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

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          <p>
            <s xml:id="echoid-s1912" xml:space="preserve">
              <pb o="75" file="0095" n="95" rhead="LIBERI."/>
            homologas ſimilium figurarum, BG, Zl, quarum & </s>
            <s xml:id="echoid-s1913" xml:space="preserve">oppoſitarum
              <lb/>
            tangentium, BE, DG, Z &</s>
            <s xml:id="echoid-s1914" xml:space="preserve">, fl, incidentes ſunt ipſæ, BD, Zf,
              <lb/>
            hæc autem etiam in cęteris traiectis planis, vt dictum eſt contingere
              <lb/>
            oſtendemus, ergo, BG, Zl, EDG, & </s>
            <s xml:id="echoid-s1915" xml:space="preserve">fl, erunt figurę incidentes
              <lb/>
            ſimilium cylindricorum, ſeu conicorum iam dictorum, & </s>
            <s xml:id="echoid-s1916" xml:space="preserve">oppoſito-
              <lb/>
            rum tangentium planorum, AE, LG, K &</s>
            <s xml:id="echoid-s1917" xml:space="preserve">, XL, ergo in his ſoli-
              <lb/>
            dis adſunt omnes conditiones defin. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1919" xml:space="preserve">vt recolenti eafdem patefiet,
              <lb/>
            igitur erunt iuxta eandem pariter ſimilia. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">Aduerte autem, quod ſup-
              <lb/>
            poſui planum, NG, tangere tam cylindricum, quam conicum, vt
              <lb/>
            etiam, Vl, ne figura nimis confunderetur, & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">vt fierent latera, E
              <lb/>
            G, & </s>
            <s xml:id="echoid-s1922" xml:space="preserve">l, communia parallelogrammis, BG, Zl, & </s>
            <s xml:id="echoid-s1923" xml:space="preserve">triangulis, D
              <lb/>
            EG, f & </s>
            <s xml:id="echoid-s1924" xml:space="preserve">l, valebit tamen eadem demonſtratio etiamſi plana ducta
              <lb/>
            per, HG, Yl, tangentia cylindricos, diuerſa ſint à planis per eaſdem,
              <lb/>
            HG, Yl, tranſeuntibus, ac tangentibus ipſos conicos, fient enim
              <lb/>
            ſemper ſimilia triangula, EDG, & </s>
            <s xml:id="echoid-s1925" xml:space="preserve">fl, etiamſi non adiaceant late-
              <lb/>
            ribus, EG, & </s>
            <s xml:id="echoid-s1926" xml:space="preserve">l, vt conſideranti facilè patebit, hæc autem nobis o-
              <lb/>
            ſtendenda erant.</s>
            <s xml:id="echoid-s1927" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div186" type="section" level="1" n="121">
          <head xml:id="echoid-head132" xml:space="preserve">THEOREMA XXX. PROPOS. XXXIII.</head>
          <p>
            <s xml:id="echoid-s1928" xml:space="preserve">SI ſolidum rotundum ſecetur plano per axem, producta in
              <lb/>
            eo figura erit, quæ per reuolutionem ipſum genuit.</s>
            <s xml:id="echoid-s1929" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1930" xml:space="preserve">Sit ſolidum rotundum, cuius axis, AM, baſis circulus, HDEF,
              <lb/>
              <note position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">Defin. 6.</note>
            hoc autem plano per axem, AM, ducto ſecetur, quod in eo produ-
              <lb/>
            cat figuram, ACDFG. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">Dico hanc
              <lb/>
            eſſe eam, quæ per reuolutionem ip-
              <lb/>
              <figure xlink:label="fig-0095-01" xlink:href="fig-0095-01a" number="51">
                <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0095-01"/>
              </figure>
            ſum ſolidum genuit. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">Intelligatur re-
              <lb/>
            uolui circa, AM, figura, quę dictum
              <lb/>
            ſolidum genuit, donec reperiatur po-
              <lb/>
            ſita in plano figuræ, ACDFG, igi-
              <lb/>
            tur vel harum figurarum perimetri
              <lb/>
            congruunt, vel non, ſi ſic ex illis fa-
              <lb/>
            cta erit vna figura, ea nempè, quæ
              <lb/>
            per reuolutionem generat dictum ſo-
              <lb/>
            lidum, ſi verò non congruant, ali-
              <lb/>
            quis punctus alterius ambituum di-
              <lb/>
            ctarum figurarum non reperietur in
              <lb/>
            reliquæ ambitu, ſit is punctus, B, qui
              <lb/>
            reperiatur in ambitu figuræ, quæ per reuolutionem dictum ſolidum
              <lb/>
            deſcripſit, quæ ſit ipſa, ABDFG, & </s>
            <s xml:id="echoid-s1933" xml:space="preserve">non in ambitu figurę, ACD
              <lb/>
            FG, cuius ambitus eſt communis ſectio plani ducti per axem, & </s>
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