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

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          <head xml:id="echoid-head11" xml:space="preserve">DE MAXIMIS, ET MINIMIS</head>
          <head xml:id="echoid-head12" xml:space="preserve">Geometrica diuinatio in V. conic.
            <lb/>
          Apoll. Pergæi.</head>
          <head xml:id="echoid-head13" style="it" xml:space="preserve">LIBER PRIMVS.</head>
          <head xml:id="echoid-head14" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s324" xml:space="preserve">_A_NTEQV AM inſtitutum opus aggrediamur, ſiquidem in
              <lb/>
            ipſo frequenter accider vti, proferreque affectiones propoſi-
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            tionum 11. </s>
            <s xml:id="echoid-s325" xml:space="preserve">12. </s>
            <s xml:id="echoid-s326" xml:space="preserve">ac 13. </s>
            <s xml:id="echoid-s327" xml:space="preserve">primi conic. </s>
            <s xml:id="echoid-s328" xml:space="preserve">non erit fortaſſe omninò
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            incongruum meas earundem demonſtrationes hic exhibere,
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            quales olim, cum primùm ad elementa conica me conuerte-
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            rem, aliter ac breuius vnico tantùm Theoremate concludi poſſe animaduer-
              <lb/>
            ti, eaſque proponi enunciationibus, vtirebar genuinis, ac proximis ad trium
              <lb/>
            coni-ſectionum, Parabolæ, nempe, Hyperbolæ, & </s>
            <s xml:id="echoid-s329" xml:space="preserve">Ellipſis laterum inuen-
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            tionem. </s>
            <s xml:id="echoid-s330" xml:space="preserve">Verùm antea mihi detur, vt quibuſdam morem gerens, qui tres
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              <lb/>
            prædictas Apollonij propoſitiones difſiciles admodum exiſtimant, ob nimium
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            in ea vſum 23. </s>
            <s xml:id="echoid-s331" xml:space="preserve">ſexti Elementorum; </s>
            <s xml:id="echoid-s332" xml:space="preserve">earundem demonſtr ationes ſingillatim
              <lb/>
            afferre poſsim eodem penitus modo, quo aliquibus, voce, & </s>
            <s xml:id="echoid-s333" xml:space="preserve">ſcriptis expli-
              <lb/>
            care ſolitus fui, hoc eſt ſine compoſita proportione, quam, neſcio quaratione
              <lb/>
            faſtidiant.</s>
            <s xml:id="echoid-s334" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s335" xml:space="preserve">Stantibus igitur ijſdem hypoteſibus, expoſitionibus, ac conſtructionibus
              <unsure/>
              <lb/>
            prædictarum Apoll. </s>
            <s xml:id="echoid-s336" xml:space="preserve">propoſitionum, adhibitiſque figuris, quæ ibi in Comman-
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            dini verſione.</s>
            <s xml:id="echoid-s337" xml:space="preserve"/>
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            <s xml:id="echoid-s338" xml:space="preserve">_QVo ad 11. </s>
            <s xml:id="echoid-s339" xml:space="preserve">primi conic. </s>
            <s xml:id="echoid-s340" xml:space="preserve">poſt ea verba_ Rectangulum igitur MLN æquale eſt
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            quadrato K L ſequatur ſic.</s>
            <s xml:id="echoid-s341" xml:space="preserve"/>
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            <s xml:id="echoid-s342" xml:space="preserve">Itaque, quoniam quadratum BC ad rectangulum BAC eſt vt HF
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            ad FA ex conſtructione, & </s>
            <s xml:id="echoid-s343" xml:space="preserve">rectangulum BAC ad rectangulum ACB vt AB
              <lb/>
            ad BC, vel vt ablata BF ad ablatam BG, hoc eſt vt reliqua FA ad reliquam
              <lb/>
            GC, ſiue ad LN, ergo ex æquo quadratum BC ad rectangulum ACB, vel
              <lb/>
            recta BC ad CA, vel BG ad GF, vel ML ad LF, erit vt HF ad LN, ideoque
              <lb/>
            rectangulum ſub extremis ML, LN, ſiue quadratum KL æquatur rectangu-
              <lb/>
            lo HFL. </s>
            <s xml:id="echoid-s344" xml:space="preserve">_Vocetur autem huiuſmodi ſectio & </s>
            <s xml:id="echoid-s345" xml:space="preserve">c._ </s>
            <s xml:id="echoid-s346" xml:space="preserve">vt ibi vſque ad finem.</s>
            <s xml:id="echoid-s347" xml:space="preserve"/>
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            <s xml:id="echoid-s348" xml:space="preserve">Quo ad 12. </s>
            <s xml:id="echoid-s349" xml:space="preserve">primi poſt ea verba, _ergo rectangulum RNS æquale eſt MN qua-_
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            _drato_, ſic dicatur.</s>
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