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

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            <s xml:id="echoid-s1367" xml:space="preserve">
              <pb o="53" file="0073" n="73" rhead="LIBER I."/>
            poſſemus habere, quot ſunt variationes inclinationum diametrorum
              <lb/>
            ad baſes, quam tamen variationem per definitionem ſupradictam
              <lb/>
            excludere neceſſarium eſſe exiſtimaui. </s>
            <s xml:id="echoid-s1368" xml:space="preserve">Suppoſito igitur, quod tali
              <lb/>
            definitioni hoc adiungatur, dico eam cum mea concordare, ſi pro
              <lb/>
              <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a" number="36">
                <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0073-01"/>
              </figure>
            ipſis ſectionibus tanquam figuris in-
              <lb/>
            telligatur. </s>
            <s xml:id="echoid-s1369" xml:space="preserve">Ductis enim per vertices,
              <lb/>
            A, R, baſibus, DF, QK, paralle-
              <lb/>
            lis, illæ tangent dictas portiones, & </s>
            <s xml:id="echoid-s1370" xml:space="preserve">
              <lb/>
            inter eaſdem ductas habebimus ip-
              <lb/>
            ſas, AE, RG, illis ad eundem an-
              <lb/>
            gulum incidentes ex eadem parte,
              <lb/>
            quibus ſimiliter ad eandem partem
              <lb/>
            diuiſis, vt in punctis, N, O; </s>
            <s xml:id="echoid-s1371" xml:space="preserve">V, X;
              <lb/>
            </s>
            <s xml:id="echoid-s1372" xml:space="preserve">& </s>
            <s xml:id="echoid-s1373" xml:space="preserve">per eadem ductis ipſis tangenti-
              <lb/>
            bus parallelis, BM, CH, SP, TL,
              <lb/>
            inuenimus eas, quęinter ipſas, AE,
              <lb/>
            RG, & </s>
            <s xml:id="echoid-s1374" xml:space="preserve">circuitum figurarum, ADF, RQK, ad eandem partem
              <lb/>
            continentur, & </s>
            <s xml:id="echoid-s1375" xml:space="preserve">diuidunt ipſas ſimiliter ad eandem partem, eodem
              <lb/>
            ordine ſumptas, eſſe in proportione ipſarum, AE, RG, nam quia,
              <lb/>
            DF, ad, EA, eſt vt, QK, ad, GR, permutando, DF, ad, QK,
              <lb/>
            erit vt, EA, ad, GR, & </s>
            <s xml:id="echoid-s1376" xml:space="preserve">quia ipſæ, AE, RG, ſunt diametri, ad
              <lb/>
            quas ordinatim applicantur dictæ parallelę, ideò ab eiſdem bifariam
              <lb/>
            diuidentur, ergo, &</s>
            <s xml:id="echoid-s1377" xml:space="preserve">, DE, ad, QG, &</s>
            <s xml:id="echoid-s1378" xml:space="preserve">, EF, ad, GK, erit vt, E
              <lb/>
            A, ad GR, eodem modo oſtendemus tum, CO, ad, TX, tum, O
              <lb/>
            H, ad, XL, eſſe vt, OA, ad, XR .</s>
            <s xml:id="echoid-s1379" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1380" xml:space="preserve">vt, EA, ad, GR, & </s>
            <s xml:id="echoid-s1381" xml:space="preserve">ſic, B
              <lb/>
            N, ad, SV, &</s>
            <s xml:id="echoid-s1382" xml:space="preserve">, NM, ad, VP, eſſe vt, NA, ad, VR .</s>
            <s xml:id="echoid-s1383" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1384" xml:space="preserve">vt, EA,
              <lb/>
            ad, GR, ſunt igitur figurę, ADF, RQK, ſimiles iuxta meam de-
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">Defin.10.</note>
            finitionem, earum verò, & </s>
            <s xml:id="echoid-s1385" xml:space="preserve">tangentium oppoſitarum (quarum duæ
              <lb/>
            ex vna parte ſuntipſæ, DF, QK,) incidentes ſunt ipſæ, AE, RG.</s>
            <s xml:id="echoid-s1386" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div154" type="section" level="1" n="104">
          <head xml:id="echoid-head115" xml:space="preserve">SCHOLIV M.</head>
          <p style="it">
            <s xml:id="echoid-s1387" xml:space="preserve">_A_Ffert Commandinus ali@m definitionem ſimilium hyperbolarum,
              <lb/>
            ſcilicet ſimiles eſſe, quarum coniuncta diametri inter ſe, vel qua-
              <lb/>
            rum figuræ latera eandem proportionem babent, quam Dauid Riualtus
              <lb/>
            in Com. </s>
            <s xml:id="echoid-s1388" xml:space="preserve">in Arch. </s>
            <s xml:id="echoid-s1389" xml:space="preserve">lib de Conoidib. </s>
            <s xml:id="echoid-s1390" xml:space="preserve">& </s>
            <s xml:id="echoid-s1391" xml:space="preserve">Sphæroidibus ad Defin.</s>
            <s xml:id="echoid-s1392" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1393" xml:space="preserve">oſten-
              <lb/>
            dit concordare cum ſupradicta Apollonij, quam videat, qui voluerit:
              <lb/>
            </s>
            <s xml:id="echoid-s1394" xml:space="preserve">Hæc igitur eodem modo, quo illa Apollonij, cummea pariter concorda-
              <lb/>
            bit (ſumpta tamen hyp@rbola tanquam figura) vnde hac quoque hypo-
              <lb/>
            teſi ſi opus fuerit, pariter vtemur ad paſſiones inde dependentes demon-
              <lb/>
            ſtranda
              <unsure/>
            s.</s>
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