Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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          <head xml:id="echoid-head231" xml:space="preserve">THEOR. II. PROP. V.</head>
          <p>
            <s xml:id="echoid-s5238" xml:space="preserve">MINIMA linearum in Hyperbola ducibilium ad ipſius pe-
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            ripheriam à puncto axis intra ſectionem ſumpto, quod diſtet à
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            vertice per interuallum, non maius quàm dimidium recti late-
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            ris, eſt idem axis ſegmentum inter punctum, & </s>
            <s xml:id="echoid-s5239" xml:space="preserve">verticem inter-
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            ceptum. </s>
            <s xml:id="echoid-s5240" xml:space="preserve">Aliarum autem, quæ cum MINIMA minorem con-
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            ſtituit angulum minor eſt.</s>
            <s xml:id="echoid-s5241" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5242" xml:space="preserve">ESto Hyperbole A B C, cuius ſegmentum axis B D non excedat dimi-
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            dium recti lateris B F (quod axi ordinatim applicetur, &</s>
            <s xml:id="echoid-s5243" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s5244" xml:space="preserve">Dico
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            D B eſſe _MINIMAM_ ducibilium ex ipſo puncto D ad Hyperbolæ peri-
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            pheriam A B C, &</s>
            <s xml:id="echoid-s5245" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5247" xml:space="preserve">Sumatur in directum axi, tranſuerſum latus B E, iungaturque regula E F,
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            & </s>
            <s xml:id="echoid-s5248" xml:space="preserve">producatur; </s>
            <s xml:id="echoid-s5249" xml:space="preserve">appliceturque per D ordinata A D C, regulæ occurrens
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            in G.</s>
            <s xml:id="echoid-s5250" xml:space="preserve"/>
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          <figure number="147">
            <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0186-01"/>
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            <s xml:id="echoid-s5251" xml:space="preserve">Iam, cum in triangulo E D G, ſit D G maior B F, & </s>
            <s xml:id="echoid-s5252" xml:space="preserve">B F maior ſegmen-
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            to B D (ex hypoteſi) erit D G eò maior ipſo ſegmento D B, quare re-
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            ctangulum G D B, ſiue quadratum A D, maius erit quadrato D B; </s>
            <s xml:id="echoid-s5253" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">Coroll.
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              primę pri.
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              mi huius.</note>
            eſt linea D A maior ipſa D B.</s>
            <s xml:id="echoid-s5254" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5255" xml:space="preserve">Eodem modò, ac in Parabola, oſtendetur D A minorem eſſe quacun-
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            que educta D H infra D A, & </s>
            <s xml:id="echoid-s5256" xml:space="preserve">D H adhuc minor D R, &</s>
            <s xml:id="echoid-s5257" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5259" xml:space="preserve">Nunc verò ſit quælibet D L ducta ex D ſupra D A, & </s>
            <s xml:id="echoid-s5260" xml:space="preserve">perL applice-
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            tur L M, quę producatur, donec regulæ E F occurrat in N. </s>
            <s xml:id="echoid-s5261" xml:space="preserve">Erit in trian-
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            gulo E D G, recta M N maior B F, ſed B F maior eſt aggregato B D </s>
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