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

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          <p>
            <s xml:id="echoid-s4424" xml:space="preserve">Inſuper, ſit alia adſcripta Ellipſis AHCI, cuius ſegmenta diametri HG,
              <lb/>
            GI ſint adhuc magis inæqualia, quàm ſegmenta EG, GF: </s>
            <s xml:id="echoid-s4425" xml:space="preserve">dico AECF mi-
              <lb/>
            rcm eſſe Ellipſi AHCI. </s>
            <s xml:id="echoid-s4426" xml:space="preserve">Oſtendetur enim, vt ſupra, rectangulum EGF ma-
              <lb/>
            ius eſſe rectangulo HGI, & </s>
            <s xml:id="echoid-s4427" xml:space="preserve">rectum latus Ellipſis AECF, minus eſſe recto
              <lb/>
            AHCI, ſiue Ellipſim AECF inſcribi poſſe AHCI, hoc eſt ipſa minorem eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s4428" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s4429" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div431" type="section" level="1" n="181">
          <head xml:id="echoid-head186" xml:space="preserve">THEOR. XLI. PROP. LXXXVI.</head>
          <p>
            <s xml:id="echoid-s4430" xml:space="preserve">MAXIMA ſemi-diametrorum, à centro Ellipſeos eductarum,
              <lb/>
            eſt ſemi-axis maior, MINIMA verò ſemi-axis minor: </s>
            <s xml:id="echoid-s4431" xml:space="preserve">aliarum
              <lb/>
            autem, quæ cum MAXIMA minorem conſtituit angulum maior
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s4432" xml:space="preserve">& </s>
            <s xml:id="echoid-s4433" xml:space="preserve">quatuor ſunt in Ellipſi æquales ſemi-diametri, quarum vna
              <lb/>
            tantùm cadit in vnoquoque Ellipſis quadrante, genito ex axium
              <lb/>
            interſectione.</s>
            <s xml:id="echoid-s4434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4435" xml:space="preserve">SIt Ellipſis ABCD, cuius axis maior BD; </s>
            <s xml:id="echoid-s4436" xml:space="preserve">minor AC, centrum E. </s>
            <s xml:id="echoid-s4437" xml:space="preserve">Dico
              <lb/>
            primùm maiorem ſemi-axim EB eſſe omnium ſemi-diametrorum _MA-_
              <lb/>
            _XIMAM_, & </s>
            <s xml:id="echoid-s4438" xml:space="preserve">ſemi-axim minorem EA omnium _MINIMAM_.</s>
            <s xml:id="echoid-s4439" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4440" xml:space="preserve">Cum centro enim E, & </s>
            <s xml:id="echoid-s4441" xml:space="preserve">interuallo EB
              <lb/>
              <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a" number="123">
                <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0156-01"/>
              </figure>
            deſcripto circulo BHD, ipſæ cadit totus
              <lb/>
            extra Ellipſim, cum eiſit
              <note symbol="a" position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">ex26. h.</note>
            vnde ſemi-diameter EB erit _MAXIMA_;
              <lb/>
            </s>
            <s xml:id="echoid-s4442" xml:space="preserve">& </s>
            <s xml:id="echoid-s4443" xml:space="preserve">facto cétro E, cum radio EA deſcripto
              <lb/>
            circulo EOC, ipſæ totus cadet intra Elli-
              <lb/>
            pſim, cum ei ſit inſcriptus, ex quo, E
              <note symbol="b" position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">ibidem.</note>
            erit _MINIMA_. </s>
            <s xml:id="echoid-s4444" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s4445" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4446" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4447" xml:space="preserve">Ampliùs in quadrãte Ellipſeos AFCE
              <lb/>
            ductæ ſint quotcunque ſemi-diametri EF,
              <lb/>
            EG, & </s>
            <s xml:id="echoid-s4448" xml:space="preserve">ſit angulus BEF minor BEG: </s>
            <s xml:id="echoid-s4449" xml:space="preserve">dico
              <lb/>
            EF maiorem eſſe EG.</s>
            <s xml:id="echoid-s4450" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4451" xml:space="preserve">Applicentur enim per F, G, ad maio-
              <lb/>
            rem axim BE rectæ KF, LG, quæ produ-
              <lb/>
            ctæ, circuli peripheriæ BIH occurrant in I,
              <lb/>
            M, & </s>
            <s xml:id="echoid-s4452" xml:space="preserve">iungantur E I, EM.</s>
            <s xml:id="echoid-s4453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4454" xml:space="preserve">Erit in ſemi-circulo BHD, quadratum ML ad IK, vt rectangulum DLB
              <lb/>
            ad DKB; </s>
            <s xml:id="echoid-s4455" xml:space="preserve">& </s>
            <s xml:id="echoid-s4456" xml:space="preserve">in ſemi-Ellipſi BCD, quadratum GL ad FK, vt idem
              <note symbol="c" position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">2 I. pri-
                <lb/>
              mi conic.</note>
            gulum DLB ad idem DKB, ergo quadratum ML ad IK, erit vt quadratum
              <lb/>
            GL ad FK, ſiue linea ML ad IK, vt pars GL ad partem FK, & </s>
            <s xml:id="echoid-s4457" xml:space="preserve">vt reliqua MG
              <lb/>
            ad reliquam IF, ſed eſt GL maior FK: </s>
            <s xml:id="echoid-s4458" xml:space="preserve">quare MG erit maior I F,
              <note symbol="d" position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">63. h.</note>
            rectangulum MGL ſub maioribus lateribus contentum, maius erit rectan-
              <lb/>
            gulo IFK ſub minoribus, & </s>
            <s xml:id="echoid-s4459" xml:space="preserve">duplum vnius, alterius duplo maius.</s>
            <s xml:id="echoid-s4460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4461" xml:space="preserve">Iam cum triangula EKI, ELM ſint rectangula ad K, L, erunt triangula
              <lb/>
            EFI, EGM obtuſiangula ad F, G, eſtque linea E I æqualis EM, ergo qua-
              <lb/>
            dradratum E I, hoc eſt duo ſimul quadrata EF, F I, cum duplo rectanguli
              <lb/>
            KEI, maiora erunt quadrato EM, ſiue duobus ſimul quadratis EG, </s>
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