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

Table of handwritten notes

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