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

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        <div xml:id="echoid-div315" type="section" level="1" n="136">
          <head xml:id="echoid-head141" xml:space="preserve">PROBL. XXII. PROP. LVI.</head>
          <p>
            <s xml:id="echoid-s3320" xml:space="preserve">Datæ Hyperbolę, per punctum intra ipſam datũ, cum dato recto
              <lb/>
            latere non excedent rectum Hyperbolæ, quæ ſimilis ſit, & </s>
            <s xml:id="echoid-s3321" xml:space="preserve">concen-
              <lb/>
            trica datæ per datum punctum adſcriptæ, MAXIMAM Hyperbo-
              <lb/>
            len inſcribere: </s>
            <s xml:id="echoid-s3322" xml:space="preserve">& </s>
            <s xml:id="echoid-s3323" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s3324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3325" xml:space="preserve">Datæ Hyperbolæ, per punctum extra ipſam datum, cum dato
              <lb/>
            recto latere MINIMAM Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s3326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3327" xml:space="preserve">Oportet autem datum punctum, vel eſſe in angulo aſymptotali,
              <lb/>
            vel in eo, qui eſt ad verticem, dummodo in primò caſu datum re-
              <lb/>
            ctum latus non ſit minus recto eius Hyperbolæ, quæ ſimilis ſit, & </s>
            <s xml:id="echoid-s3328" xml:space="preserve">
              <lb/>
            concentrica datæ per datum punctum adſcriptæ, in ſecundò verò
              <lb/>
            ſit cuiuslibet magnitudinis.</s>
            <s xml:id="echoid-s3329" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3330" xml:space="preserve">SIt data Hyperbole ABC, cuius centrum D, & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">datũ intra ipſam punctum
              <lb/>
            ſit E: </s>
            <s xml:id="echoid-s3332" xml:space="preserve">oportet primò per E, cum dato recto EF _MAXIMAM_ Hyperbo-
              <lb/>
            len inſcribere.</s>
            <s xml:id="echoid-s3333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3334" xml:space="preserve">Iungatur ED ſecãs
              <lb/>
              <figure xlink:label="fig-0123-01" xlink:href="fig-0123-01a" number="88">
                <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0123-01"/>
              </figure>
            ABC in B, & </s>
            <s xml:id="echoid-s3335" xml:space="preserve">per E
              <lb/>
            concipiatur
              <note symbol="a" position="right" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">6. huius.</note>
            bi Hyperbole EN ſi-
              <lb/>
            milis, & </s>
            <s xml:id="echoid-s3336" xml:space="preserve">concentrica
              <lb/>
            datę ABC, cuius re-
              <lb/>
            ctum ſit EG, quod ex
              <lb/>
            more, ordinatim ap-
              <lb/>
            plicetur diametro E
              <lb/>
            B, & </s>
            <s xml:id="echoid-s3337" xml:space="preserve">cum dato recto
              <lb/>
            EF, quod non ſit ma-
              <lb/>
            ius E G, adſcribatur
              <lb/>
            ipſi ABC ſimilis Hy,
              <lb/>
            perbole HEK, cuius centrum ſit I; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">erunt ergo Hyperbolæ EH, EN inter ſe
              <lb/>
            ſimiles, quare vt rectum EF, ad rectum EG, ita ſemi-tranſuerſum EI ad ſe-
              <lb/>
            mi-tranſuerſum ED, & </s>
            <s xml:id="echoid-s3339" xml:space="preserve">ponitur EF non maius EG, quare EI non maius erit
              <lb/>
            ED, ſiue punctum I centrum ſectionis EH, vel cadet in ipſo D, vel infra D
              <lb/>
            centrum ABC, quapropter ipſa EH datæ ABC erit inſcripta.</s>
            <s xml:id="echoid-s3340" xml:space="preserve"/>
          </p>
          <note symbol="b" position="right" xml:space="preserve">48. h.</note>
          <p>
            <s xml:id="echoid-s3341" xml:space="preserve">Ampliùs: </s>
            <s xml:id="echoid-s3342" xml:space="preserve">dico ipſam EH eſſe _MAXIMAM_ quæſitam. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">Nam quælibet alia
              <lb/>
            per E adſcripta, cum eodem recto EF, ſed cum ſemi-tranſuerſo, quod ma-
              <lb/>
            ius ſit ipſo EI, eſt minor ſectione EH, quæ verò cum eodem recto EF,
              <note symbol="c" position="right" xlink:label="note-0123-03" xlink:href="note-0123-03a" xml:space="preserve">3. Co-
                <lb/>
              roll. 19. h.</note>
            cum ſemi-tranſuerſo EO, quod minus ſit EI, qualis ponatur eſſe ſectio EN,
              <lb/>
            eſt quidem maior eadem EH, ſed omnino ſecat datam ABC: </s>
            <s xml:id="echoid-s3344" xml:space="preserve">quoniam
              <note symbol="d" position="right" xlink:label="note-0123-04" xlink:href="note-0123-04a" xml:space="preserve">ibidem.</note>
            ctis DL, IM aſymptotis ſectionum ABC, EH, ipſæ erunt inter ſe parallelæ:</s>
            <s xml:id="echoid-s3345" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-0123-05" xlink:href="note-0123-05a" xml:space="preserve">48. h.</note>
            ductaque OP aſymptoto ſectionis EN, ipſa OP ſecabit IM infra
              <note symbol="f" position="right" xlink:label="note-0123-06" xlink:href="note-0123-06a" xml:space="preserve">Coroll.
                <lb/>
              36. huius.</note>
            tem, ex communi ſectionum vertice E, & </s>
            <s xml:id="echoid-s3346" xml:space="preserve">producta alteri æquidiſtanti </s>
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