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

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        <div xml:id="echoid-div242" type="section" level="1" n="157">
          <pb o="101" file="0121" n="121" rhead="LIBER II."/>
        </div>
        <div xml:id="echoid-div244" type="section" level="1" n="158">
          <head xml:id="echoid-head171" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2454" xml:space="preserve">_E_X hoc habetur ſingula puncta recti tranſitus, vel obliqui, inciden-
              <lb/>
            tis lineæ, nedum eſſe communes ſectiones illius, & </s>
            <s xml:id="echoid-s2455" xml:space="preserve">ſingulorum,
              <lb/>
            quæ collecta dicuntur, omnia plana propoſiti ſolidi, ſed etiam, ſi per
              <lb/>
            talem incidentem extendatur planum, eſſe communes ſectiones illius,
              <lb/>
            & </s>
            <s xml:id="echoid-s2456" xml:space="preserve">ſingularum, quæ collectæ dicuntur : </s>
            <s xml:id="echoid-s2457" xml:space="preserve">Omnes lineæ planæ figuræ, cuius
              <lb/>
            oppoſitætangentes ſunt communes ſectiones plani eiuſdem figuræ, & </s>
            <s xml:id="echoid-s2458" xml:space="preserve">
              <lb/>
            oppoſitarum tangentium dicti ſolidi : </s>
            <s xml:id="echoid-s2459" xml:space="preserve">nam motum planum deſignat in
              <lb/>
            plano ſecante rectam lineam, & </s>
            <s xml:id="echoid-s2460" xml:space="preserve">inſimul punctum in ineidente, quod
              <lb/>
            reperitur in illa recta linea, & </s>
            <s xml:id="echoid-s2461" xml:space="preserve">ideò idem punctum eſt communis ſectio
              <lb/>
            tum moti plani & </s>
            <s xml:id="echoid-s2462" xml:space="preserve">rectæ incidentis, tum vnius earum, quæ dicuntur om-
              <lb/>
            nes lineæ datæ figuræ planæ (ita tamen productæ, vt hanc incidentem ſe-
              <lb/>
            care poſſint) & </s>
            <s xml:id="echoid-s2463" xml:space="preserve">eiuſdem incidentis.</s>
            <s xml:id="echoid-s2464" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div245" type="section" level="1" n="159">
          <head xml:id="echoid-head172" xml:space="preserve">IV.</head>
          <p>
            <s xml:id="echoid-s2465" xml:space="preserve">SI inter alterum extremorum punctorum propoſitæ rectæ
              <lb/>
            lineæ, & </s>
            <s xml:id="echoid-s2466" xml:space="preserve">ſingula puncta, quæ ſimul collecta dicuntur
              <lb/>
            omnia puncta recti, veleiuſdem obliqui tranſitus eiuſdem,
              <lb/>
            fumamus interiacentes lineas, dicantur iſtæ ſimul collectæ:
              <lb/>
            </s>
            <s xml:id="echoid-s2467" xml:space="preserve">Omnes abſciſſæ propoſitæ lineæ, quas (etiam ſi non expri-
              <lb/>
            matur) vocari ſupponemus recti tranſitus, ſi puncta ſint recti
              <lb/>
            tranſitus, vel eiuſdem obliqui tranſitus, ſi puncta ſint eiu-
              <lb/>
            ſdem obliqui tranſitus.</s>
            <s xml:id="echoid-s2468" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div246" type="section" level="1" n="160">
          <head xml:id="echoid-head173" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s2469" xml:space="preserve">REctæ lineæ verò in antecedentis deſinitionis propoſita
              <lb/>
            linea inter eadem puncta, & </s>
            <s xml:id="echoid-s2470" xml:space="preserve">reliquum extremorum in-
              <lb/>
            teria centes, dicentur: </s>
            <s xml:id="echoid-s2471" xml:space="preserve">Reſiduæ omnium abſciſſarum propo-
              <lb/>
            ſitæ lineæ recti tranſitus, ſi puncta ſint rectitranſitus, vel eiu-
              <lb/>
            idem obliquitranſitus, ſi ſumpta puncta ſint eiuſdem obliqui
              <lb/>
            tranſitus.</s>
            <s xml:id="echoid-s2472" xml:space="preserve"/>
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