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

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            <s xml:id="echoid-s13738" xml:space="preserve">
              <pb o="531" file="0551" n="551" rhead="LIBER VII."/>
            gulum ſolidum ſub trapezijs, ADEC, CESR, erit vt rectan-
              <lb/>
            gulum, DES, ad rectangulum ſub, DE, & </s>
            <s xml:id="echoid-s13739" xml:space="preserve">compoſita ex, SF,
              <lb/>
            & </s>
            <s xml:id="echoid-s13740" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13741" xml:space="preserve">FE, vna cum rectangulo ſub, EF, & </s>
            <s xml:id="echoid-s13742" xml:space="preserve">compoſita ex {1/6}. </s>
            <s xml:id="echoid-s13743" xml:space="preserve">E
              <lb/>
            F, & </s>
            <s xml:id="echoid-s13744" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13745" xml:space="preserve">FS.</s>
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          <p>
            <s xml:id="echoid-s13747" xml:space="preserve">Hæc etiam vt antecedentes abſoluetur.</s>
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        <div xml:id="echoid-div1228" type="section" level="1" n="741">
          <head xml:id="echoid-head774" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13749" xml:space="preserve">HVcuſq; </s>
            <s xml:id="echoid-s13750" xml:space="preserve">Propoſitionibus Lib. </s>
            <s xml:id="echoid-s13751" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13752" xml:space="preserve">quæ reſtauratione indigere
              <lb/>
            videbantur ſatisfactum eſſe manifeſto apparet. </s>
            <s xml:id="echoid-s13753" xml:space="preserve">Reliquum
              <lb/>
            eſt, vt & </s>
            <s xml:id="echoid-s13754" xml:space="preserve">ſequentium Librarum Propoſitiones denuò perpenden-
              <lb/>
            tes, per hanc nouam methodum à nobis quoq; </s>
            <s xml:id="echoid-s13755" xml:space="preserve">& </s>
            <s xml:id="echoid-s13756" xml:space="preserve">ipſæ reſtauren-
              <lb/>
            tur, quod maiori, qua fieri poterit, breuitate, ac facilitate, nunc
              <lb/>
            præſtare conabimur.</s>
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        <div xml:id="echoid-div1229" type="section" level="1" n="742">
          <head xml:id="echoid-head775" xml:space="preserve">THEOREMA XX. PROPOS. XX.</head>
          <p>
            <s xml:id="echoid-s13758" xml:space="preserve">ASſumpto ex Schemate Prop. </s>
            <s xml:id="echoid-s13759" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13760" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s13761" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13762" xml:space="preserve">ſemicircolo,
              <lb/>
            vel ſemiellipſi, EPR, circa diametrum, ER, ſimul cũ
              <lb/>
            applicata, BP, quæ etiam ſit regula, & </s>
            <s xml:id="echoid-s13763" xml:space="preserve">parallelogrammo, H
              <lb/>
            B, iuxta quemlibet trium ibi allatorum caſuum nunc oſten-
              <lb/>
            demus, conſpecta etiam illa figura, quadratum ſolidum
              <lb/>
            portionis, DEP, ad quadratum ſolidum parallelogrammi,
              <lb/>
            FP, eſſe vt compoſita ex {1/6}. </s>
            <s xml:id="echoid-s13764" xml:space="preserve">EB, & </s>
            <s xml:id="echoid-s13765" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13766" xml:space="preserve">BR, ad ipſam, BR.</s>
            <s xml:id="echoid-s13767" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13768" xml:space="preserve">Producantur enim indefinitè verius, B, E, ipſę, PB, HE, & </s>
            <s xml:id="echoid-s13769" xml:space="preserve">fiant,
              <lb/>
            B℟, EG, ſingulæ æquales ipſi, RE, & </s>
            <s xml:id="echoid-s13770" xml:space="preserve">iungantur, G℟, capiaturq;
              <lb/>
            </s>
            <s xml:id="echoid-s13771" xml:space="preserve">BX, æqualis ipſi, BE, & </s>
            <s xml:id="echoid-s13772" xml:space="preserve">per, X, agatur, XL, parallela, ER, & </s>
            <s xml:id="echoid-s13773" xml:space="preserve">iun-
              <lb/>
            gatur, XE, ac ſit quæcumque, CN, applicata in ſemiportione, EP
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            B, quæ producatur indefinitè
              <lb/>
            hinc inde vt ſecet, HP, vt in, M,
              <lb/>
            EX, vt in, D, LX, vt in, Z, & </s>
            <s xml:id="echoid-s13774" xml:space="preserve">G℟,
              <lb/>
            vt in, Q; </s>
            <s xml:id="echoid-s13775" xml:space="preserve">ſunt ergo, GB, LB, G
              <lb/>
            X, parallelogramma, &</s>
            <s xml:id="echoid-s13776" xml:space="preserve">, ℟X, eſt
              <lb/>
            æqualis, RB, XB, autem ipſi, B
              <lb/>
            E, vnderectangulum, ℟XB, eſt
              <lb/>
            æquale rectangulo, RBE, hoc
              <lb/>
            eſt, in circulo quadrato, BP: </s>
            <s xml:id="echoid-s13777" xml:space="preserve">ea-
              <lb/>
            dem ratione oſtendemus tum rectangulum, QZC, æquari quadra-
              <lb/>
            to, CM, tum rectangulnm, QDC, æquari quadrato, CN, & </s>
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