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

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            <s xml:id="echoid-s3506" xml:space="preserve">
              <pb o="148" file="0168" n="168" rhead="GEOMETRIÆ"/>
            ipſi, FD, quæ eſi vna maximarum abſciſſarum ipſius, FD, vnde hac via
              <lb/>
            colligemus omnes lineas trianguli, FCD, regula, CD, dum latus, FD,
              <lb/>
            æquatur ipſi, DC, eſſe æquales omnibus abſciſſis ipſius, FD; </s>
            <s xml:id="echoid-s3507" xml:space="preserve">& </s>
            <s xml:id="echoid-s3508" xml:space="preserve">omnes
              <lb/>
              <note position="left" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">_Defin. 4._
                <lb/>
              _huius._</note>
            lineas trianguli, AFC, eſſe æquales reſiduis omnium abſciſſarum, FD,
              <lb/>
              <note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">_Defin. 5._
                <lb/>
              _huius._</note>
            & </s>
            <s xml:id="echoid-s3509" xml:space="preserve">omnes lineas par allelogrammi. </s>
            <s xml:id="echoid-s3510" xml:space="preserve">AD, æquari maximis abſciſſarum,
              <lb/>
            FD, quæ dicuntur eiuſdem obliqui tranſitus, ſi angulus, CDF, non ſit
              <lb/>
              <note position="left" xlink:label="note-0168-03" xlink:href="note-0168-03a" xml:space="preserve">_Defin. 6._
                <lb/>
              _huius._</note>
            rectus, & </s>
            <s xml:id="echoid-s3511" xml:space="preserve">rectitranſitus, ſi ſit rectus; </s>
            <s xml:id="echoid-s3512" xml:space="preserve">vnde ſicuti oſtendimus, paralle,
              <lb/>
            logrammum, AD, duplum eſſe trianguli, FCD, vel, ACF, & </s>
            <s xml:id="echoid-s3513" xml:space="preserve">ſubin-
              <lb/>
            de etiam omnes lineas, AD, regula CD duplas eſſe omnium linearum
              <lb/>
            trianguli, FCD, vel, ACF, ſic etiam vt demonſtratum recipi potest
              <lb/>
              <note position="left" xlink:label="note-0168-04" xlink:href="note-0168-04a" xml:space="preserve">_3. huius._</note>
            propoſitæ linearectæ, vt ipſius, FD, vtcunque, maximas abſciſſarum,
              <lb/>
            duplas eſſe omnium abſciſſarum eiuſdem, vel reſiduarum omnium abſciſ-
              <lb/>
            ſarum, vnde & </s>
            <s xml:id="echoid-s3514" xml:space="preserve">omnes abſctſſas patebit æquari reſiduis omnium abſciſ-
              <lb/>
            ſarum eiuſdem lineæ, ijs vel recti, vel eiuſdem obliqui tranſitus ſumptis,
              <lb/>
            quæ ad ſequentium intelligentiam diligenter ſunt adnotanda.</s>
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          </p>
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        <div xml:id="echoid-div365" type="section" level="1" n="222">
          <head xml:id="echoid-head237" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s3516" xml:space="preserve">SIt magnitudo, A, ad quotcunque magnitudines, E, O, ſingil-
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            latim ad vnamquamque, vt magnitudo, V, ad tot alias, P, S,
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              <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a" number="97">
                <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0168-01"/>
              </figure>
            ſingillatim ad vnamquamq; </s>
            <s xml:id="echoid-s3517" xml:space="preserve">nempè ſit, A, ad, E,
              <lb/>
            vt, V, ad, P; </s>
            <s xml:id="echoid-s3518" xml:space="preserve">A, ad, O, vt, V, ad, S. </s>
            <s xml:id="echoid-s3519" xml:space="preserve">Dico, A,
              <lb/>
            ad, E, O, ſimul eſſe, vt, V, ad, P, S, ſimul iun-
              <lb/>
            ctas. </s>
            <s xml:id="echoid-s3520" xml:space="preserve">Etenim conuertendo erit prima, E, ad ſecun-
              <lb/>
            dam, A, vttertia, P, ad quartam, V, ſed etiam
              <lb/>
            conuertendo quinta, O, eſt ad ſecundam, A, vt
              <lb/>
              <note position="left" xlink:label="note-0168-05" xlink:href="note-0168-05a" xml:space="preserve">24. Quin.
                <lb/>
              Elem.</note>
            ſexta, S, ad quartam, V, ergo compoſita ex prima,
              <lb/>
            E, & </s>
            <s xml:id="echoid-s3521" xml:space="preserve">quinta, O, erit ad ſecundam, A, vt compo-
              <lb/>
            ſita ex tertia, P, & </s>
            <s xml:id="echoid-s3522" xml:space="preserve">ſexta, S, ad quartam, V, ergo
              <lb/>
            conuertendo, A, ad, EO, ſimul erit, vt, V, ad, P,
              <lb/>
              <note position="left" xlink:label="note-0168-06" xlink:href="note-0168-06a" xml:space="preserve">Defin. 13.
                <lb/>
              huius.</note>
            S, ſimul iunctas, qui arguendi modus dicitur à me,
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            colligere, ſeu colligendo.</s>
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        <div xml:id="echoid-div367" type="section" level="1" n="223">
          <head xml:id="echoid-head238" xml:space="preserve">THE OREMA XX. PROPOS. XX.</head>
          <p>
            <s xml:id="echoid-s3524" xml:space="preserve">ASſumpta Propoſ. </s>
            <s xml:id="echoid-s3525" xml:space="preserve">antecedentis figura, dimiſſa, BM, re-
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            tineatur, NE, pro vna ex ductis vtcunque parallela
              <lb/>
            ipſi, CD, producta autem, CD, vtcunque in, M, comple-
              <lb/>
            toque parallelogrammo, OD. </s>
            <s xml:id="echoid-s3526" xml:space="preserve">Dico parallelogrammum, A
              <lb/>
            M, ad trapezium, FCMO, eſſe vt, CM, ad, MD, ſimul
              <lb/>
            cum {1/2}, CD.</s>
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