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

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        <div xml:id="echoid-div228" type="section" level="1" n="147">
          <p>
            <s xml:id="echoid-s2356" xml:space="preserve">
              <pb o="96" file="0116" n="116" rhead="GEOMETRIÆ"/>
            erunt axes baſium eorundem ſolidorum, ipſarum nempè figurarum,
              <lb/>
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">Elicitur
                <lb/>
              ex 37. hu-
                <lb/>
              ius.</note>
            FGHN, BDCE, ſunt. </s>
            <s xml:id="echoid-s2357" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2358" xml:space="preserve">ſolida rotunda, & </s>
            <s xml:id="echoid-s2359" xml:space="preserve">plana, FMH, BA
              <lb/>
            C, per axes tranſeuntia ſunt baſibus erecta. </s>
            <s xml:id="echoid-s2360" xml:space="preserve">Sint autem ſolidorum
              <lb/>
            iam dictorum axes, necnon axes, ſeu diametri figurarum, FMH,
              <lb/>
            BAC, ipſæ, OM, XA. </s>
            <s xml:id="echoid-s2361" xml:space="preserve">Qura ergo ſiguræ, FMH, BAC, ſunt
              <lb/>
            fimiles portionum coni ſectiones, quarum baſes, ſiue ad earum axes,
              <lb/>
            vel diametros, MO, AX, ordinatim applicatæ ſunt, FH, BC, e-
              <lb/>
            runt homologarum earundem regulæ, ac tangentes ipſas figuras ex
              <lb/>
            vna parte, ex alia verò, quo per vertices, M, A, eiſdem ducentur æ-
              <lb/>
            quidiſtantes, earundem verò oppoſitarum tangentium, acipſarum
              <lb/>
            figurarum incidentes, MO, AX, eritque, FH, ad, BC, vt, MO,
              <lb/>
              <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">28. huius.</note>
            ad, AX. </s>
            <s xml:id="echoid-s2362" xml:space="preserve">Si ergo baſes, FGHN, BDCE, ſint circuli erunt figurę
              <lb/>
            ſimiles, quarum & </s>
            <s xml:id="echoid-s2363" xml:space="preserve">oppoſitarum tangentium per extrema, FH, du-
              <lb/>
              <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">Lẽma 31.
                <lb/>
              huius.</note>
            ctarum incidentes fient diametri, FH, BC. </s>
            <s xml:id="echoid-s2364" xml:space="preserve">Si verò ſint ſimiles el-
              <lb/>
              <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="65">
                <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0116-01"/>
              </figure>
            lipſes, quoniam, FH, BC, ſunt axes,
              <lb/>
            facilè probabimus, ſicut pro circulo fa-
              <lb/>
            ctum eſt ad Lemma Propoſ. </s>
            <s xml:id="echoid-s2365" xml:space="preserve">31. </s>
            <s xml:id="echoid-s2366" xml:space="preserve">huius,
              <lb/>
            auxilio Propoſ. </s>
            <s xml:id="echoid-s2367" xml:space="preserve">40. </s>
            <s xml:id="echoid-s2368" xml:space="preserve">huius, ipſas, FH,
              <lb/>
            BC, eſſe incidentes ſimilium figurarum,
              <lb/>
            FGHN, BDCE, & </s>
            <s xml:id="echoid-s2369" xml:space="preserve">oppoſitarum
              <lb/>
            tangentium, quę per puncta, F, H; </s>
            <s xml:id="echoid-s2370" xml:space="preserve">B,
              <lb/>
            C, ducuntur (quę ipſis, FH, BC, exi-
              <lb/>
            ſtent perpendiculares, cum ſint axes ea-
              <lb/>
            rundem figurarum.) </s>
            <s xml:id="echoid-s2371" xml:space="preserve">Et eodem modo
              <lb/>
            ſi dicta ſolida ſecentur alijs planis præ-
              <lb/>
            fatis baſibus parallelis (ita tamen vt illa
              <lb/>
            diuidant ſimiliter ad eandem partem ip-
              <lb/>
            ſas, MO, AX, & </s>
            <s xml:id="echoid-s2372" xml:space="preserve">ſubinde etiam altitudines ipſorum ſolidorum re-
              <lb/>
              <note position="left" xlink:label="note-0116-04" xlink:href="note-0116-04a" xml:space="preserve">17. Vnd.
                <lb/>
              Elem.</note>
            ſpectu dictarum baſium aſſumptas) oſtendemus & </s>
            <s xml:id="echoid-s2373" xml:space="preserve">productas in ſo-
              <lb/>
            lidis figuras eſſe ſimiles, & </s>
            <s xml:id="echoid-s2374" xml:space="preserve">earum, ac oppoſitarum tangentium (æ-
              <lb/>
            quidiſtantium tanquam regulis duabus oppoſitis tangentibus ba-
              <lb/>
            ſium, FH, BC, per extrema, F, H; </s>
            <s xml:id="echoid-s2375" xml:space="preserve">B, C, iam ductarum) inci-
              <lb/>
            dentes eſſe communes ipſarum ſectiones cum figuris, FMH, BAC,
              <lb/>
            quæ omnes erunt lineæ homologæ ſimilium figurarum, FMH, B
              <lb/>
            AC, quarum regulę, FH, BC. </s>
            <s xml:id="echoid-s2376" xml:space="preserve">Ergo, ductis per, M, A, duobus
              <lb/>
            planis baſibus parallelis, quæ ipſa ſolida contingent, incidunt hiſce
              <lb/>
            oppoſitis tangentibus planisad eundem angulum ex eadem parte
              <lb/>
            plana figurarum, FMH, BAC, ſectis autem ſolidis planis paralle-
              <lb/>
            lis, vt dictum eſt, fiunt in ipſis ſimiles figuræ planæ, & </s>
            <s xml:id="echoid-s2377" xml:space="preserve">earum inci-
              <lb/>
            dentes capiuntur omnes in ſimilibus figuris, FMH, BAC, quarum
              <lb/>
            ſunt homologæ, earumque regulæ ipſæ, FH, BC, & </s>
            <s xml:id="echoid-s2378" xml:space="preserve">lineæ homo-
              <lb/>
            logæ figurarum homologarum duabus quibuſdam regulis, </s>
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