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

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        <div xml:id="echoid-div142" type="section" level="1" n="81">
          <p>
            <s xml:id="echoid-s1688" xml:space="preserve">
              <pb o="49" file="0073" n="73" rhead=""/>
            rum laterum. </s>
            <s xml:id="echoid-s1689" xml:space="preserve">Dico hanc eſſe _MINIMAM_ quæſitam: </s>
            <s xml:id="echoid-s1690" xml:space="preserve">Nam quælibet alia, quę
              <lb/>
            adſcribitur cum recto maiore ipſo BL, maior eſt ipſa ABC, quælibet
              <note symbol="a" position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">2. Co-
                <lb/>
              rol. 19. h.</note>
            quæ adſcribitur cum recto minore ipſo BL, eſt quidem minor ABC,
              <note symbol="b" position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">ibidem.</note>
            vel ſecat Hyperbolen ABC, quod accidet, cum rectum latus terminet inter
              <lb/>
            E, & </s>
            <s xml:id="echoid-s1691" xml:space="preserve">L, vt in O, nam iuncta regula GO, ſi producatur, infra
              <note symbol="c" position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">1. Co-
                <lb/>
              rol. 19. h.</note>
            BO cum regula DE conueniret, ideoque, & </s>
            <s xml:id="echoid-s1692" xml:space="preserve">ſectiones; </s>
            <s xml:id="echoid-s1693" xml:space="preserve">veltota cadit intra
              <lb/>
            HBI quod fit quando rectum latus, vel ſit idem cum recto BE, vel
              <note symbol="d" position="right" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve">3. 1. Co-
                <lb/>
              rol. 19. h.</note>
            ipſo BE, quale eſt BF, quoniam ſi iungatur regula GF, ipſa, atque regula
              <lb/>
            DE ſe mutuò ſecarent ſupra contingentem BE, ideoque infra diſiunctim ſi-
              <lb/>
            mul procederent. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">Quare huiuſmodi Hyperbole ABC, quæ ſimilis eſt datæ
              <lb/>
            HBI erit _MINIMA_ circumſcripta quæſita. </s>
            <s xml:id="echoid-s1695" xml:space="preserve">Quod ſecundò faciendum erat.</s>
            <s xml:id="echoid-s1696" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div149" type="section" level="1" n="82">
          <head xml:id="echoid-head87" xml:space="preserve">PROBL. IX. PROP. XXIV.</head>
          <p>
            <s xml:id="echoid-s1697" xml:space="preserve">Datæ Hyperbolæ, cum dato recto latere, quod recto datæ ſit
              <lb/>
            minus, per eius verticem MAXIMAM Hyperbolen inſcribere,
              <lb/>
            & </s>
            <s xml:id="echoid-s1698" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1699" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1700" xml:space="preserve">Datæ Hyperbolæ, cum dato recto latere, quod maius ſit recto
              <lb/>
            datę, per eius verticem MAXIMAM Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s1701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1702" xml:space="preserve">SIt data Hyperbole ABC, cuius tranſuerſum BD, rectum BE, & </s>
            <s xml:id="echoid-s1703" xml:space="preserve">regula
              <lb/>
            DE; </s>
            <s xml:id="echoid-s1704" xml:space="preserve">oportet per eius verticem B, cum dato recto BF, quod minus ſit re-
              <lb/>
            cto BE, _MAXIMAM_ Hyperbolen inſcribere.</s>
            <s xml:id="echoid-s1705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1706" xml:space="preserve">Ducatur FG parallela ad ED, & </s>
            <s xml:id="echoid-s1707" xml:space="preserve">cũ
              <lb/>
              <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a" number="43">
                <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0073-01"/>
              </figure>
            tranſuerſo BG, rectoque BF adſcriba-
              <lb/>
            tur per B ipſi ABC, Hyperbole
              <note symbol="a" position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve">6. huius.</note>
            quæ datæ ABC erit ſimilis (cum ipſa-
              <lb/>
            rum latera ſint proportionalia) eritque
              <lb/>
            inſcripta (cum ſit minorum
              <note symbol="b" position="right" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve">5. Co-
                <lb/>
              rol. 19. h.</note>
            quàm dico eſſe _MAXIMAM_ quæſitam:
              <lb/>
            </s>
            <s xml:id="echoid-s1708" xml:space="preserve">quoniam quælibet alia adſcripta cum
              <lb/>
            recto BF, ſed cum tranſuerſo, quod ex-
              <lb/>
            cedat BG minor eſt ipſa HBI,
              <note symbol="c" position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve">3. Co-
                <lb/>
              rol. 19. h.</note>
            que verò adſcripta cum eodem recto
              <lb/>
            BE, ſed cum tranſuerſo, quod ſit minus
              <lb/>
            tranſuerſo BG, quale eſt BL, eſt quidẽ
              <lb/>
            maior ipſa HBI, ſed omnino ſecat
              <note symbol="d" position="right" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">ibidem.</note>
            perbolen ABC cum iũcta regula
              <note symbol="e" position="right" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve">1. Co-
                <lb/>
              rol. 19. h.</note>
            & </s>
            <s xml:id="echoid-s1709" xml:space="preserve">producta, regulam DE infra contin-
              <lb/>
            gentem BE omnino ſecet: </s>
            <s xml:id="echoid-s1710" xml:space="preserve">quare ipſa
              <lb/>
            HBI erit _MAXIMA_ inſcripta cum dato
              <lb/>
            recto BF, Quod primò, &</s>
            <s xml:id="echoid-s1711" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1713" xml:space="preserve">Sit iam data Hyperbole HBI, cuius
              <lb/>
            regula GF, & </s>
            <s xml:id="echoid-s1714" xml:space="preserve">datum rectum latus ſit BE ipſo BF maius, cum quo oporteat
              <lb/>
            _MINIMAM_ Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s1715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1716" xml:space="preserve">Agatur ED ipſi FG æ quidiſtans, & </s>
            <s xml:id="echoid-s1717" xml:space="preserve">cum regula ED, datæ Hyperbolæ </s>
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