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

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        <div xml:id="echoid-div226" type="section" level="1" n="146">
          <p>
            <s xml:id="echoid-s2330" xml:space="preserve">
              <pb o="95" file="0115" n="115" rhead="LIBER I."/>
            oriuntur dictæ ſphæroides, & </s>
            <s xml:id="echoid-s2331" xml:space="preserve">proinde erunt ſimiles tum iuxta defi-
              <lb/>
            nit. </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Apollonij, tum iuxta definit. </s>
            <s xml:id="echoid-s2333" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2334" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s2335" xml:space="preserve">Et quoniam ſi ſecentur
              <lb/>
            planis ad axem rectis in dictis ſphæroidibus gignuntur circuli, vt ex.
              <lb/>
            </s>
            <s xml:id="echoid-s2336" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2337" xml:space="preserve">BNDO, EXGV, (qui ſecent axes, AC, FH, ſimiliter ad ean-
              <lb/>
              <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">34. huius.</note>
            dem partem in punctis, M, I,) quorum diametri ſunt communes ſe-
              <lb/>
            ctiones cum figuris per axem tranſeuntibus, vt ipſę, BD, BG, ideò
              <lb/>
            iſtæ erunt incidentes ipſorum circulorum, BNDO, EXGV, & </s>
            <s xml:id="echoid-s2338" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">Lẽma 31.
                <lb/>
              huius.</note>
            oppoſitarum tangentium in punctis, B, D; </s>
            <s xml:id="echoid-s2339" xml:space="preserve">E, G; </s>
            <s xml:id="echoid-s2340" xml:space="preserve">quod etiam de
              <lb/>
            cæteris intelligemus. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">Ergo ſi per axium, AC, FH, extrema ducta
              <lb/>
            ſint duo oppoſita tangentia plana, quæ erunt circulis, BNDO, E
              <lb/>
            XGV, parallela, habebimus plana ellipſium, ABCD, FEHG,
              <lb/>
            illis incidentia ad eundem angulum ex eadem parte; </s>
            <s xml:id="echoid-s2342" xml:space="preserve">nam adilla ſunt
              <lb/>
            erecta, in quibus reperientur ſimiles figuræ, ellipſes nempè iam di-
              <lb/>
            ctæ, & </s>
            <s xml:id="echoid-s2343" xml:space="preserve">homologarum earundem regulæ erunt communes ſectiones
              <lb/>
            earundem productorum planorum cum oppoſitis tangentibus pla-
              <lb/>
            nis, quæ homologę erunt incidentes homologarum figurarum (qua-
              <lb/>
            rum regulæ ſunt dicta tangentia plana) & </s>
            <s xml:id="echoid-s2344" xml:space="preserve">oppoſitarum tangentium
              <lb/>
            per earundem extrema ductarum, quæ ſemper duabus quibuſdam re-
              <lb/>
            gulis æquidiſtabunt. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">Ergo dictæ ſphæroides ſimiles erunt iuxta de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s2346" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2347" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s2348" xml:space="preserve">earum, ac dictorum oppoſitorum tangentium pla-
              <lb/>
            norum figuræ incidentes erunt eædem ellipſes, ABCD, FEHG,
              <lb/>
            per axes tranſeuntes, quod &</s>
            <s xml:id="echoid-s2349" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2350" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div228" type="section" level="1" n="147">
          <head xml:id="echoid-head158" xml:space="preserve">THEOREMA XLVII. PROPOS. L:</head>
          <p>
            <s xml:id="echoid-s2351" xml:space="preserve">P Oſita definitione ſimilium portionum ſphæràrum, vel
              <lb/>
            ſphæroidum, aut conoidum, ſiue earundem portionum,
              <lb/>
            ſequitur etiam definitio generalis ſimilium 4olidorum.</s>
            <s xml:id="echoid-s2352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2353" xml:space="preserve">Sint ſolida, FMH, BAC, ſimiles
              <lb/>
              <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="64">
                <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0115-01"/>
              </figure>
            portiones ſphęrarum, vel ſphæroidum,
              <lb/>
            vel ſimiles conoides, ſeu conoidum por-
              <lb/>
            tiones iuxta particularem definitionem
              <lb/>
              <note position="right" xlink:label="note-0115-03" xlink:href="note-0115-03a" xml:space="preserve">Def. 9.</note>
            de illis allatam. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">Dico eadem eſſe ſimi-
              <lb/>
            lia iuxta definitionem generalem ſimi-
              <lb/>
            lium ſolidorum. </s>
            <s xml:id="echoid-s2355" xml:space="preserve">Baſes ergo erunt vel
              <lb/>
            circuli, vel ſimiles ellipſes, nempè, F
              <lb/>
            GHN, BDCE, ductis autem planis
              <lb/>
            per axes ad rectos angulos baſibus fiant
              <lb/>
            in ipſis figuræ, FMH, BAC, quæ e-
              <lb/>
            runt ſimiles ſectionum coni portiones, & </s>
            <s xml:id="echoid-s2356" xml:space="preserve">earum baſes, FH, </s>
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