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

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            dratum D C ad quadratum B G, quare quadratum B F maius eſt quadra-
              <lb/>
            to B G; </s>
            <s xml:id="echoid-s551" xml:space="preserve">ideoque punctum F cadit extra ſectionem, vt & </s>
            <s xml:id="echoid-s552" xml:space="preserve">quodcunque
              <lb/>
            aliud punctum rectæ A C F, præter C. </s>
            <s xml:id="echoid-s553" xml:space="preserve">Erit ergo recta A C F Parabolen
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            contingens in in C. </s>
            <s xml:id="echoid-s554" xml:space="preserve">Quod erat faciendum.</s>
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        <div xml:id="echoid-div36" type="section" level="1" n="26">
          <head xml:id="echoid-head31" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s556" xml:space="preserve">PRopoſitio 34. </s>
            <s xml:id="echoid-s557" xml:space="preserve">primi conic. </s>
            <s xml:id="echoid-s558" xml:space="preserve">licet ab Apollonio negatiuè ſit demon-
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            ſtrata, facilè tamen ad affirmatiuam reducitur, ſi ex ip-
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            ſa in principio demantur ea verba. </s>
            <s xml:id="echoid-s559" xml:space="preserve">_Si enim fieri po-_
              <lb/>
            _teſt, ſecet vt E C F_, ad finem verò. </s>
            <s xml:id="echoid-s560" xml:space="preserve">_Quod fieri non_
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            _poteſt_; </s>
            <s xml:id="echoid-s561" xml:space="preserve">nam ibi linea H G oſtenditur minor G F, vnde punctum F
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            cadet extra ſectionem, & </s>
            <s xml:id="echoid-s562" xml:space="preserve">ſic quodcunque aliud punctum rectæ E C H
              <lb/>
            præter C, quare ipſa E C H ſectionem continget in C: </s>
            <s xml:id="echoid-s563" xml:space="preserve">ſed vt clariùs
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            idem pateat, en afferemus noſtram directè concluſam demonſtrationem,
              <lb/>
            de qua in præcedenti Monito, præmiſſo tantùm (vice propoſitionis 169.
              <lb/>
            </s>
            <s xml:id="echoid-s564" xml:space="preserve">ſeptimi Pappi, qua indiget Apolloniana propoſitio) ſequenti Lemmate, in
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            quo interim duæ ſimul circuli proprietates detegentur haud iniucundæ.</s>
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          <head xml:id="echoid-head32" xml:space="preserve">LEMMAI. PROP. III.</head>
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            <s xml:id="echoid-s566" xml:space="preserve">Si circuli diameter A B inæqualiter ſecetur in C, & </s>
            <s xml:id="echoid-s567" xml:space="preserve">ad mino-
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            rem partem C B producatur, ita vt ſit A D ad D B, vt A C ad
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            C B, & </s>
            <s xml:id="echoid-s568" xml:space="preserve">ex C erigatur perpendicularis C E, iungaturque D E.
              <lb/>
            </s>
            <s xml:id="echoid-s569" xml:space="preserve">Dico quadratum ipſius D E æquari rectangulo A D B.</s>
            <s xml:id="echoid-s570" xml:space="preserve"/>
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            <s xml:id="echoid-s571" xml:space="preserve">Si verò in recto angulo D C E, quælibet alia ſubtenſa F G
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            applicetur ipſi D E æquidiſtans, productam diametri partem
              <lb/>
            ſecans in F, aut infra D, aut ſupra, & </s>
            <s xml:id="echoid-s572" xml:space="preserve">perpendicularem C E in
              <lb/>
            G. </s>
            <s xml:id="echoid-s573" xml:space="preserve">Dico ampliùs quadratum applicatæ F G ſemper excedere
              <lb/>
            rectangulum A F B.</s>
            <s xml:id="echoid-s574" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s575" xml:space="preserve">QVò ad primum, ſit circuli centrum H, & </s>
            <s xml:id="echoid-s576" xml:space="preserve">iungatur H E.</s>
            <s xml:id="echoid-s577" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s578" xml:space="preserve">Iam cum ſit A D ad D B, vt A C ad C B, erit componendo A D
              <lb/>
            cum D B ad D B, vt A B ad B C, & </s>
            <s xml:id="echoid-s579" xml:space="preserve">ſumptis antecedentium
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            ſubduplis, erit H D ad D B, vt H B ad B C, & </s>
            <s xml:id="echoid-s580" xml:space="preserve">perlconuerſionem rationis
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            D H ad H B, vt B H ad H C, vel vt D H ad H E (ipſi H B æqualis) ita
              <lb/>
            H E ad H C: </s>
            <s xml:id="echoid-s581" xml:space="preserve">quare triangula D H E, E H C, cum habeant circa com-
              <lb/>
            munem angulnm H latera proportionalia, ſimilia erunt, vnde angulus
              <lb/>
            D E H æquabitur angulo E C H, ſiue rectus erit, ideoque D E circulum
              <lb/>
            continget, hoc eſt quadratum D E æquabitur rectangulo A D B. </s>
            <s xml:id="echoid-s582" xml:space="preserve">Quod
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            primò, &</s>
            <s xml:id="echoid-s583" xml:space="preserve">c.</s>
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            <s xml:id="echoid-s585" xml:space="preserve">Ampliùs iungantur E B, E A, quas, recta F G producta ſecet, in I &</s>
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