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

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        <div xml:id="echoid-div1141" type="section" level="1" n="684">
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            <s xml:id="echoid-s12578" xml:space="preserve">
              <pb o="492" file="0512" n="512" rhead="GEOMETRIÆ"/>
            ſpatio, CQPD, maior erit ſpatio, HTYL, & </s>
            <s xml:id="echoid-s12579" xml:space="preserve">multò maior erit figu-
              <lb/>
            ra iam deſcripta, ab eodem ſpatio, HTYL, compi ehenſa, quod eſt
              <lb/>
              <note position="left" xlink:label="note-0512-01" xlink:href="note-0512-01a" xml:space="preserve">Ex antec.
                <lb/>
              Lem.</note>
            abſurdum, cum enim parallelogiammum, E&</s>
            <s xml:id="echoid-s12580" xml:space="preserve">, æquetur, OV, Ι℟,
              <lb/>
            ipſi, RX, necnon, NP, ipſi, SY, tota toti adæquator contra præ-
              <lb/>
            demonſtrata, nec ergo figura, HTYL, minor eſſe poteſt figura, C
              <lb/>
            QPD, ſed neque eadem maior, vt oſtenſum eſt, ergo eidem æqua-
              <lb/>
            lis etit, quod demonſtrare oportebat. </s>
            <s xml:id="echoid-s12581" xml:space="preserve">Vnamquamque autem di-
              <lb/>
            ctarum figurarum, CQPD, HTYL, pręfatas conditiones haben-
              <lb/>
            tium, figuram in alteram partem deficientem appellabimus, regu-
              <lb/>
            la baſi, ſeu quacunq; </s>
            <s xml:id="echoid-s12582" xml:space="preserve">illi ęquidiſtante.</s>
            <s xml:id="echoid-s12583" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1144" type="section" level="1" n="685">
          <head xml:id="echoid-head718" xml:space="preserve">LEMMA III.</head>
          <p>
            <s xml:id="echoid-s12584" xml:space="preserve">SI curua linea quæcunq; </s>
            <s xml:id="echoid-s12585" xml:space="preserve">tota ſit in eodem plano, cuioc-
              <lb/>
            currat recta in duobus punctis, aut rectis lineis, vel in
              <lb/>
            recta, & </s>
            <s xml:id="echoid-s12586" xml:space="preserve">puncto, poterimus aliam rectam lineam præfatæ
              <lb/>
            æquidiſtantem ducere, quæ tangat portionem curuæ lineæ
              <lb/>
            inter duos predictos occurſus continuatam.</s>
            <s xml:id="echoid-s12587" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1145" type="section" level="1" n="686">
          <head xml:id="echoid-head719" xml:space="preserve">DEFINITIO. +</head>
          <p style="it">
            <s xml:id="echoid-s12588" xml:space="preserve">_T_Angere autem dico rectam lineam aliam quamcunque curuam
              <lb/>
            totam in eodem plano cum ea exiſtantem, cum ipſa recta linea
              <lb/>
            ſiue in puncto, ſiue in recta linea, euruæ, occurrente, eadem curua vel
              <lb/>
            tota eſt ad eandem partem, vel illius nihil eſt ad alteram partem illi
              <lb/>
            occurrentis rectæ lineæ.</s>
            <s xml:id="echoid-s12589" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12590" xml:space="preserve">Sit curua linea, BAC, tota in eodem exiſtens plano, cui recta, B
              <lb/>
            C, occurrat in duobus punctis, ſeu rectis lineis, vel in recta, & </s>
            <s xml:id="echoid-s12591" xml:space="preserve">pun-
              <lb/>
              <figure xlink:label="fig-0512-01" xlink:href="fig-0512-01a" number="342">
                <image file="0512-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0512-01"/>
              </figure>
            cto, B, C. </s>
            <s xml:id="echoid-s12592" xml:space="preserve">Dico nos aliam rectam
              <lb/>
            ipſi, BC, æquidiſtantem ducere poſ-
              <lb/>
            ſe, quæ tangat portionem curuæ li-
              <lb/>
            neæ inter duos occurſus, B, C, con-
              <lb/>
            tinuatam. </s>
            <s xml:id="echoid-s12593" xml:space="preserve">Quoniam ergo recta eſt,
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s12594" xml:space="preserve">curua, BAC, ideò inter ſe ſpa-
              <lb/>
            tium comprehendent, figuramque,
              <lb/>
            vt, BAC, conſtituent, ergo poſſibi-
              <lb/>
            le erit figuræ, BAC, reſpectu rectæ, BC, verticem inuenire, ſit is
              <lb/>
              <note position="left" xlink:label="note-0512-02" xlink:href="note-0512-02a" xml:space="preserve">1. lib. 7.</note>
            punctum, A, per quod ducatur, DF, parallela, BC, igitur, BF, tan-
              <lb/>
            get figuram, BAC, ergo totus ambitus, BAC, eſt ad eandem </s>
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