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

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        <div xml:id="echoid-div210" type="section" level="1" n="136">
          <pb o="87" file="0107" n="107" rhead="LIBERI."/>
        </div>
        <div xml:id="echoid-div212" type="section" level="1" n="137">
          <head xml:id="echoid-head148" xml:space="preserve">THEOREMA XLII. PROPOS. XLV.</head>
          <p>
            <s xml:id="echoid-s2155" xml:space="preserve">SI ſphæroides, vel conoides parabolicum, ſeu hyperboli-
              <lb/>
            cum ſecentur quomodocumq; </s>
            <s xml:id="echoid-s2156" xml:space="preserve">planis parallelis ad axem
              <lb/>
            rectis, ſiue inclinatis, communes ſectiones ſimiles erunt, & </s>
            <s xml:id="echoid-s2157" xml:space="preserve">
              <lb/>
            diametri eiuſdem rationis erunt omnes in eadem figura per
              <lb/>
            axem tranſeunte, rectè eaſdem ſecante.</s>
            <s xml:id="echoid-s2158" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2159" xml:space="preserve">Hæc colliguntur in Coroll. </s>
            <s xml:id="echoid-s2160" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2161" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s2162" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2163" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2164" xml:space="preserve">Arch. </s>
            <s xml:id="echoid-s2165" xml:space="preserve">de Conoidibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s2166" xml:space="preserve">Sphæroidibus, & </s>
            <s xml:id="echoid-s2167" xml:space="preserve">ibidem etiam à Federico Commandino in ſuis in
              <lb/>
            Arch. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Comment. </s>
            <s xml:id="echoid-s2169" xml:space="preserve">demonſtrantur. </s>
            <s xml:id="echoid-s2170" xml:space="preserve">Hęc verò circa ipſas ſectionum fi-
              <lb/>
            guras verificari pariter manifeſtum eſt, hoc autem dico, vtor enim
              <lb/>
            ijſdem ſectionum nominibus tamquam figuras ſub ipſis comprehen-
              <lb/>
            fas ſignificantibus.</s>
            <s xml:id="echoid-s2171" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div213" type="section" level="1" n="138">
          <head xml:id="echoid-head149" xml:space="preserve">THEOREMA XLIII. PROPOS. XLVI.</head>
          <p>
            <s xml:id="echoid-s2172" xml:space="preserve">EXpoſitis prædictis coni ſectionibus, circulo nempè, El-
              <lb/>
            lipſi, Parabola, & </s>
            <s xml:id="echoid-s2173" xml:space="preserve">Hyperbola, ſi, quę ad earundem axes
              <lb/>
            ordinatim applicantur, diametri eſſe intelligantur circulo-
              <lb/>
            rum ab ipſis deſcriptorum, qui ſint erecti pianis ipſarum figu-
              <lb/>
            rarum, periphærię deſcriptorum circulorum in ſectione, quę
              <lb/>
            eſt circulus, erunt omnes in ſuperficie ſphęrę, in Ellipſi verò
              <lb/>
            in ſuperficie ſphæroidis, in Parab. </s>
            <s xml:id="echoid-s2174" xml:space="preserve">in ſuperficie conoidis pa-
              <lb/>
            rabolici, & </s>
            <s xml:id="echoid-s2175" xml:space="preserve">in Hyperbola in ſuperficie conoidis Hyperbolici.</s>
            <s xml:id="echoid-s2176" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2177" xml:space="preserve">Sint prædictę ſectiones figurę
              <lb/>
              <figure xlink:label="fig-0107-01" xlink:href="fig-0107-01a" number="60">
                <image file="0107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0107-01"/>
              </figure>
            ſcilicet, ipſæ, ABCD, earum
              <lb/>
            axes, AC, vna ex ordinatim ad
              <lb/>
            axim applicatis, BD, quæ in-
              <lb/>
            telligatur eſſe diameter ab ea
              <lb/>
            deſcripti circuli, BNDE. </s>
            <s xml:id="echoid-s2178" xml:space="preserve">Di-
              <lb/>
            co circumferentiam, BNDE,
              <lb/>
            eſſe in dicta ſuperficie. </s>
            <s xml:id="echoid-s2179" xml:space="preserve">Intelli-
              <lb/>
            gantur dictę figuræ reuolui circa
              <lb/>
            ſuos axes, vt ex circulo fiat ſphę-
              <lb/>
            ra, ex ellipſi ſphæroides, ex pa-
              <lb/>
            rabola conoides parabolicum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2180" xml:space="preserve">ex hyperbola hyperbolicum,
              <lb/>
            ſecentur autem planis ad axem
              <lb/>
            rectis, eundem axem ſecantibus in eodem puncto, in quo </s>
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