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

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          <pb o="73" file="0093" n="93" rhead="LIBERI."/>
          <p>
            <s xml:id="echoid-s1862" xml:space="preserve">Sint cylindrici quicunque, AH, KY; </s>
            <s xml:id="echoid-s1863" xml:space="preserve">ſeu conici in ijſdem baſibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s1864" xml:space="preserve">altitudinibus (vt vna vice vtriuſq; </s>
            <s xml:id="echoid-s1865" xml:space="preserve">demonſtrationem abſoluamus)
              <lb/>
            NLH, VXY, ſimiles iuxta definit. </s>
            <s xml:id="echoid-s1866" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Dico eoſdem etiam
              <lb/>
            eſſe ſimiles iuxta definit. </s>
            <s xml:id="echoid-s1869" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">Quoniam ergo vtraque prædicta ſolida
              <lb/>
              <note position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">Defin. 7.</note>
            ſunt ſimilia, erunt baſes, LH, XY, ſimiles, ducantur earum oppo-
              <lb/>
            ſitę tangentes, quę ſint homologarum regulę, ipſę, LD, HG, X f,
              <lb/>
              <note position="right" xlink:label="note-0093-02" xlink:href="note-0093-02a" xml:space="preserve">Coroll. 1.</note>
              <figure xlink:label="fig-0093-01" xlink:href="fig-0093-01a" number="49">
                <image file="0093-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0093-01"/>
              </figure>
            Y l, quarum, & </s>
            <s xml:id="echoid-s1871" xml:space="preserve">prædictarum ſimi-
              <lb/>
              <note position="right" xlink:label="note-0093-03" xlink:href="note-0093-03a" xml:space="preserve">B. Def. 10.</note>
            lium figurarum incidentes ſint ipſæ,
              <lb/>
            DG, f l, quæ etiam pro regulis alia-
              <lb/>
              <note position="right" xlink:label="note-0093-04" xlink:href="note-0093-04a" xml:space="preserve">Coroll.
                <lb/>
              23.</note>
            rum homologarum ſumi poterunt,
              <lb/>
            ſint ergo duę quæcunque homologę
              <lb/>
            parallelę incidentibus, D G, fl, ip-
              <lb/>
            ſæ, LH, XY, ſi ergo per has, & </s>
            <s xml:id="echoid-s1872" xml:space="preserve">la-
              <lb/>
              <note position="right" xlink:label="note-0093-05" xlink:href="note-0093-05a" xml:space="preserve">Defin. 7.</note>
            tera cylindricorum, vel conicorum
              <lb/>
            iam dictorum extendantur plana, ab
              <lb/>
            ijs producentur in cylindricis ſimilia
              <lb/>
            parallelogramma, & </s>
            <s xml:id="echoid-s1873" xml:space="preserve">in conicis ſimi-
              <lb/>
            lia triangula, quę etiam erunt ad ba-
              <lb/>
            ſes æquè ad eandem partem inclina-
              <lb/>
            ta. </s>
            <s xml:id="echoid-s1874" xml:space="preserve">Extendantur ergo per oppoſitas
              <lb/>
            tangentes, LD, HG; </s>
            <s xml:id="echoid-s1875" xml:space="preserve">Xf, Yl, pla-
              <lb/>
            na tangentia tam cylindricos, quam
              <lb/>
            conicos iam dictos, & </s>
            <s xml:id="echoid-s1876" xml:space="preserve">hęc ſimul cum
              <lb/>
            planis baſium indefinitè producan-
              <lb/>
            tur ad partes incidentium, DG, fl,
              <lb/>
            & </s>
            <s xml:id="echoid-s1877" xml:space="preserve">tandem per, DG, fl, cum ſint
              <lb/>
            parallelæ, extendantur plana ipſis,
              <lb/>
            AH, KY, parallela ſecantia iam pro-
              <lb/>
            ducta plana in rectis, DG, GE, E
              <lb/>
            B, BD, DE, fl, l &</s>
            <s xml:id="echoid-s1878" xml:space="preserve">, & </s>
            <s xml:id="echoid-s1879" xml:space="preserve">Z, Zf, f
              <lb/>
              <note position="right" xlink:label="note-0093-06" xlink:href="note-0093-06a" xml:space="preserve">Defin. 13.
                <lb/>
              vndec. El.</note>
            &</s>
            <s xml:id="echoid-s1880" xml:space="preserve">, erunt ergo parallelepipeda, AG,
              <lb/>
            Kl, & </s>
            <s xml:id="echoid-s1881" xml:space="preserve">priſmata, LNGD, XVlf,
              <lb/>
              <note position="right" xlink:label="note-0093-07" xlink:href="note-0093-07a" xml:space="preserve">24. Vnd.
                <lb/>
              Elem.</note>
            ergo erit parallelogrammum, BG,
              <lb/>
            ſimile ipſi, AH, &</s>
            <s xml:id="echoid-s1882" xml:space="preserve">, Zl, ſimile, K
              <lb/>
            Y, quæ cum ſint inter ſe ſimilia, e-
              <lb/>
            tiam, BG, Zl, erunt ſimilia, ſic e-
              <lb/>
            tiam oſtendemus triangula, EDG,
              <lb/>
            & </s>
            <s xml:id="echoid-s1883" xml:space="preserve">fl, eſſe ſimilia, ſub intellige iuxta
              <lb/>
            definitionem Euclidis, ergo erunt e-
              <lb/>
            tiam ſimilia iuxta defin. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">Ducantur duo plana oppoſitis tangenti-
              <lb/>
              <note position="right" xlink:label="note-0093-08" xlink:href="note-0093-08a" xml:space="preserve">27. huius.</note>
            bus intermedia, ac parallela, altitudines dictorum ſolidorum reipectu
              <lb/>
            baſium, LH, XY, ſumptas, ſimiliter ad eandem partem </s>
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