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

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            <s xml:id="echoid-s597" xml:space="preserve">
              <pb o="18" file="0038" n="38" rhead="GEOMETRIÆ"/>
            ducamus rectam, VN, parallelam ipſi, AB, tranſibit hæc per
              <lb/>
              <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">Vide di-
                <lb/>
              cta lib 7.
                <lb/>
              Annot.
                <lb/>
              Prop. 3.</note>
            punctum, E, qui eſt etiam vertex rcſpectu ipſius, AB, igitur ſeca-
              <lb/>
            bit, HM, quod eſt abſurdum, nam vtræque ſunt parallelæ eidem,
              <lb/>
            AB, & </s>
            <s xml:id="echoid-s598" xml:space="preserve">ideò inter ſe ſunt parallelæ, vel, VN, extendetur ſuper, H
              <lb/>
            M, & </s>
            <s xml:id="echoid-s599" xml:space="preserve">ſic, HM, tranſiret per, C, in ipſoq; </s>
            <s xml:id="echoid-s600" xml:space="preserve">tangeret figuram con-
              <lb/>
            tra ſuppoſitum, quod etiam eſt abſurdum, non igitur, HM, tanget
              <lb/>
              <note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">Ex A. De-
                <lb/>
              fin. 1. hu-
                <lb/>
              ius.</note>
            figuram, CARB, ſed erit tota extra figuram, ſi nullibi concurrat
              <lb/>
            cum ambitu figuræ, vel, tranſiens per aliquem punctum, eandem
              <lb/>
            ſecabit, ſi is punctus non ſit ex illis, qui funt vertices ipſius figuræ ex
              <lb/>
            hac parte, vel ex oppofito reſpectu ipſius, AB; </s>
            <s xml:id="echoid-s601" xml:space="preserve">quod ſimiliter in ſo-
              <lb/>
            lidis oſtendemus pro rectis lineis, AB, HM, VN, plana intelligen-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s602" xml:space="preserve">ipſam, CARB, eſſe figuram ſolidam ſupponentes, quæ
              <lb/>
            oſtendere opus erat.</s>
            <s xml:id="echoid-s603" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div73" type="section" level="1" n="57">
          <head xml:id="echoid-head68" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s604" xml:space="preserve">_H_Inc patet à quolibet puncto ambitus datæ figuræ planæ, vel ſolidæ
              <lb/>
            ductam lineam, vel planum æquidiſtans illi, reſpectu cuius ſumi-
              <lb/>
            tur vertex (ſi ſumptus punctus non ſit vnus ex verticalibus dictis) ſeca-
              <lb/>
            rè figuram, cum, vt oſtenſum eſt, tangens eſſe non poſſit, & </s>
            <s xml:id="echoid-s605" xml:space="preserve">ideò ſem-
              <lb/>
            per inter duo oppoſita tangentia, reſpectu regulæ, penes quam ſumitur
              <lb/>
            vertex, aſſumpta linea cadet, licet indefinitè producatur.</s>
            <s xml:id="echoid-s606" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div74" type="section" level="1" n="58">
          <head xml:id="echoid-head69" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s607" xml:space="preserve">_E_T quia ſi recta linea, vel planum, ſecat duas parallelas, vel duo
              <lb/>
            æquidiſtantia plana, ſecat etiam omnia intermedia illis æquidi-
              <lb/>
            ſtantia; </s>
            <s xml:id="echoid-s608" xml:space="preserve">ideò ſi recta linea, vel planum, tranſeat per verticem, & </s>
            <s xml:id="echoid-s609" xml:space="preserve">baſim,
              <lb/>
            ſiue per oppoſitos vertices datæ figuræ planæ, vel ſolidæ, ſecabit etiam om-
              <lb/>
            nes in figura oppoſitis tangentibus æquidiſtantes intra figuram, vel ea-
              <lb/>
            ſdem productas extra figuram.</s>
            <s xml:id="echoid-s610" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div75" type="section" level="1" n="59">
          <head xml:id="echoid-head70" xml:space="preserve">THEOREMA II. PROPOS. V.</head>
          <p>
            <s xml:id="echoid-s611" xml:space="preserve">SI à quocumque puncto circuitus cylindrici, per quam fit
              <lb/>
            reuolutio verſus cylindricum ducta fuerit recta linea
              <lb/>
              <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">D. fin. 3.</note>
            paralleìa regulæ lateris cylindrici, hæc eritlatus cylindrici
              <lb/>
            in talibaſi conſtituti.</s>
            <s xml:id="echoid-s612" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s613" xml:space="preserve">Sit cylindricus, CB, In baſi, AFB, in cuius circuitu ſumpto vt-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s614" xml:space="preserve">puncto, F, ab eo ducta ſit verſus cylindricum quædam </s>
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