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

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        <div xml:id="echoid-div68" type="section" level="1" n="54">
          <p>
            <s xml:id="echoid-s572" xml:space="preserve">
              <pb o="17" file="0037" n="37" rhead="LIBER I."/>
            tium, ACBD, AB, CD, & </s>
            <s xml:id="echoid-s573" xml:space="preserve">producantur donec ſibi occurrant, oc-
              <lb/>
            current autem, quia hæc planis ſe inuicem ſecantibus ſunt parallela,
              <lb/>
            & </s>
            <s xml:id="echoid-s574" xml:space="preserve">ſit ab illis comprehenſum ſolidum, ZF, erit igitur, ZF, paralle-
              <lb/>
            ſepipedum, cum eius oppoſita plana ſint inuicem parallela, quæ tan-
              <lb/>
            gunt ſolidum, ACBD, vt in punctis, A, C, B, D, E, X, & </s>
            <s xml:id="echoid-s575" xml:space="preserve">ideò
              <lb/>
            erit ſolido, ACBD, circumſcriptum, habens plana oppoſita pro-
              <lb/>
              <note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">Def. 15.</note>
            poſitis planis ſe ſecantibus parallela; </s>
            <s xml:id="echoid-s576" xml:space="preserve">quod efficere opus erat.</s>
            <s xml:id="echoid-s577" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div70" type="section" level="1" n="55">
          <head xml:id="echoid-head66" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s578" xml:space="preserve">_P_Oteſt autem contingere in antecedentis Propoſ. </s>
            <s xml:id="echoid-s579" xml:space="preserve">figura ipſam eſſepa-
              <lb/>
            railelogrammum, & </s>
            <s xml:id="echoid-s580" xml:space="preserve">line as rectas ſe ſecantes, qutbus parallelo-
              <lb/>
            grammi circumſcriptibilis latera debent eſſe parallela, eſſe ipſa paralle-
              <lb/>
            logrammi latera, in quo caſu idem eſſet parallelogrammum circumſcri-
              <lb/>
            ptum, & </s>
            <s xml:id="echoid-s581" xml:space="preserve">cui circumſcriberetur: </s>
            <s xml:id="echoid-s582" xml:space="preserve">V eluti hic etiam ſi ſolidum, ACBD,
              <lb/>
            eſſet parallelepipedum, cuius oppoſitis planis, plana circum ſcrip tibilis
              <lb/>
            deberent eſſe pacallela, tunc enim idem eſſet parallelepipedum circum-
              <lb/>
            ſcriptum, & </s>
            <s xml:id="echoid-s583" xml:space="preserve">cui cir cumſcriberetur: </s>
            <s xml:id="echoid-s584" xml:space="preserve">Contactus autem in antecedenti po-
              <lb/>
            teſt etiam eſſe in linea, & </s>
            <s xml:id="echoid-s585" xml:space="preserve">in bac tum in linea, tum in planis, licet con-
              <lb/>
            tactus, qui fit in punctis tantum expoſitus fuerit.</s>
            <s xml:id="echoid-s586" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div71" type="section" level="1" n="56">
          <head xml:id="echoid-head67" xml:space="preserve">THEOREMA I. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s587" xml:space="preserve">DAta quacumq; </s>
            <s xml:id="echoid-s588" xml:space="preserve">figura plana, vel ſolida, & </s>
            <s xml:id="echoid-s589" xml:space="preserve">in plana da-
              <lb/>
            ta recta linea, in ſolida verò dato plano; </s>
            <s xml:id="echoid-s590" xml:space="preserve">qualibet li-
              <lb/>
            nea, vel planum, quod indefinitè productum non tangat fi-
              <lb/>
            guram dictam planam, vel ſolidam, in vertice ſumpto reſpe-
              <lb/>
            ctu dictæ lineæ, vel plani, vel totum extra, vel aliquid eius
              <lb/>
            intra figuram cadit, nempè figuram ſecat, ſi linea lineæ, vel
              <lb/>
            planum plano æquidiſtet.</s>
            <s xml:id="echoid-s591" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s592" xml:space="preserve">Sit data figura plana, CARB,
              <lb/>
              <figure xlink:label="fig-0037-01" xlink:href="fig-0037-01a" number="12">
                <image file="0037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0037-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s593" xml:space="preserve">in ea recta, AB, ſit vertex vnus
              <lb/>
            reſpectuipſius, AB, punctus, C,
              <lb/>
            & </s>
            <s xml:id="echoid-s594" xml:space="preserve">ſit recta, HM, parallela ipſi,
              <lb/>
            AB, quæ etiam indefinitè produ-
              <lb/>
            cta non tangat figuram, ARBC,
              <lb/>
            in, C, vertice. </s>
            <s xml:id="echoid-s595" xml:space="preserve">Dico, HM, vel
              <lb/>
            totam extra figuram cadere, vel
              <lb/>
            eandem ſecare. </s>
            <s xml:id="echoid-s596" xml:space="preserve">Neutrum efficiat
              <lb/>
            ſi poſſibile eſt, igitur, HM, tan-
              <lb/>
            get figuram, CARB, & </s>
            <s xml:id="echoid-s597" xml:space="preserve">non in,
              <lb/>
            C, igitur in alio puncto, vt in, E,
              <lb/>
            igitur, E, erit vertex figuræ, CA
              <lb/>
            RB, reſpectu ipſius, AB, eſt e-
              <lb/>
              <note position="right" xlink:label="note-0037-02" xlink:href="note-0037-02a" xml:space="preserve">A. Def. @
                <lb/>
              huius.</note>
            tiam, C, vertēx eiuſdem reſpectu eiuſdem, AB, ergo ſi per, </s>
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