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

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        <div xml:id="echoid-div149" type="section" level="1" n="82">
          <p>
            <s xml:id="echoid-s1717" xml:space="preserve">
              <pb o="50" file="0074" n="74" rhead=""/>
            adſcribatur per B Hyperbole ABC, quæ ipſi HBI erit ſimilis (cum
              <note symbol="a" position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">5. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            latera ſint proportionalia) eritque ei circumſcripta (cum ſit maiorum late- rum) & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">erit _MINIMA_ quæſita. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Nam quælibet alia adſcripta cum recto BE,
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve">3. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſed cum tranſuerſo, quod ipſo BD ſit minus eſt maior ipfa ABC; </s>
            <s xml:id="echoid-s1720" xml:space="preserve">quælibet verò adſcripta cum eodem recto BE, ſed cum tranſuerſo BM, quod excedat
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve">ibidem.</note>
            BD eſt quidem minor ipſa ABC, ſed omnino ſecat Hyperbolen HBI, cum
              <lb/>
            iuncta regula ME, & </s>
            <s xml:id="echoid-s1721" xml:space="preserve">producta omnino ſecet regulam GF infra contingen-
              <lb/>
            tem BE. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">Vnde ipſa ABC erit _MINIMA_ circumſcripta cum dato recto BE,
              <lb/>
            vti quærebatur. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">Quod vltimò faciendum erat.</s>
            <s xml:id="echoid-s1724" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="1" n="83">
          <head xml:id="echoid-head88" xml:space="preserve">PROBL. X. PROP. XXV.</head>
          <p>
            <s xml:id="echoid-s1725" xml:space="preserve">Datæ Ellipſi, cum dato latere, quodminus ſit eius recto, per ip-
              <lb/>
            ſius verticem MAXIMAM Ellipſim inſcribere: </s>
            <s xml:id="echoid-s1726" xml:space="preserve">& </s>
            <s xml:id="echoid-s1727" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1729" xml:space="preserve">Datæ Ellipſi, cum dato recto latere, quod maius ſit eius recto,
              <lb/>
            per ipſius verticem MINIMAM Ellipſim circumſcribere.</s>
            <s xml:id="echoid-s1730" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1731" xml:space="preserve">SIt data Ellipſis ABC, cuius tranſuerſum BD, rectum BE, regula DE:
              <lb/>
            </s>
            <s xml:id="echoid-s1732" xml:space="preserve">oportet per verticem B, cum dato recto BF _MAXIMAM_ Ellipſim inſcri-
              <lb/>
            bere, neceſſe eſt autem, quod rectum datum BF
              <lb/>
              <figure xlink:label="fig-0074-01" xlink:href="fig-0074-01a" number="44">
                <image file="0074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0074-01"/>
              </figure>
            minus ſit recto BE (ſi enim ei æquale eſſet, vel
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0074-04" xlink:href="note-0074-04a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            maius, etiam deſcribenda Ellipſis, vel eſſet ea- dem cum data ABC, vel hanc ipſam ſecaret, vt
              <lb/>
            ſatis patet, cum vel ipſarum regulæ ſimul con-
              <lb/>
            gruerent, vel ſe mutuò ſecarent.)</s>
            <s xml:id="echoid-s1733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1734" xml:space="preserve">Adſcribatur cum eodem trãſuerſo BD,
              <note symbol="b" position="left" xlink:label="note-0074-05" xlink:href="note-0074-05a" xml:space="preserve">7. huius.</note>
            que dato recto BF, per verticem B, Ellipſis GBL:
              <lb/>
            </s>
            <s xml:id="echoid-s1735" xml:space="preserve">& </s>
            <s xml:id="echoid-s1736" xml:space="preserve">hæc erit _MAXIMA_ quæſita. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">Nam quælibet alia
              <lb/>
            eidem ABC adſcripta cum recto BF, ſed cum
              <lb/>
            tranſuerſo, quod minus ſit BD, eſt minor
              <note symbol="c" position="left" xlink:label="note-0074-06" xlink:href="note-0074-06a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            GBL, quælibet verò adſcripta cum tranſuerſo
              <lb/>
            BM, quod excedat BD eſt quidem maior
              <note symbol="d" position="left" xlink:label="note-0074-07" xlink:href="note-0074-07a" xml:space="preserve">ibidem.</note>
            GBL, ſed omnino ſecat Ellipſim datam ABC cum & </s>
            <s xml:id="echoid-s1738" xml:space="preserve">iuncta regula
              <note symbol="e" position="left" xlink:label="note-0074-08" xlink:href="note-0074-08a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            omnino ſecet regulam ED. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">Quare Ellipſis GBL erit _MAXIMA_ quæſita in-
              <lb/>
            ſcripta cum recto dato BF. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1741" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1743" xml:space="preserve">Sit iam data Ellipſis GBL, cuius tranſuerſum BD, rectum BF, regula DF,
              <lb/>
            & </s>
            <s xml:id="echoid-s1744" xml:space="preserve">circumſcribenda ſit ci _MINIMA_ Ellipſis cum dato recto BE, quod debet
              <lb/>
            quidem eſſe maius recto BF (nam ſi æquale, vel minus eſſet, deſcribenda
              <lb/>
            quoque Ellipſis, vel eadem eſſet cum data GBL, vel huic eſſet
              <note symbol="f" position="left" xlink:label="note-0074-09" xlink:href="note-0074-09a" xml:space="preserve">ibidem.</note>
            cum vel harum regulæ ſimul congruerent, vel regula deſcribendæ caderet
              <lb/>
            tota intra regulam deſcriptæ GBL.)</s>
            <s xml:id="echoid-s1745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1746" xml:space="preserve">Adſcribatur cum tranſuerſo BD, datoque recto BE, per verticem B,
              <note symbol="g" position="left" xlink:label="note-0074-10" xlink:href="note-0074-10a" xml:space="preserve">7. huius.</note>
            lipſis ABC, quæ erit _MINIMA_ circumſcripta quæſita. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">Quoniam quæcun-
              <lb/>
            que alia adſcripta datæ GBL cum recto BE, ſed cum tranſuerſo, quod maius
              <lb/>
              <note symbol="h" position="left" xlink:label="note-0074-11" xlink:href="note-0074-11a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſit BD, maior eſt ipſa GBL; </s>
            <s xml:id="echoid-s1748" xml:space="preserve">quælibet verò adſcripta cum tranſuerſo BN, quod minus ſit tranſuerſo BD, eſt quidem minor ipſa ABC, ſed omnino
              <note symbol="i" position="left" xlink:label="note-0074-12" xlink:href="note-0074-12a" xml:space="preserve">ibidem.</note>
            </s>
          </p>
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