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

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            cioppoſitas, ſit infinitæ extenſionis, ſecaret omnino Parabolen AGC, vt
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            per ſe patet: </s>
            <s xml:id="echoid-s4188" xml:space="preserve">quapropter Hyperbole ABC erit _MINIMA_ circumſcripta quę-
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            ſita. </s>
            <s xml:id="echoid-s4189" xml:space="preserve">Quod ſecundò faciendum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s4190" xml:space="preserve"/>
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        <div xml:id="echoid-div405" type="section" level="1" n="170">
          <head xml:id="echoid-head175" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s4191" xml:space="preserve">HAEC de MAXIMARVM, & </s>
            <s xml:id="echoid-s4192" xml:space="preserve">MINIMARVM coni- ſe-
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            ctionum, circuli, & </s>
            <s xml:id="echoid-s4193" xml:space="preserve">anguli reciproca inſcriptione, ac circumſcri-
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            ptione, per punctum in ipſis, vel intra, vel extra datum, iuxta
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            ſæpius memoratam definitionem, hactenus pertractaſſe ſuffi-
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            iat, quæ ſi grata vobis fuiſſe perceperimus, multa his ſimilia, & </s>
            <s xml:id="echoid-s4194" xml:space="preserve">alia
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            quàm plurima ad aliud tempus proferemus. </s>
            <s xml:id="echoid-s4195" xml:space="preserve">Cæterum, in proximè ſequenti-
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            bus, quæ ad vberiorem doctrinam, & </s>
            <s xml:id="echoid-s4196" xml:space="preserve">alteri præſertim huius operis parti ma-
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            xime conducunt, hac omiſſa definitione, inſcriptio, & </s>
            <s xml:id="echoid-s4197" xml:space="preserve">circumſcriptio aliter fiet,
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            prout in ipſis propoſitionibus exponetur.</s>
            <s xml:id="echoid-s4198" xml:space="preserve"/>
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        <div xml:id="echoid-div406" type="section" level="1" n="171">
          <head xml:id="echoid-head176" xml:space="preserve">LEMMA XI. PROP. LXXIX.</head>
          <p>
            <s xml:id="echoid-s4199" xml:space="preserve">Si recta AB ſecta fuerit in C, & </s>
            <s xml:id="echoid-s4200" xml:space="preserve">in D, ita vt AB ad BC, ſit vt
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            AD ad DC: </s>
            <s xml:id="echoid-s4201" xml:space="preserve">Dico ſi BD bifariam ſecetur in E, punctum E cadere
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            inter B, & </s>
            <s xml:id="echoid-s4202" xml:space="preserve">C, & </s>
            <s xml:id="echoid-s4203" xml:space="preserve">rectangulum AEC, æquari quadrato ED.</s>
            <s xml:id="echoid-s4204" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4205" xml:space="preserve">CVm ſit enim AB ad BC, vt AD ad DC, erit permu-
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              <figure xlink:label="fig-0148-01" xlink:href="fig-0148-01a" number="114">
                <image file="0148-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0148-01"/>
              </figure>
            tando BA ad AD, vt BC ad CD, ſed eſt BA ma-
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            ior AD, quare BC erit maior CD: </s>
            <s xml:id="echoid-s4206" xml:space="preserve">ex quo punctum E
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            bifariam ſecans BD cadit inter B, & </s>
            <s xml:id="echoid-s4207" xml:space="preserve">C.</s>
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          </p>
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            <s xml:id="echoid-s4209" xml:space="preserve">Ampliùs producatur BA ad F, & </s>
            <s xml:id="echoid-s4210" xml:space="preserve">ſecetur AF æqualis
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            AD.</s>
            <s xml:id="echoid-s4211" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4212" xml:space="preserve">Iam cum demonſtratum ſit eſſe BA ad AD, vt BC ad
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            CD, erit BA ad AF, vt BC ad CD; </s>
            <s xml:id="echoid-s4213" xml:space="preserve">& </s>
            <s xml:id="echoid-s4214" xml:space="preserve">componendo BF
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            ad FA, vt BD ad DC; </s>
            <s xml:id="echoid-s4215" xml:space="preserve">& </s>
            <s xml:id="echoid-s4216" xml:space="preserve">ſumptis antecedentium dimi-
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            dijs, EA ad AF, ſiue ad AD, vt ED ad DC, & </s>
            <s xml:id="echoid-s4217" xml:space="preserve">per con-
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            uerſionem rationis, AE ad ED, vt DE ad EC, vnde re-
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            ctãgulum AEC ęquabitur quadrato ED. </s>
            <s xml:id="echoid-s4218" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s4219" xml:space="preserve">c.</s>
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