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

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        <div xml:id="echoid-div1202" type="section" level="1" n="720">
          <pb o="523" file="0543" n="543" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1203" type="section" level="1" n="721">
          <head xml:id="echoid-head754" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s13491" xml:space="preserve">SImiliter ſi compleautur parallelogramma, PC, CR, CO, ſolidum
              <lb/>
            rectangulum ſub, RC, CP, ſeu ſub, OC, CP, contentum, quod eſt
              <lb/>
            parallelepipedum, triplum erit contenti ſub triangulis prædictis ideſt
              <lb/>
            pyramidis, AEC. </s>
            <s xml:id="echoid-s13492" xml:space="preserve">Contentum verò ſub parallelogrammis, TC, &</s>
            <s xml:id="echoid-s13493" xml:space="preserve">, C
              <lb/>
            X, ad contentum ſub dictis trapezijs hoc eſt ad fruſtum pyramidis, GE
              <lb/>
            CI, erit vt quadratum, BC, rectangulum ſub, XI, IM, vna cum {1/3}. </s>
            <s xml:id="echoid-s13494" xml:space="preserve">qua.
              <lb/>
            </s>
            <s xml:id="echoid-s13495" xml:space="preserve">
              <note position="right" xlink:label="note-0543-01" xlink:href="note-0543-01a" xml:space="preserve">_10.huius._</note>
            drat. </s>
            <s xml:id="echoid-s13496" xml:space="preserve">XM, retentis ſemper ijſdem reg. </s>
            <s xml:id="echoid-s13497" xml:space="preserve">BC, CF. </s>
            <s xml:id="echoid-s13498" xml:space="preserve">Hæc autem V
              <unsure/>
            era ſunt
              <lb/>
            ſiue latus, AC, ſit commune præfatis triangulis, ſeu parallelogram -
              <lb/>
            mis, ſiue non, ac ſine latus, IC, ſit cõmune predictis trapezijs, ſeu paral
              <lb/>
            lelogrammis, ſiue nõvt facilè intuenti innoteſcet.</s>
            <s xml:id="echoid-s13499" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1205" type="section" level="1" n="722">
          <head xml:id="echoid-head755" xml:space="preserve">COROLLARIVM III.</head>
          <p style="it">
            <s xml:id="echoid-s13500" xml:space="preserve">_P_Atet vltimo ſolida rectangula ſub dictis triangulis, regulis iam
              <lb/>
            dictis, contenta, ſe babereinter ſe, vt ipſæ pyramides, nempè
              <lb/>
            æquè alta eſſe in pro portione baſium, & </s>
            <s xml:id="echoid-s13501" xml:space="preserve">in eadem, vel æqualiqus ba-
              <lb/>
            ſibus exiſtentia eſſe in proportione altitudinem reſpectu baſium aſſum-
              <lb/>
            ptarum, quod eſt ſimile illi, quod animaduerſum eſt in Cor. </s>
            <s xml:id="echoid-s13502" xml:space="preserve">I. </s>
            <s xml:id="echoid-s13503" xml:space="preserve">& </s>
            <s xml:id="echoid-s13504" xml:space="preserve">2,
              <lb/>
            prop. </s>
            <s xml:id="echoid-s13505" xml:space="preserve">ant. </s>
            <s xml:id="echoid-s13506" xml:space="preserve">circa parallelogramma ſolida rectangula continentia.</s>
            <s xml:id="echoid-s13507" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1206" type="section" level="1" n="723">
          <head xml:id="echoid-head756" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13508" xml:space="preserve">ADuerte autem cum ſolidum rectangulum fuerit quadratum,
              <lb/>
            tunc vnam ſufficere exponi figuram, vt ex. </s>
            <s xml:id="echoid-s13509" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13510" xml:space="preserve">triangulum, A
              <lb/>
            BC, quod tunc æquipollet duobus expoſitis, ABC, ACD; </s>
            <s xml:id="echoid-s13511" xml:space="preserve">& </s>
            <s xml:id="echoid-s13512" xml:space="preserve">con-
              <lb/>
            tentum ſolidum ſub, ABC, ACD, tunc etiam dicimus quadratum
              <lb/>
            ſolidum ipſius, ABC, regulis, BC, CF, hæc autem planarum figu-
              <lb/>
            rarum quadrata ſolida mentaliter quoque vt plurimum deſcripta
              <lb/>
            eſſe intelligemus, vt etiam ſuperius animaduerſum fuit. </s>
            <s xml:id="echoid-s13513" xml:space="preserve">His au-
              <lb/>
            tem præpoſitis, nunc illa ſubiungemus, quæ aſſimilantur Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s13514" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s13515" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s13516" xml:space="preserve">ac iuxta methodum indiuiſibilium lib. </s>
            <s xml:id="echoid-s13517" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13518" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s13519" xml:space="preserve">23. </s>
            <s xml:id="echoid-s13520" xml:space="preserve">oſtẽ-
              <lb/>
            ſa fuere.</s>
            <s xml:id="echoid-s13521" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1207" type="section" level="1" n="724">
          <head xml:id="echoid-head757" xml:space="preserve">THEOREMA XV. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s13522" xml:space="preserve">SI duæ expoſitæ fuerint ſuperficies ſolidum rectangulũ
              <lb/>
            iuxta datas regulas continentes, altera autem earum
              <lb/>
            fuerit in quotcunq; </s>
            <s xml:id="echoid-s13523" xml:space="preserve">partes diuiſa per lineas ſecantes quaſ-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s13524" xml:space="preserve">ſuæ regulæ intra dictam ſuperficiem parallelas, </s>
          </p>
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