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

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          <p>
            <s xml:id="echoid-s2729" xml:space="preserve">
              <pb o="115" file="0135" n="135" rhead="LIBER II."/>
            go prima ad ſecundam erit, vt tertia ad quartam, ſcilicet figura ſo-
              <lb/>
              <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">Def. Qui.
                <lb/>
              5. Elem.</note>
            lida, A, ad figuram ſolidam, D, erit vt omnia plana, A, ad om-
              <lb/>
            nia plana, D, cum quibuſuis regulis aſſumpta, quod & </s>
            <s xml:id="echoid-s2730" xml:space="preserve">in figuris ſo-
              <lb/>
            lidis oſtendere opus erat.</s>
            <s xml:id="echoid-s2731" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div281" type="section" level="1" n="178">
          <head xml:id="echoid-head193" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2732" xml:space="preserve">_L_Iquet ex hoc, quod, vt inueniamus, quam rationem habeant inter
              <lb/>
            ſe duæ figuræ planæ, vel ſolidæ, ſuſſiciet nobis reperire, quam, in
              <lb/>
            figuris planis, inter ſe rationem habeant earundem omnes lineæ, &</s>
            <s xml:id="echoid-s2733" xml:space="preserve">, in
              <lb/>
            figuris ſolidis, earundem omnia plana iuxta quamuis regulam aſſumpta,
              <lb/>
            quod nouæ huius meæ Geometriæ veluti maximum iacio fundamentum,.</s>
            <s xml:id="echoid-s2734" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div282" type="section" level="1" n="179">
          <head xml:id="echoid-head194" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s2735" xml:space="preserve">SI duæ figuræ planæ, vel ſolidæ, in eadem altitudine fue-
              <lb/>
            rint conſtitutæ, ductis autem in planis rectis lineis, & </s>
            <s xml:id="echoid-s2736" xml:space="preserve">
              <lb/>
            in figuris ſolidis ductis planis vtcumque inter ſe parallelis,
              <lb/>
            quorum reſpectu prædicta ſumpta ſit altitudo, repertum fue-
              <lb/>
            rit ductarum linearum portiones figuris planis interceptas,
              <lb/>
            ſeu ductorum planorum portiones figuris ſolidis interceptas,
              <lb/>
            eſſe magnitudines proportionales, homologis in eadem figu-
              <lb/>
            ra ſemper exiſtentibus, dictæ figuræ erunt inter ſe, vt vnum
              <lb/>
            quodlibet eorum antecedentium, ad ſuum conſequens in a-
              <lb/>
            lia figura eidem correſpondens.</s>
            <s xml:id="echoid-s2737" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2738" xml:space="preserve">Sint primò duæ figurę planæ in eadem altitudine conſtitutæ, CA
              <lb/>
            M, CME, in quibus duæ vtcunque rectæ lineæ inuicem parallelæ
              <lb/>
            ductæ intelligantur, AE, BD, reſpectu quarum communis altitu-
              <lb/>
              <figure xlink:label="fig-0135-01" xlink:href="fig-0135-01a" number="75">
                <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0135-01"/>
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            do aſſumpta intelligatur, ſint au-
              <lb/>
            tem portiones figuris interceptæ
              <lb/>
            ipſæ, AM, BR, in fig. </s>
            <s xml:id="echoid-s2739" xml:space="preserve">CAM,
              <lb/>
            &</s>
            <s xml:id="echoid-s2740" xml:space="preserve">, ME, RD, in fig. </s>
            <s xml:id="echoid-s2741" xml:space="preserve">CME,
              <lb/>
            reperiatur autem, vt, AM, ad,
              <lb/>
            ME, ita eſſe, BR, ad, RD.
              <lb/>
            </s>
            <s xml:id="echoid-s2742" xml:space="preserve">Dico figu am, CAM, ad figu-
              <lb/>
            ram, CME, eſſe vt, AM, ad,
              <lb/>
            ME, vel, BR, ad, RD, quoniam enim, BD, AE, vtcumq; </s>
            <s xml:id="echoid-s2743" xml:space="preserve">du-
              <lb/>
            ctæ ſunt inter ſe æquidiſtantes, patet, quod quęlibet earum, quę di-
              <lb/>
            cuntur omnes lineæ figuræ, CAM, ſumptæ regula altera </s>
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