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

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          <p>
            <s xml:id="echoid-s4302" xml:space="preserve">
              <pb o="128" file="0152" n="152" rhead=""/>
            tam AC deſcribatur Ellipſis ALCN. </s>
            <s xml:id="echoid-s4303" xml:space="preserve">Dico hanc eſſe _MAXIMAM_
              <note symbol="*" position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">Coroll.
                <lb/>
              57. h.</note>
            quæſitam.</s>
            <s xml:id="echoid-s4304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4305" xml:space="preserve">Nam, in qualibet figura, cum
              <lb/>
            ſit rectangulum DHE, ſiue NGL
              <lb/>
              <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a" number="119">
                <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0152-01"/>
              </figure>
            æquale quadrato HI, ſiue GF,
              <lb/>
            erit NG ad GF, vt GF ad GL, & </s>
            <s xml:id="echoid-s4306" xml:space="preserve">
              <lb/>
            componendo NG cum GF, hoc
              <lb/>
            eſt NK, erit ad GF, vt FG cum
              <lb/>
            GL, ſiue vt KL ad GL, & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">permu-
              <lb/>
            tando NK ad KL, vt GF ad GL,
              <lb/>
            vel vt NG ad GF, vel vt NF
              <note symbol="a" position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">Coroll.
                <lb/>
              12. h.</note>
            FL, quæ ſunt differentiæ, trium
              <lb/>
            proportionalium NG, GF, GL;
              <lb/>
            </s>
            <s xml:id="echoid-s4308" xml:space="preserve">ergo recta KAM tanget
              <note symbol="b" position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">4. h.</note>
            pſim ALCN, ſiue hæc angulo
              <lb/>
            ABC erit inſcripta, ſed in alijs fi-
              <lb/>
            guris, ipſa KAM tangit quoque
              <lb/>
            datã ei ſimul adſcriptam ſectio-
              <lb/>
            nem ABC, (ex conſtructione)
              <lb/>
            adūdem terminum cõmunis ap-
              <lb/>
            plicatæ AC, quapropter Ellipſis ALCN datæ ſectioni, vel circulo
              <note symbol="c" position="left" xlink:label="note-0152-04" xlink:href="note-0152-04a" xml:space="preserve">61. h.</note>
            inſcripta.</s>
            <s xml:id="echoid-s4309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4310" xml:space="preserve">Dico demum hanc eſſe _MAXIMAM_: </s>
            <s xml:id="echoid-s4311" xml:space="preserve">quoniam quæ ipſi adſcribitur per
              <lb/>
            eoſdem terminos applicatæ AC, & </s>
            <s xml:id="echoid-s4312" xml:space="preserve">cum tranſuerſa diametro æquali ipſi LN,
              <lb/>
            _licet minor fuerit eadem ALCN_, ſecat contingentem KAM, in A, atque
              <note symbol="d" position="left" xlink:label="note-0152-05" xlink:href="note-0152-05a" xml:space="preserve">81. h.</note>
            ad partes AK, ſi nempe vertex nouiter adſcriptæ cadat ſupra L; </s>
            <s xml:id="echoid-s4313" xml:space="preserve">vel ad par-
              <lb/>
            tes AM, ſi cadat infra, vt ex ipſa 81. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">huius facilè elicitur: </s>
            <s xml:id="echoid-s4315" xml:space="preserve">cum ergo inouiter
              <lb/>
            adſcripta Ellipſis ſecet contingentem KAM, in ſe ipſam rediens, ſecabit om-
              <lb/>
            nino datam ſectionem ABC, quare Ellipſis ALCN, eſt _MAXIMA_ dato an-
              <lb/>
            gulo, vel ſectioni ABC inſcripta, circa datam applicatam, & </s>
            <s xml:id="echoid-s4316" xml:space="preserve">cum data
              <lb/>
            tranſuerſa diametro DE, immo potiùs ipſa ALCN eſt vnica huiuſmodi con-
              <lb/>
            ditionibus inſcriptibilius. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Quod faciendum, & </s>
            <s xml:id="echoid-s4318" xml:space="preserve">demonſtrandum erat.</s>
            <s xml:id="echoid-s4319" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div419" type="section" level="1" n="175">
          <head xml:id="echoid-head180" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s4320" xml:space="preserve">EX hac conſtat interceptum diametri ſegmentum inter quamlibet appli-
              <lb/>
            tam, & </s>
            <s xml:id="echoid-s4321" xml:space="preserve">verticem, æquale eſſe (in Parabola) intercepto ſegmento eiuſ-
              <lb/>
            dem diametri inter verticem, & </s>
            <s xml:id="echoid-s4322" xml:space="preserve">occurſum contingentis, ductæ ex termino
              <lb/>
            applicatæ, cum diametro: </s>
            <s xml:id="echoid-s4323" xml:space="preserve">in Hyperbola, verò maius, ſed in Ellipſi, vel cir-
              <lb/>
            culo minus eſſe.</s>
            <s xml:id="echoid-s4324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4325" xml:space="preserve">Demonſtratum eſt enim, in ſecunda figura, KB æ qualem eſſe BF, in ter-
              <lb/>
            tia verò KB, minorem BF, & </s>
            <s xml:id="echoid-s4326" xml:space="preserve">in quarta KB maiorem BF.</s>
            <s xml:id="echoid-s4327" xml:space="preserve"/>
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