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

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          <p>
            <s xml:id="echoid-s3121" xml:space="preserve">
              <pb o="132" file="0152" n="152" rhead="GEOMETRIÆ"/>
            vt figura tertiæ ad figuram quartæ. </s>
            <s xml:id="echoid-s3122" xml:space="preserve">Et ſi fuerint quatuor fi-
              <lb/>
            guræ planæ proportionales, ita vt quæ ſunt termini eiuſdem
              <lb/>
            proportionis ſint figuræ ſimiles, deſcriptæ ab eorundem li-
              <lb/>
            neis, vel lateribus homologis; </s>
            <s xml:id="echoid-s3123" xml:space="preserve">lineæ, vel latera homologa
              <lb/>
            deſcribentia erunt proportionalia.</s>
            <s xml:id="echoid-s3124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3125" xml:space="preserve">Sint quatuor rectæ lineæ proportionales, AB, CD, FG, HM,
              <lb/>
            prima verò, & </s>
            <s xml:id="echoid-s3126" xml:space="preserve">ſecunda deſcribant fig. </s>
            <s xml:id="echoid-s3127" xml:space="preserve">planas ſimiles, AXB, CVD,
              <lb/>
              <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a" number="89">
                <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0152-01"/>
              </figure>
            &</s>
            <s xml:id="echoid-s3128" xml:space="preserve">, FG, HM, ſimiles figuras pla-
              <lb/>
            nas, FOG, HNM, licet prędictis
              <lb/>
            diſſimiles eſſent, & </s>
            <s xml:id="echoid-s3129" xml:space="preserve">ſint deſcribentes
              <lb/>
            figurarum deſcriptarum lineæ, vel
              <lb/>
            latera homologa. </s>
            <s xml:id="echoid-s3130" xml:space="preserve">Dico, AXB, ad,
              <lb/>
            CVD, eſſe vt, FOG, ad, HNM.
              <lb/>
            </s>
            <s xml:id="echoid-s3131" xml:space="preserve">Sit, R, tertia proportionalis ipſa-
              <lb/>
            rum, AB, CD, &</s>
            <s xml:id="echoid-s3132" xml:space="preserve">, I, tertia pro-
              <lb/>
            portionalis ipſarum, FG, HM; </s>
            <s xml:id="echoid-s3133" xml:space="preserve">eſt
              <lb/>
            igitur, AXB, ad, CVD, vt, AB,
              <lb/>
            ad, R, .</s>
            <s xml:id="echoid-s3134" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">in ratione dupla eius, quam habet, AB, ad, CD, .</s>
            <s xml:id="echoid-s3136" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">eius,
              <lb/>
              <note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">Coroll. 2.
                <lb/>
              antec.</note>
            quam habet, FG, ad, HM, .</s>
            <s xml:id="echoid-s3138" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3139" xml:space="preserve">vt, FG, ad, I, quę eſt, vt, FOG,
              <lb/>
            ad, HNM, ergo vt, AXB, ad, CVD, ita erit, FOG, ad, H
              <lb/>
            NM.</s>
            <s xml:id="echoid-s3140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3141" xml:space="preserve">Sit nunc figura, AXB, ad, CVD, ſibi ſimilem, vt, FOG, ad,
              <lb/>
            HNM, ſibi ſimilem, licet iſtæ eſſent prædictis diſſimiles, & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">eas de-
              <lb/>
            ſcribentes ſint earum lineæ, vel latera homologa. </s>
            <s xml:id="echoid-s3143" xml:space="preserve">Dico, AB, ad,
              <lb/>
            CD, eſſe vt, FG, ad, HM, ſit adhuc, R, tertia proportionalis ip-
              <lb/>
            ſarum, AB, CD, &</s>
            <s xml:id="echoid-s3144" xml:space="preserve">, I, tertia proportionalis ipſarum, FG, HM,
              <lb/>
              <note position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              antec.</note>
            eſt ergo, vt figura, AXB, ad, CVD, ita, AB, ad, R, vt verò fi-
              <lb/>
            gura, FOG, ad, HNM, ita, FG, ad, I, eſt verò, vt, AXB, ad,
              <lb/>
            CVD, ita, FOG, ad, HNM, ergo vt, AB, ad, R, ſic, FG, ad,
              <lb/>
            I, eſtautem, AB, ad, R, dupla rationis ipſius, AB, ad, CD, &</s>
            <s xml:id="echoid-s3145" xml:space="preserve">,
              <lb/>
            FG, ad, I, dupla rationis ipſius, FG, ad, HM, ergo vt, AB, ad,
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            CD, ita, FG, ad, HM, quæ oſtendere opus erat.</s>
            <s xml:id="echoid-s3146" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div338" type="section" level="1" n="207">
          <head xml:id="echoid-head222" xml:space="preserve">SCHOLIV M.</head>
          <p style="it">
            <s xml:id="echoid-s3147" xml:space="preserve">_P_Ropoſitionis proximè ſubſequentis nimia fortaſſe prolixitas faſti-
              <lb/>
            dium potius Lectori, quam delectationem pariet, veruntamen, qui
              <lb/>
            hoc veretur, ac tantum otij, aut tolerantiæ habere nequit, vt illius ſa-
              <lb/>
            tis tongam texturam percurrere Valeat, ipſam ſupponat, ac prætereat,
              <lb/>
            ijs enim præcipuè à me dirigitur, quibus nec otium deeſt, nec </s>
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