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

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            <s xml:id="echoid-s12769" xml:space="preserve">
              <pb o="501" file="0521" n="521" rhead="LIBER VII."/>
            ipſæ verò figuræ, MEGF, QRY, NSTV, ΖΩΔ, ſint proportiona-
              <lb/>
              <note position="right" xlink:label="note-0521-01" xlink:href="note-0521-01a" xml:space="preserve">Conuerſ.
                <lb/>
              Deſin. 4.
                <lb/>
              Qui, El.</note>
            les, & </s>
            <s xml:id="echoid-s12770" xml:space="preserve">homologæ, MEGF, NSTV, ideò ſi figura, MCGF, fuerit
              <lb/>
            æqualis figuræ, QRX, etiam figura, NBTV, erit æqualis figuræ,
              <lb/>
            ΖΩ℟, & </s>
            <s xml:id="echoid-s12771" xml:space="preserve">quælibet alia in ſolido, AMCGF, ſibi reſpondenti in alio
              <lb/>
            ſolido, PQRX, vnde & </s>
            <s xml:id="echoid-s12772" xml:space="preserve">ſolidum, AMCGF, æquabitur ſolido, PQ
              <lb/>
            RX. </s>
            <s xml:id="echoid-s12773" xml:space="preserve">Et ſi figura, MCGF, ſuperauerit figuram, QRX, eodem
              <lb/>
              <note position="right" xlink:label="note-0521-02" xlink:href="note-0521-02a" xml:space="preserve">Ex 1. hu-
                <lb/>
              ius.</note>
            modo oſtendemus, quod ſolidum, AMCGF, ſuperabit ſolidum, P
              <lb/>
            QRX, & </s>
            <s xml:id="echoid-s12774" xml:space="preserve">ſi illa ſuperabitur, etiam hoc ſuperabitur, ergo prima ad
              <lb/>
            ſecundam erit, vt tertia ad quartam, hoc eſt ſolidum, AMEGF, ad
              <lb/>
            ſolidum, PQRY, erit vt figura, MEGF, ad figuram, QRY, vel vt
              <lb/>
            figura, NSTV, ad figuram, ΖΩΔ, vel vt alia quælibet eiuſmodi
              <lb/>
              <note position="right" xlink:label="note-0521-03" xlink:href="note-0521-03a" xml:space="preserve">Defi.5.
                <lb/>
              Qui. El.</note>
            in ſolido, AMEGF, ad ſibi reipo identem in alio ſolido, PQRY,
              <lb/>
            hoc eſt ad exiſtentem in eodem cum ipſa plano quod oſtendere o-
              <lb/>
            erat. </s>
            <s xml:id="echoid-s12775" xml:space="preserve">Dicantur autem figuræ proportionaliter analogæ, iuxta re-
              <lb/>
            gulas, MEGF, QRY.</s>
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        <div xml:id="echoid-div1156" type="section" level="1" n="692">
          <head xml:id="echoid-head725" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s12777" xml:space="preserve">HÆc, & </s>
            <s xml:id="echoid-s12778" xml:space="preserve">antecedens methodo Indiuiſibilium oſtenſæ quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s12779" xml:space="preserve">fuerunt Lib. </s>
            <s xml:id="echoid-s12780" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12781" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s12782" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12783" xml:space="preserve">cum verò prima, ſecunda, & </s>
            <s xml:id="echoid-s12784" xml:space="preserve">tertia
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s12785" xml:space="preserve">eiuſdem libri ſint illius methodi fundamenta, hinc opus erit
              <lb/>
            in præſenti Lib. </s>
            <s xml:id="echoid-s12786" xml:space="preserve">quaſcumq; </s>
            <s xml:id="echoid-s12787" xml:space="preserve">illas ſubſequentes, & </s>
            <s xml:id="echoid-s12788" xml:space="preserve">ex dicta indiui-
              <lb/>
            ſibilium methodo Propoſitiones dependentes, aliter demonſtra-
              <lb/>
            re, vt vel ſcrupoloſo cuiq; </s>
            <s xml:id="echoid-s12789" xml:space="preserve">Geometrę ſatisfiat. </s>
            <s xml:id="echoid-s12790" xml:space="preserve">Igitur ab hac Lib. </s>
            <s xml:id="echoid-s12791" xml:space="preserve">
              <lb/>
            2. </s>
            <s xml:id="echoid-s12792" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s12793" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12794" xml:space="preserve">incipientes, curabimus, vt, quę per illam methodum
              <lb/>
            vera eſſe demonſtrata ſunt, etiam per noua hæc fundamenta con-
              <lb/>
            firmentur. </s>
            <s xml:id="echoid-s12795" xml:space="preserve">Primi Lib. </s>
            <s xml:id="echoid-s12796" xml:space="preserve">autem Prop. </s>
            <s xml:id="echoid-s12797" xml:space="preserve">nullatenus à dicta methodo
              <lb/>
            pendere manifeſtum eſt circa nonnullas tamen obiter prius hæc
              <lb/>
            pauca maioris facilitatis gratia libuit declarare.</s>
            <s xml:id="echoid-s12798" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12799" xml:space="preserve">In Prop. </s>
            <s xml:id="echoid-s12800" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12801" xml:space="preserve">igitur Lib. </s>
            <s xml:id="echoid-s12802" xml:space="preserve">primi ſciat Lector tacitè ſupponi omnes
              <lb/>
            vertices datę figuræ, reſpectu eiuſdem regulę aſſumptos, eſſe in ea-
              <lb/>
            dem recta linea regulæ parallela; </s>
            <s xml:id="echoid-s12803" xml:space="preserve">ſeu, pro figuris ſolidis, in eodem
              <lb/>
            plano regulæ æquidiſtante, diffinitionibus conformiter; </s>
            <s xml:id="echoid-s12804" xml:space="preserve">quod ob
              <lb/>
            ſui claritatem inter axiomata poterat recenſeri.</s>
            <s xml:id="echoid-s12805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12806" xml:space="preserve">In Prop. </s>
            <s xml:id="echoid-s12807" xml:space="preserve">26. </s>
            <s xml:id="echoid-s12808" xml:space="preserve">prætermiſſa fuit demonſtratio pręſentis caſus, cum
              <lb/>
            nempe, AG, contingit eſſe perpendicularem, GV, & </s>
            <s xml:id="echoid-s12809" xml:space="preserve">hoc cum fa-
              <lb/>
            cile, intellecto difficiliori caſu (qui ibidem explicatur) hoc probari
              <lb/>
            poſſet; </s>
            <s xml:id="echoid-s12810" xml:space="preserve">concludetur autem hoc modo, quod prætendimus, nempe
              <lb/>
            in tali caſu etiam, KY, eſſe perpendicularem ipſi, ΥΔ, & </s>
            <s xml:id="echoid-s12811" xml:space="preserve">ſecunda
              <lb/>
            plana, AV, ΚΔ, ad plana, HV, &</s>
            <s xml:id="echoid-s12812" xml:space="preserve">Δ, æquè ad eandem partem in-
              <lb/>
            clinari. </s>
            <s xml:id="echoid-s12813" xml:space="preserve">Sit, AG, ad, GP, vt, KY, ad, YX, iunctis, AP, PE, KX, </s>
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