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

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            <s xml:id="echoid-s12723" xml:space="preserve">
              <pb o="499" file="0519" n="519" rhead="LIBER VII."/>
            ſupereretur à, φ2, ergo prima ad ſecundam erit, vt tertia ad quar-
              <lb/>
            tam. </s>
            <s xml:id="echoid-s12724" xml:space="preserve">f. </s>
            <s xml:id="echoid-s12725" xml:space="preserve">figura, Β&</s>
            <s xml:id="echoid-s12726" xml:space="preserve">℟ΚΓΔ, ad figuram, Cφλ, erit, vt aggregatum
              <lb/>
            ex, &</s>
            <s xml:id="echoid-s12727" xml:space="preserve">℟, ΓΔ; </s>
            <s xml:id="echoid-s12728" xml:space="preserve">ad, φλ, vel vt aggregatum ex, HI, LM, ad, NO, ſeu
              <lb/>
            vt quælibet aliæ duæ ſimiliter ſumptę, quod erat oſtendendum,
              <lb/>
            Dicantur autem dictę figuræ proportionaliter analogę iuxta regu-
              <lb/>
            lam, AD, vel, ΧΩ.</s>
            <s xml:id="echoid-s12729" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1154" type="section" level="1" n="691">
          <head xml:id="echoid-head724" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s12730" xml:space="preserve">FIguræ ſolidæ quæcumq; </s>
            <s xml:id="echoid-s12731" xml:space="preserve">in eiſdem planis parallelis
              <lb/>
            conſtitutæ, in quibus ductis quibuſcumque planis di-
              <lb/>
            ctis parallelis æquidiſtantibus, coneeptæ cuiuſcumq; </s>
            <s xml:id="echoid-s12732" xml:space="preserve">ſic
              <lb/>
            ducti plani in ipſis ſolidis figurę planę ſunt inter ſe, vt eiuſ-
              <lb/>
            modi cuiuſlibet alterius plani in eiſdem ſolis conceptæ ſi-
              <lb/>
            guræ (homologis tamen in eodem ſolido ſemper exiſter ti-
              <lb/>
            bus) eandem inter ſe, quam dictæ iam-conceptæ cuiuſcũq;
              <lb/>
            </s>
            <s xml:id="echoid-s12733" xml:space="preserve">plani figuræ, rationem habebunt. </s>
            <s xml:id="echoid-s12734" xml:space="preserve">Dicanrur autem figurę
              <lb/>
            proportionaliter analogæ, iuxta regulas ipſa plana paral-
              <lb/>
            lela, in quibus exiſtunt.</s>
            <s xml:id="echoid-s12735" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12736" xml:space="preserve">Sint duę quelibet fig. </s>
            <s xml:id="echoid-s12737" xml:space="preserve">ſolidę, AMEGF, PQRY, in eiſdem planis
              <lb/>
            parallelis conſtitutę; </s>
            <s xml:id="echoid-s12738" xml:space="preserve">ductis verò quibuſcumq; </s>
            <s xml:id="echoid-s12739" xml:space="preserve">planis præfatis pa-
              <lb/>
            rallelis ęquidiſtantibus, eorum conceptę, in ſolidis figurę ſint vnius
              <lb/>
            plani ex. </s>
            <s xml:id="echoid-s12740" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12741" xml:space="preserve">figuræ, NSTV, ΖΩΔ, alteriusautem, MEGF, QRY,
              <lb/>
            vel contingat has eſſe ſolidorum baſes, ac in altero planorum pa-
              <lb/>
            rallelorum, ſolida, AMEGF, PQRY, contingentium, ſit verò figu-
              <lb/>
            ra, MEGF, ad figuram, QRY, vt figura, NSTV, ad figuram, ΖΩ
              <lb/>
            Δ, homologis nempè in eodem ſolido exiſtentibus. </s>
            <s xml:id="echoid-s12742" xml:space="preserve">Dico ſolidum,
              <lb/>
            AMEGF, ad ſolidum, PQRY, eſſe vt, NSTV, figura, ad figuram,
              <lb/>
            ΖΩΔ, vel vt figura, MEGF, ad figuram, QRY. </s>
            <s xml:id="echoid-s12743" xml:space="preserve">Ducatur enim in
              <lb/>
            figura, MEGF, vtcumq; </s>
            <s xml:id="echoid-s12744" xml:space="preserve">recta, EF, ad illius ambitum terminata,
              <lb/>
            cui ducta parallela, SV, in figura, NSTV, producantur ambæ in-
              <lb/>
            definitè verſus puncta, S, E, in quibus ſumantur vtcũq; </s>
            <s xml:id="echoid-s12745" xml:space="preserve">ęquè mul-
              <lb/>
            tiplices, BS, CE, ſimiliter in eiſdem figuris ductis ali js eiſ dem, SV.
              <lb/>
            </s>
            <s xml:id="echoid-s12746" xml:space="preserve">EF, ęquidiſtantibus, ſumãtur earum pariter ęquè, multiplices iux-
              <lb/>
            ta prędictarum multiplicitatem, & </s>
            <s xml:id="echoid-s12747" xml:space="preserve">omnium termini ſint in lineis,
              <lb/>
            NBT, MICHG, ſicut ipſarum partium termini ſint in lineis, NST,
              <lb/>
            NOT, NBT, MEG, MDG, MCG, traductis verò alijs quotcumq; </s>
            <s xml:id="echoid-s12748" xml:space="preserve">
              <lb/>
            planis pręfatis parallelis, ac ipſa ſolida ſecantibus, hoc idem fiat
              <lb/>
            circa ipſorum figuras in ipſis ſolidis conceptas, omnium verò </s>
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