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

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          <head xml:id="echoid-head232" xml:space="preserve">THEOR. III. PROP. VI.</head>
          <p>
            <s xml:id="echoid-s5279" xml:space="preserve">MAXIMA linearum ad vniuerſam Ellipſis peripheriam du-
              <lb/>
            cibilium, à puncto maioris axis, quod non ſit centrum, ea eſt,
              <lb/>
            in qua centrum. </s>
            <s xml:id="echoid-s5280" xml:space="preserve">Et eductarum ad peripheriam maioris Ellipti-
              <lb/>
            cæ portionis, cuius baſis, ſit recta ad axim ordinatim ducta, ex
              <lb/>
            prędicto puncto; </s>
            <s xml:id="echoid-s5281" xml:space="preserve">quę cum MAXIMA minorem conſtituit an-
              <lb/>
            gulum, maior eſt. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">MINIMA verò in eadem portione, eſt ip-
              <lb/>
            ſa ſemi-applicata.</s>
            <s xml:id="echoid-s5283" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5284" xml:space="preserve">ESto Ellipſis A B C D, cuius axis maior B D, minor H I, centrum E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5285" xml:space="preserve">quodlibet aliud punctum in maiori axe ſit F. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Dico _MAXIMAM_
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            ducibilium ab F ad vniuerſam Ellipſis peripheriam eſſe F D, in qua cen-
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            trum.</s>
            <s xml:id="echoid-s5287" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5288" xml:space="preserve">Nam, quod D F ſit maior reliqua F B patet, cum F D, maior ſit axis
              <lb/>
            dimidio, F B verò minor.</s>
            <s xml:id="echoid-s5289" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5290" xml:space="preserve">Iam, ad quodcunque Ellipticæ peri-
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              <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a" number="148">
                <image file="0188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0188-01"/>
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            pheriæ punctum G, ſit quædam educta
              <lb/>
            F G, & </s>
            <s xml:id="echoid-s5291" xml:space="preserve">iungatnr E G. </s>
            <s xml:id="echoid-s5292" xml:space="preserve">Itaque cum ſe-
              <lb/>
            mi-axis maior E D, ſit _MAXIMA_
              <note symbol="a" position="left" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">86. pri-
                <lb/>
              mi huius.</note>
            mi-diametrorum, ipſa maior erit E G,
              <lb/>
            quibus communi addita E F, erit tota
              <lb/>
            D F maior duobus G E, E F, & </s>
            <s xml:id="echoid-s5293" xml:space="preserve">eò ma-
              <lb/>
            ior vnica F G. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">Quare F D eſt ad vni-
              <lb/>
            uerſam peripheriam ducibilium _MAXI_-
              <lb/>
            _MA_.</s>
            <s xml:id="echoid-s5295" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5296" xml:space="preserve">Inſuper applicetur ex F axi ordinata
              <lb/>
            A F C, & </s>
            <s xml:id="echoid-s5297" xml:space="preserve">ad peripheriam eiuſdem qua-
              <lb/>
            drantis H D E, ductæ ſint ex F duę quę-
              <lb/>
            libet F L, F M, & </s>
            <s xml:id="echoid-s5298" xml:space="preserve">F L minorem, F M
              <lb/>
            verò maiorem angulum efficiat cum
              <lb/>
            _MAXIMA_ F D. </s>
            <s xml:id="echoid-s5299" xml:space="preserve">Dico F L maiorem eſſe
              <lb/>
            F M. </s>
            <s xml:id="echoid-s5300" xml:space="preserve">Iunctis enim E L, E M; </s>
            <s xml:id="echoid-s5301" xml:space="preserve">erit E
              <note symbol="b" position="left" xlink:label="note-0188-02" xlink:href="note-0188-02a" xml:space="preserve">ibidem.</note>
            maior E M, quæ producatur, & </s>
            <s xml:id="echoid-s5302" xml:space="preserve">fiat E O æqualis E L, & </s>
            <s xml:id="echoid-s5303" xml:space="preserve">iungatur F O:
              <lb/>
            </s>
            <s xml:id="echoid-s5304" xml:space="preserve">erunt igitur duo latera F E, E L, duobus F E, E O æqualia, alterum al-
              <lb/>
            teri, ſed angulus F E L maior eſt angulo F E O, ergo baſis F L, maior eſt
              <lb/>
            F O, ſed F O maior eſt F M, (cum in triangulo F M O angulus ad M ob-
              <lb/>
            tuſus ſit, eò quod ſit maior obtuſo F E M) quare F L eò maior erit ipſa
              <lb/>
            F M, quę cum _MAXIMA_ maiorem efficit angulum: </s>
            <s xml:id="echoid-s5305" xml:space="preserve">ſimili modo oſtende-
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            tur F M maiorem eſſe educta F H.</s>
            <s xml:id="echoid-s5306" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5307" xml:space="preserve">De eductis verò ad portionem peripheriæ H A, ita ratiocinabimur.
              <lb/>
            </s>
            <s xml:id="echoid-s5308" xml:space="preserve">Sit enim quælibet F P, & </s>
            <s xml:id="echoid-s5309" xml:space="preserve">per H ſit Ellipſim contingens H Q, quæ cum
              <lb/>
            æquidiſtet axi B F D, ſecabit omnino productam F P extra Ellipſim in Q; </s>
            <s xml:id="echoid-s5310" xml:space="preserve">
              <lb/>
            eritque in triangulo F Q H, latus F H maius latere F Q (cum </s>
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