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

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            <s xml:id="echoid-s5496" xml:space="preserve">
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            axium vertices contingat recta A E, cui intra ſectionem ducta ſit perpen-
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            dicularis A D, quæ priùs maiori axi occurret, vt in D. </s>
            <s xml:id="echoid-s5497" xml:space="preserve">Dico
              <note symbol="a" position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">88. pri-
                <lb/>
              mih.</note>
            D A, & </s>
            <s xml:id="echoid-s5498" xml:space="preserve">quamlibet ipſa minorem F A, eſſe _MINIMAM_ ducibilium ad ſe-
              <lb/>
            ctionis peripheriam A B C, ex punctis D, vel F.</s>
            <s xml:id="echoid-s5499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5500" xml:space="preserve">Nam facto centro D, inter-
              <lb/>
              <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a" number="156">
                <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0196-01"/>
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            uallo D A, ac circulo deſcripto
              <lb/>
            A C G, ipſe cadet totus
              <note symbol="b" position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">92. pri-
                <lb/>
              mi h.</note>
            fectionem A B C, in duobus tan-
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            tùm punctis A, C, eam contin-
              <lb/>
            gens: </s>
            <s xml:id="echoid-s5501" xml:space="preserve">quare quę ducentur ex D
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            ad ſectionis peripheriam, pręter
              <lb/>
            ad puncta A, C, interuallo D A
              <lb/>
            maiores erunt: </s>
            <s xml:id="echoid-s5502" xml:space="preserve">exquo ipſa D A,
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            vel D C erit _MINIMA_, &</s>
            <s xml:id="echoid-s5503" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5504" xml:space="preserve">Si
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            verò interuallum F A minus ſit
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            ipſo D A. </s>
            <s xml:id="echoid-s5505" xml:space="preserve">Cum in circulo A C
              <lb/>
            G ipſum F A diametri ſegmen-
              <lb/>
            tum, in quo centrum non repe-
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            ritur, ſit rectarum _MINIMA_ ad
              <lb/>
            circuli peripheriam ducibilium,
              <lb/>
            eò magis eadem F A _MINIMA_
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            erit ducibilium ex F, ad peri-
              <lb/>
            pheriam circumſcriptę ſectionis
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            A B C. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s5507" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5508" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5509" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5510" xml:space="preserve">Iam, in tertia figura, ſit Elli-
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            pſis A B C, circa minorem axim B D, & </s>
            <s xml:id="echoid-s5511" xml:space="preserve">contingens linea ad punctum A,
              <lb/>
            quod non ſit axium vertex, ſit A E, cui ex contactu A, ducta ſit intra.
              <lb/>
            </s>
            <s xml:id="echoid-s5512" xml:space="preserve">fectionem recta A D, quę poſt occurſum cum maiori axe, occurret quo-
              <lb/>
            que minori, vt in D. </s>
            <s xml:id="echoid-s5513" xml:space="preserve">Dico rectam D A, & </s>
            <s xml:id="echoid-s5514" xml:space="preserve">quamlibet aliam F A ipſa.</s>
            <s xml:id="echoid-s5515" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">88. pri-
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              mi huius.</note>
            D A maiorem, _MAXIMAM_ eſſe ducibilium ex D, vel F, ad Ellipſis peri-
              <lb/>
            pheriam A B C.</s>
            <s xml:id="echoid-s5516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5517" xml:space="preserve">Deſcripto enim circulo A C G ex radio D A, ipſe cadet totus
              <note symbol="d" position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">92. pri-
                <lb/>
              mihuius.</note>
            Ellipſim A B C hanc tantùm contingens in duobus punctis A, C; </s>
            <s xml:id="echoid-s5518" xml:space="preserve">qua-
              <lb/>
            propter, quæ ducentur ex D ad Ellipſis peripheriam, præter ad puncta
              <lb/>
            A, C, diſtantia D A minores erunt: </s>
            <s xml:id="echoid-s5519" xml:space="preserve">vnde D A, vel D C erit _MAXIMA_, &</s>
            <s xml:id="echoid-s5520" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s5521" xml:space="preserve">Si autem interuallum F A maius fuerit ipſo D A. </s>
            <s xml:id="echoid-s5522" xml:space="preserve">Cum in circulo
              <lb/>
            A C G in diametri ſegmento F A ſit circuli centrum, ipſam F
              <lb/>
            A, erit _MAXIMA_ ad circuli peripheriam A C G ducibi-
              <lb/>
            lium, & </s>
            <s xml:id="echoid-s5523" xml:space="preserve">eò magis eadem F A _MAXIMA_ ducibilium
              <lb/>
            ex F, ad peripheriam inſcriptæ Ellipſis A B C. </s>
            <s xml:id="echoid-s5524" xml:space="preserve">
              <lb/>
            Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s5525" xml:space="preserve"/>
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