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

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            <s xml:id="echoid-s4941" xml:space="preserve">
              <pb o="201" file="0221" n="221" rhead="LIBER III."/>
            ad rectangulum ſub, BM, &</s>
            <s xml:id="echoid-s4942" xml:space="preserve">, MOA, quod verum eſſe oſtendetur,
              <lb/>
            vt in antecedente, etiam ſi parallelogrammum, DN, non ſit circa
              <lb/>
            axim, vel diametrum, BM, vnde patet, &</s>
            <s xml:id="echoid-s4943" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4944" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div503" type="section" level="1" n="303">
          <head xml:id="echoid-head320" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s4945" xml:space="preserve">SI intra circulum, velellipſim, duæ ad axim, vel diame-
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            trum ordinatim applicentur rectæ lineę, ſit autem paral-
              <lb/>
            lelogrammum, & </s>
            <s xml:id="echoid-s4946" xml:space="preserve">triangulum in eadem altitudine cum por-
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            tione inter applicatas concluſa, ſed in baſi altera applicata-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s4947" xml:space="preserve">Omnia quadrata dicti parallelogrammia ad omnia qua-
              <lb/>
            drata concluſę portionis (regula baſi) erunt, vt rectangulum
              <lb/>
            ſub partibus axis, vel diametri per baſim conſtitutis ad re-
              <lb/>
            ctangulum ſub abſciſſa per baſim ab extremitate axis, vel
              <lb/>
            diametri, & </s>
            <s xml:id="echoid-s4948" xml:space="preserve">ſub compoſita ex medietate portionis axis, vel
              <lb/>
            diametri eiſdem applicatis intermedię, & </s>
            <s xml:id="echoid-s4949" xml:space="preserve">abſciſſa per aliam
              <lb/>
            applicatam ab eiuſdem extremitate, vna cum rectangulo ſub
              <lb/>
            eadem intermedia, & </s>
            <s xml:id="echoid-s4950" xml:space="preserve">ſub compoſita ex, @, eiuſdem, &</s>
            <s xml:id="echoid-s4951" xml:space="preserve">, {1/2}, ab-
              <lb/>
            ſciſſæ per eandem applicatam ab eiuſdem extremitate: </s>
            <s xml:id="echoid-s4952" xml:space="preserve">Om-
              <lb/>
            nia verò quadrata incluſę portionis ad omnia quadrata dicti
              <lb/>
            trianguli erunt, vt rectangulum ſub compoſita ex abſciſſis ab
              <lb/>
            axi, vel diametro per ordinatim applicatas verſus terminum,
              <lb/>
            cui baſis propinquior eſt, & </s>
            <s xml:id="echoid-s4953" xml:space="preserve">ſub ſexquialtera abſciſſæ ab alio
              <lb/>
            extremo per applicatam, quę non eſt baſis, vna cum rectan-
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            gulo ſub huius reliqua, & </s>
            <s xml:id="echoid-s4954" xml:space="preserve">ſub dupla abſciſſę per baſim ab ex-
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            tremo, cui ipſa baſis propinquior eſt, ad rectangulum ſub
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            partibus axis, vel diametri per baſim conſtitutis.</s>
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            <s xml:id="echoid-s4956" xml:space="preserve">Sit ergo circulus, velellipſis, ACDF,
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                <image file="0221-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0221-01"/>
              </figure>
            centrum, O, axis, vel diameter, AD, duæ
              <lb/>
            ad ipſam ordinatim applicatæ ſint, IS, C
              <lb/>
            F, intercipientes portionem, ICFS, ſit
              <lb/>
            autem parallelogrammum, BF, in baſi
              <lb/>
            vtrauis applicatarum, vt in, CF, & </s>
            <s xml:id="echoid-s4957" xml:space="preserve">eadem
              <lb/>
            altitudine cum fruſto, CISF, ſit etiam
              <lb/>
            nunc circa axim, vel diametrum, MR, re-
              <lb/>
            gula verò, CF; </s>
            <s xml:id="echoid-s4958" xml:space="preserve">Dico ergo omnia quadra-
              <lb/>
            ta parallelogrammi, BF, ad omnia qua-
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            drata portionis, ICFS, eſſe vt rectangulum, DRA, ad </s>
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