Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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            _NIMA_ verò in hoc caſn, tum in quarta, tum in quinta figura eſt
              <note symbol="a" position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">9. huius
                <lb/>
              ad num. 4.</note>
            G D; </s>
            <s xml:id="echoid-s5968" xml:space="preserve">niſi punctum G cadat in ipſo D; </s>
            <s xml:id="echoid-s5969" xml:space="preserve">tunc enim _MINIMA_ abit in pun-
              <lb/>
            ctum.</s>
            <s xml:id="echoid-s5970" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5971" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5972" xml:space="preserve">At, ſi, vt in ſexta figura, quando interuallum G B minus eſt dimidio
              <lb/>
            B E, punctum G cadat inter B, & </s>
            <s xml:id="echoid-s5973" xml:space="preserve">E, tunc ſi concipiatur D eſſe Ellipſis
              <lb/>
            verticem, reliquum interuallum D G, vel erit non minus, vel minus di-
              <lb/>
            midio B F, quo in caſu duæ _MAXIMAE_ reperientur ad partem periphe-
              <lb/>
            riæ A D C: </s>
            <s xml:id="echoid-s5974" xml:space="preserve">eadem conſtructione, & </s>
            <s xml:id="echoid-s5975" xml:space="preserve">demonſtratione, ac ad num. </s>
            <s xml:id="echoid-s5976" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5977" xml:space="preserve">& </s>
            <s xml:id="echoid-s5978" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s5979" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s5980" xml:space="preserve">reliqua G B erit _MINIMA_, &</s>
            <s xml:id="echoid-s5981" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5982" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5983" xml:space="preserve">9. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">Si denique datum pun-
              <lb/>
            ctum G fuerit inter ſemi-
              <lb/>
              <figure xlink:label="fig-0214-01" xlink:href="fig-0214-01a" number="176">
                <image file="0214-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0214-01"/>
              </figure>
            axes, aut extra ſectioné,
              <lb/>
            vt in ſeptima figura; </s>
            <s xml:id="echoid-s5985" xml:space="preserve">vel
              <lb/>
            intra, vt in octaua; </s>
            <s xml:id="echoid-s5986" xml:space="preserve">vel in
              <lb/>
            ipſa ſectione, vt in nona.
              <lb/>
            </s>
            <s xml:id="echoid-s5987" xml:space="preserve">Iungatur E G, quæ hinc
              <lb/>
            inde producatur, & </s>
            <s xml:id="echoid-s5988" xml:space="preserve">fiat,
              <lb/>
            vt tranſuerſum D B ad re-
              <lb/>
            ctum B F, ita E H ad
              <note symbol="b" position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">Coroll.
                <lb/>
              16. h.</note>
            G, ac ita G I ad I E, & </s>
            <s xml:id="echoid-s5989" xml:space="preserve">
              <lb/>
            ex H, I, ducantur H L,
              <lb/>
            minori axi A C, & </s>
            <s xml:id="echoid-s5990" xml:space="preserve">I L
              <lb/>
            maiori D B parallelę, quę
              <lb/>
            ſimul occurrent in L, & </s>
            <s xml:id="echoid-s5991" xml:space="preserve">
              <lb/>
            in angulo H L I per pun-
              <lb/>
            ctum E (quod eſt cen-
              <lb/>
            trum Ellipſis) deſcriba-
              <lb/>
            tur Hyperbole M G
              <note symbol="c" position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">4. ſecun-
                <lb/>
              diconic.</note>
            N, quæ neceſſariò
              <note symbol="d" position="left" xlink:label="note-0214-04" xlink:href="note-0214-04a" xml:space="preserve">17. h.</note>
            ſibit per G (cum ſegmen-
              <lb/>
            ta G H, E I rectæ H I ap-
              <lb/>
            plicatæ in angulo aſym-
              <lb/>
            ptotali H L I, ſint ęqua-
              <lb/>
            lia,) & </s>
            <s xml:id="echoid-s5992" xml:space="preserve">in duobus tantùm
              <lb/>
            punctis M, N, Ellipſis
              <lb/>
            peripheriam ſecabit. </s>
            <s xml:id="echoid-s5993" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-0214-05" xlink:href="note-0214-05a" xml:space="preserve">18. h.</note>
            co has interſectiones da-
              <lb/>
            re puncta quæſita: </s>
            <s xml:id="echoid-s5994" xml:space="preserve">hoc
              <lb/>
            eſt iunctam G N in ſepti-
              <lb/>
            ma, octaua, & </s>
            <s xml:id="echoid-s5995" xml:space="preserve">nona fi-
              <lb/>
            gura eſſe _MAXIMAM_, & </s>
            <s xml:id="echoid-s5996" xml:space="preserve">
              <lb/>
            G M _MINIMAM_, in ſe-
              <lb/>
            ptima, & </s>
            <s xml:id="echoid-s5997" xml:space="preserve">octaua figura, tantùm, quoniam in nona ipſa _MINIMA_ abit in
              <lb/>
            punctum.</s>
            <s xml:id="echoid-s5998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5999" xml:space="preserve">Quò autem ad _MINIMAM_ oſtendendam. </s>
            <s xml:id="echoid-s6000" xml:space="preserve">Ducatur ex M, Ellipſim
              <lb/>
            contingens M P maiori axi occurrens in P; </s>
            <s xml:id="echoid-s6001" xml:space="preserve">appliceturque M Q.</s>
            <s xml:id="echoid-s6002" xml:space="preserve"/>
          </p>
          <note symbol="f" position="left" xml:space="preserve">25. primi
            <lb/>
          conic.</note>
          <p>
            <s xml:id="echoid-s6003" xml:space="preserve">Et quoniam in angulo aſymptotali H L I ſumptum eſt punctum Q, ex-
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