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

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          <p>
            <s xml:id="echoid-s5762" xml:space="preserve">
              <pb o="234" file="0254" n="254" rhead="GEOMETRI Æ"/>
            neo, TGEOX, eſſe ve, RF, adportion
              <unsure/>
            em, SET, ergo ex æquali
              <lb/>
            o nnia quadrata portionis, SMT, cum rectangulis bis ſub eadem,
              <lb/>
            & </s>
            <s xml:id="echoid-s5763" xml:space="preserve">ſub quadrilineo, MTXC, ad omnia quadrata portionis, SET,
              <lb/>
            cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5764" xml:space="preserve">ſub quadrilineo, TGEOX,
              <lb/>
            erunt vt portio, SMT, ad portionem, SET, quod oſtendere o-
              <lb/>
            portebat.</s>
            <s xml:id="echoid-s5765" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div573" type="section" level="1" n="339">
          <head xml:id="echoid-head356" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5766" xml:space="preserve">_H_INC patet omnia quadrata parallelogrammorum in eadem al-
              <lb/>
            titudine cum portionibus, vel portionum fruſtibus exiſtentium,
              <lb/>
            vna cum rectangulis bis ſub ijſdem parallelogrammis, & </s>
            <s xml:id="echoid-s5767" xml:space="preserve">reliquis pa-
              <lb/>
            rallelogram nis illis in directum exiſtentibus, ad omnia quadrata por.
              <lb/>
            </s>
            <s xml:id="echoid-s5768" xml:space="preserve">tionum, vel fruſtorum eorundem, ſimul cumrectangulis bis ſub ijſdem,
              <lb/>
            & </s>
            <s xml:id="echoid-s5769" xml:space="preserve">ſub quadrilineis illis in directum iacentibus, veluti fuerunt quadri-
              <lb/>
            lineun, MTXC, TGEOX, eſſe, vt dicta parallelogramma ad di-
              <lb/>
            ctas portiones, vel portionum fruſta; </s>
            <s xml:id="echoid-s5770" xml:space="preserve">quodex prædictis clarè patet; </s>
            <s xml:id="echoid-s5771" xml:space="preserve">
              <lb/>
            Vnde ex. </s>
            <s xml:id="echoid-s5772" xml:space="preserve">g. </s>
            <s xml:id="echoid-s5773" xml:space="preserve">omnia quadrata, RG, ſimul cum rectangulis bis ſub paral-
              <lb/>
            lelogrammis, RG, GX, ad omnia quadrata fruſti, SBGT, cum re-
              <lb/>
            ctangulis bis ſub, SGBT, & </s>
            <s xml:id="echoid-s5774" xml:space="preserve">quadrilineo, TG, PX, erunt vt paral-
              <lb/>
            lelogrammum, RG, ad fruſtum, SBGT, hoc .</s>
            <s xml:id="echoid-s5775" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5776" xml:space="preserve">pariter oſtendetur,
              <lb/>
            veluti probatum eſt omnia quadrata, HV, ſimul cum rectangulis bis
              <lb/>
            ſub, HV, VC, ad omnia quadrata portionis, SMT, ſimul cum re-
              <lb/>
            ctingulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5777" xml:space="preserve">ſub quadrilineo, MTXC, eſſe vt, HV,
              <lb/>
            ad portionem, SMT, vnde manifeſtum eſt, quod in hoc Corollaris
              <lb/>
            colligitur.</s>
            <s xml:id="echoid-s5778" xml:space="preserve"/>
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        <div xml:id="echoid-div574" type="section" level="1" n="340">
          <head xml:id="echoid-head357" xml:space="preserve">THEOREMA XX. PROPOS. XXI.</head>
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            <s xml:id="echoid-s5779" xml:space="preserve">SIin circulo, vel ellipſi apteturrecta linea, per cuius ex-
              <lb/>
            trema puncta ducantur duæ rectæ lineæ, quæ ſint (exi-
              <lb/>
            ſtente apta parallela vniaxium, vel diametrorum) paralle-
              <lb/>
            læ ſecundo axi, vel diametro, quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s5780" xml:space="preserve">Re-
              <lb/>
            ctangula ſub portione minori abſciſſa per aptatam, & </s>
            <s xml:id="echoid-s5781" xml:space="preserve">ſub
              <lb/>
            quadrilineo, quodaptata, & </s>
            <s xml:id="echoid-s5782" xml:space="preserve">duabus dictis parallelis vſque
              <lb/>
            ad curuam circuli, vel ellipſis productis, & </s>
            <s xml:id="echoid-s5783" xml:space="preserve">ab ijſdem inclu-
              <lb/>
            ſa curua comprehenditur, in circulo, erunt æqualia rectan-
              <lb/>
            gulis ſub duobus triangulis per diametrum quadrati, vel
              <lb/>
            rhombi (& </s>
            <s xml:id="echoid-s5784" xml:space="preserve">hoc in ellipſicum diametri coniugatę ſe obliquę
              <lb/>
            ſecabunt, quibus latera dictirhombi ſint æquidiſtantia) </s>
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