec.</s>
            <s xml:id="echoid-s13351" xml:space="preserve"/>
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