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

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        <div xml:id="echoid-div124" type="section" level="1" n="75">
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          <p>
            <s xml:id="echoid-s1509" xml:space="preserve">Præterea ſit data Ellipſis, vel circulus GHB, cuius diameter BG, rectum
              <lb/>
            BE, regula EG, & </s>
            <s xml:id="echoid-s1510" xml:space="preserve">oporteat per verticem B, _MINIMAM_ Parabolen in pri-
              <lb/>
            ma figura, vel cum dato quocunque tranſuerſo BF, _MINIMAM_ Hyperbo-
              <lb/>
            len in ſecunda figura, ſiue cum dato tranſuerſo BF, quod in tertia, & </s>
            <s xml:id="echoid-s1511" xml:space="preserve">quarta
              <lb/>
            figura excedat tranſuerſum BG datæ Ellipſis, vel circuli, _MINIMAM_ Elli-
              <lb/>
            pſin circumſcribere.</s>
            <s xml:id="echoid-s1512" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1513" xml:space="preserve">Adſcribatur Ellipſi GHB per verticem B in prima figura parabole
              <note symbol="a" position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">5. 6. 7. h.</note>
            & </s>
            <s xml:id="echoid-s1514" xml:space="preserve">in ſecunda Hyperbole ABC, cum dato tranſuerſo BF, & </s>
            <s xml:id="echoid-s1515" xml:space="preserve">in tertia, & </s>
            <s xml:id="echoid-s1516" xml:space="preserve">quar-
              <lb/>
            ta Ellipſis ABC cum dato tranſuerſo BF; </s>
            <s xml:id="echoid-s1517" xml:space="preserve">& </s>
            <s xml:id="echoid-s1518" xml:space="preserve">harum omnium ſectionum re-
              <lb/>
            ctum latus idem ſit cum recto BE datæ Ellipſis. </s>
            <s xml:id="echoid-s1519" xml:space="preserve">Iam patet ipſam ſectionem
              <lb/>
            ABC datæ GHB circumſcriptam eſſe. </s>
            <s xml:id="echoid-s1520" xml:space="preserve">Inſuper dico talem ſectionem
              <note symbol="b" position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s1521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1522" xml:space="preserve">Nam, in prima figura, quælibet parabola, vel in reliquis, quæcunque eiuſ-
              <lb/>
            dem nominis ſectio adſcripta ſectioni ABC per verticem B, cum eodem
              <lb/>
            tranſuerſo BF, ſed cum recto BL, quod excedat rectum BE ſectionis ABC
              <lb/>
            eadem ſectione eſt maior, quælibet verò adſcripta ſectio cum recto BI,
              <note symbol="c" position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            minus ſit recto BE minor eſt ſectione ABC, ſed Ellipſim GHB omninò
              <note symbol="d" position="right" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
              <note symbol="e" position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            cat cum ipſarum regulæ IN, GE infra contingentem ex vertice ſe mutuò ſe-
              <lb/>
            cent. </s>
            <s xml:id="echoid-s1523" xml:space="preserve">Quare ſectio Parabolæ, vel Hyperbole, aut Ellipſis ABC eſt _MINI_-
              <lb/>
            _MA_ circumſcriptibilium datæ Ellipſi, vel circulo GHB. </s>
            <s xml:id="echoid-s1524" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s1525" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1526" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div129" type="section" level="1" n="76">
          <head xml:id="echoid-head81" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s1527" xml:space="preserve">HInc ſolutio problematum. </s>
            <s xml:id="echoid-s1528" xml:space="preserve">Videlicet: </s>
            <s xml:id="echoid-s1529" xml:space="preserve">Datæ coni-ſectioni circa maio-
              <lb/>
            rem axem, per eius verticem _MAXIMVM_ circulum inſcribere.</s>
            <s xml:id="echoid-s1530" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1531" xml:space="preserve">Item datæ Ellipſi circa minorem axem, per eius verticem _MIMIMVM_ cir-
              <lb/>
            culum circumſcribere.</s>
            <s xml:id="echoid-s1532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1533" xml:space="preserve">Si enim in tribus primis ſuperioribus figuris concipiatur diametrum BD
              <lb/>
            datæ Parabolæ, vel Hyperbolæ, aut Ellipſis ABC eſſe propriæ ſectionis
              <lb/>
            maiorem axem, eiuſque ſegmentum BG æquari recto lateri BE, circa quod
              <lb/>
            adſcripta ſit Ellipſis GHB cũ recto BE: </s>
            <s xml:id="echoid-s1534" xml:space="preserve">ipſa vt ſuperius oſtensũ fuit, erit
              <note symbol="f" position="right" xlink:label="note-0067-06" xlink:href="note-0067-06a" xml:space="preserve">7. prop.
                <lb/>
              huius.</note>
            _XIMA_ inſcriptibilium, eritque Ellipſis æqualium laterum circa axim, quam
              <lb/>
            in Monito poſt primam huius, animaduerſum fuit circulum eſſe. </s>
            <s xml:id="echoid-s1535" xml:space="preserve">Vnde da-
              <lb/>
            tæ coni-ſectioni circa maiorem axim inſcriptus erit _MAXIMVS_ circulus per
              <lb/>
            verticem ſectionis. </s>
            <s xml:id="echoid-s1536" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1537" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1539" xml:space="preserve">Siverò, vt in quarta figura, datæ Ellipſi GHB circa minorem axim BG, & </s>
            <s xml:id="echoid-s1540" xml:space="preserve">
              <lb/>
            cuius rectum latus BE _MINIMVS_ circulorum ſit circumſcribendus; </s>
            <s xml:id="echoid-s1541" xml:space="preserve">ſumpta
              <lb/>
            BF æquali recto BE, ipſa excedet tranſuerſum latus BG datæ Ellipſis GHB
              <lb/>
            (nam ſemper in Ellipſi minor axis ad maiorem, eſt vt maior axis ad latus re-
              <lb/>
            ctum) itaque ſi circa BF Ellipſis adſcribatur ABC, cum recto BE datæ Elli-
              <lb/>
            pſis, ipſa, per ſecundam partem propoſitionis huius, erit _MINIMA_ datæ
              <lb/>
            Ellipſi circumſcriptibilium, ſed talis Ellipſis ABC per Monitũ poſt 1. </s>
            <s xml:id="echoid-s1542" xml:space="preserve">huius,
              <lb/>
            cum ſit æqualium laterum, & </s>
            <s xml:id="echoid-s1543" xml:space="preserve">circa axim, idem eſt, ac circulus. </s>
            <s xml:id="echoid-s1544" xml:space="preserve">Quare da-
              <lb/>
            tæ Ellipſi circa minorem axem per eius verticem _MINIMVS_ circulus circũ-
              <lb/>
            ſcriptus erit. </s>
            <s xml:id="echoid-s1545" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s1546" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1547" xml:space="preserve"/>
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