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

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        <div xml:id="echoid-div177" type="section" level="1" n="116">
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">
              <pb o="70" file="0090" n="90" rhead="GEOMETRIÆ"/>
            hos circulos eſſe ſimiles iuxta meam definitionem ſimilium plana-
              <lb/>
            rum figurarum, & </s>
            <s xml:id="echoid-s1786" xml:space="preserve">eorum, & </s>
            <s xml:id="echoid-s1787" xml:space="preserve">ductarum oppoſitarum tangentium in-
              <lb/>
            cidentes eſſe ipſas diametros, AC, OQ, quæ etiam de ſemicirculis
              <lb/>
            verificantur. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">Diametri ergo, AC, OQ, diuidantur fimiliter ad ean-
              <lb/>
            dem partem in punctis, E, M, à quibus vſque ad circumferentiam
              <lb/>
            ducantur ipſæ, EB, MN, parallelæ dictis tangentibus, quæ cum
              <lb/>
            ad angulos rectos diametros diuidant, etiam ipſę, BE, NM, erunt
              <lb/>
              <figure xlink:label="fig-0090-01" xlink:href="fig-0090-01a" number="47">
                <image file="0090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0090-01"/>
              </figure>
            illis perpendiculares, igitur quadratum,
              <lb/>
            BE, erit ęquale rectangulo, AEC, ſi-
              <lb/>
            cuti quadratum, NM, æquale rectan-
              <lb/>
            gulo, OMQ, rectangulum autem, A
              <lb/>
            EC, ad quadratum, EC, eſt vt, AE,
              <lb/>
            ad, EC, ideſt vt, OM, ad, MQ, ideſt
              <lb/>
              <note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">1. Sex. El.</note>
            vt rectangulum, OMQ, ad quadratum,
              <lb/>
            MQ, ideſt vt quadratum, NM, ad qua-
              <lb/>
            dratum, MQ, ergo quadratum, BE,
              <lb/>
            ad quadratum, EC, eſt vt quadratum,
              <lb/>
            NM, ad quadratum, MQ, (quæ au-
              <lb/>
            tem hic ſupponuntur, vel petantur ex
              <lb/>
            Eucl. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">vel ex ſequenti meo lib.
              <lb/>
            </s>
            <s xml:id="echoid-s1792" xml:space="preserve">
              <note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">8. Lib. 2.
                <lb/>
              ſequen.
                <lb/>
              vel 20.
                <lb/>
              Sex. El.</note>
            in quo, quæ hic aſſumuntur indepen-
              <lb/>
            denter ab hoc Lemmate demonſtratur)
              <lb/>
            ergo, BE, ad, EC, erit vt, NM, ad,
              <lb/>
            MQ, permutando, BE, ad, NM, e-
              <lb/>
            rit vt, EC, ad, MQ, vel vt, AC, ad, OQ, igitur, quæ æquidi-
              <lb/>
            ſtant ipſis tangentibus, FA, HO, & </s>
            <s xml:id="echoid-s1793" xml:space="preserve">ſimiliter ad eandem partem
              <lb/>
            vtcumque diuidunt ipſas, AC, OQ, & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">iacent inter ipſas, & </s>
            <s xml:id="echoid-s1795" xml:space="preserve">circui-
              <lb/>
            tus ſemicirculorum, ABC, ONQ, ad eandem partem, eodem or-
              <lb/>
            dine ſumptæ, ſunt vt ipſæ, AC, OQ, quæ dictis tangentibus inci-
              <lb/>
              <note position="left" xlink:label="note-0090-03" xlink:href="note-0090-03a" xml:space="preserve">Defin. 10.</note>
            dunt ad eundem angulum ex eadem parte, quęideò ſunt earum inci-
              <lb/>
            dentes, ergo ſemicirculi, ABC, ONQ, ſunt figuræ planæ fimiles
              <lb/>
            ſuxta meam definitionem, quarum & </s>
            <s xml:id="echoid-s1796" xml:space="preserve">oppoſitarum tangentium, quę
              <lb/>
            ab extremitate diametrorum ducuntur, incidentes ſunt ipſi diame-
              <lb/>
            tri; </s>
            <s xml:id="echoid-s1797" xml:space="preserve">ſic etiam patebit ſemicirculos, ADC, OZQ, necnon circu-
              <lb/>
            los, AC, OQ, eſſe ſimiles, iuxta eandem definitionem; </s>
            <s xml:id="echoid-s1798" xml:space="preserve">quod oſten-
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            dendum erat.</s>
            <s xml:id="echoid-s1799" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div179" type="section" level="1" n="117">
          <head xml:id="echoid-head128" xml:space="preserve">THEOREMA XXVIII. PROPOS. XXXI.</head>
          <p>
            <s xml:id="echoid-s1800" xml:space="preserve">POſitis infraſcriptis definitionibus ſimilium cylindro-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s1801" xml:space="preserve">conorum, ſequitur definitio generalis, quam
              <lb/>
            de ſimilibus ſolidis ipſe attuli.</s>
            <s xml:id="echoid-s1802" xml:space="preserve"/>
          </p>
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