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

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          <p>
            <s xml:id="echoid-s1575" xml:space="preserve">
              <pb o="45" file="0069" n="69" rhead=""/>
            eſt quidem maior; </s>
            <s xml:id="echoid-s1576" xml:space="preserve">ſed omnino ſecat Hyperbolen ABC, quoniam
              <note symbol="a" position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">ibidem.</note>
              <note symbol="b" position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            regula MN infra contingentem BM ſecat regulam EFO. </s>
            <s xml:id="echoid-s1577" xml:space="preserve">Vnde Parabole
              <lb/>
            GHB erit _MAXIMA_ inſcripta, &</s>
            <s xml:id="echoid-s1578" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1579" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1580" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1582" xml:space="preserve">Sit verò data Parabole GBH, cuius vertex B, diameter BD, rectum BF,
              <lb/>
            & </s>
            <s xml:id="echoid-s1583" xml:space="preserve">regula FI, & </s>
            <s xml:id="echoid-s1584" xml:space="preserve">circumſcribenda ſit ei cum dato tranſuerſo BE _MINIMA_
              <lb/>
            Hyperbole.</s>
            <s xml:id="echoid-s1585" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1586" xml:space="preserve">Adſcribatur Parabolæ GBH, per verticem B, cum dato tranſuerſo
              <note symbol="c" position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">6. prop.
                <lb/>
              19. huius.</note>
            Hyperbole ABC, cuius rectum latus idem ſit, ac rectum BF datæ Parabolæ.
              <lb/>
            </s>
            <s xml:id="echoid-s1587" xml:space="preserve">Dico huiuſmodi Hyperbolen eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s1588" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1589" xml:space="preserve">Nam quælibet alia Hyperbole per verticem B datæ Hyperbolæ ABC ad-
              <lb/>
            ſcripta, cum eodem tranſuerſo BE, ſed cum recto BM, quod maius ſit recto
              <lb/>
            BF ipſa ABC maior eſt; </s>
            <s xml:id="echoid-s1590" xml:space="preserve">quælibet verò adſcripta cum recto BL, quod
              <note symbol="d" position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ciat à recto BF, eadem ABC eſt quidem minor, ſed omnino ſecat
              <note symbol="e" position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">ibidem.</note>
              <note symbol="f" position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">1. corol.
                <lb/>
              prop. 19.
                <lb/>
              huius.</note>
            bolen GBH, cum eius regula ELP infra contingentem BF producta ſecet re-
              <lb/>
            gulam FI datæ Parabolæ GBH. </s>
            <s xml:id="echoid-s1591" xml:space="preserve">Quare huiuſmodi Hyperbole ABC erit _MI_-
              <lb/>
            _NIMA_ circumſcriptibilium datæ Parabolæ ABC per verticem B, & </s>
            <s xml:id="echoid-s1592" xml:space="preserve">cum
              <lb/>
            dato tranſuerſo BE. </s>
            <s xml:id="echoid-s1593" xml:space="preserve">Quod erat ſecundò, &</s>
            <s xml:id="echoid-s1594" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1595" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div137" type="section" level="1" n="79">
          <head xml:id="echoid-head84" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s1596" xml:space="preserve">ALiquis forſan hoc loco vereri poſſet enunciationes, vel ſaltem ar-
              <lb/>
            gumentum MAXIMARVM, MINIMARV MQVE ſe-
              <lb/>
            ctionum inſcriptibilium, ac circumſ criptibilium habuiſſe me à
              <lb/>
            celeberrimo ſui æui Mathematico Maurolico, & </s>
            <s xml:id="echoid-s1597" xml:space="preserve">hoc quidem,
              <lb/>
            vt fateor, haud temerè; </s>
            <s xml:id="echoid-s1598" xml:space="preserve">nam quod in duabus præcedentibus propoſitionibus
              <lb/>
            exponitur, profertur quoque in eius quinto conicorum libro, ab ipſo, vnà
              <lb/>
            cum ſexto iam ſupra nonaginta annos proprio Marte ſuppleto, quamuis typis
              <lb/>
            Meſſanæ tradito non antea annum 1654. </s>
            <s xml:id="echoid-s1599" xml:space="preserve">ſedula opera eximij Mathemati-
              <lb/>
            ci, ac Philoſophi præſtantiſsimi 10. </s>
            <s xml:id="echoid-s1600" xml:space="preserve">Alphonſi Borelli, qui, vt ipſemet aſſerit,
              <lb/>
            ex multis Maurolici poſthumis lucubrationibus, apud Auctoris hæredes tunc
              <lb/>
            extantibus, prædictum opus publici iuris fieri curauit, idemque mihi à duobus
              <lb/>
            circiter annis primò mdicauit, quod è Meſſana anxiè petiens, tandem ab hinc
              <lb/>
            paucis menſibus conſecutus fui. </s>
            <s xml:id="echoid-s1601" xml:space="preserve">At quicunque æquo, gratoque animo Mau-
              <lb/>
            rolici demonſtrationes, cum meis conferat, dum diuerſa, expeditaque metho-
              <lb/>
            do generatim oſtenditur, ex præmiſſo Theoremate Lemmatico, duobus tan-
              <lb/>
            tum Problematibus, vnicoque Corollario, totum id, quod integro libro pecu-
              <lb/>
            liariter à Maurolico 24. </s>
            <s xml:id="echoid-s1602" xml:space="preserve">Propoſitionibus, decẽque, aut Corollarijs, aut Scho-
              <lb/>
            lijs demonſtratur; </s>
            <s xml:id="echoid-s1603" xml:space="preserve">curabitque vlterius procedendo, reliquum mei operis per-
              <lb/>
            currere, in quo, tot aliæ, ex his cmanantes concluſiones reperiuntur, à nemi-
              <lb/>
            ne, quod ſciam, hactenus animaduerſæ, hic quidem, vt ſpero, à tali ſuſpi-
              <lb/>
            cione omnino remouebitur, & </s>
            <s xml:id="echoid-s1604" xml:space="preserve">de prædictis promeritum ius, qualecunque ſit,
              <lb/>
            mihi facilè tribuet. </s>
            <s xml:id="echoid-s1605" xml:space="preserve">Sed ne tempus fruſtra teramus, incæptum opus proſe-
              <lb/>
            quamur.</s>
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