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

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            <s xml:id="echoid-s3160" xml:space="preserve">
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            nor ſit ſemi-tranſuerſo DB: </s>
            <s xml:id="echoid-s3161" xml:space="preserve">(ſi enim datum punctum eſſet in angulis, qui
              <lb/>
            deinceps ſunt, recta linea per ipſum datum punctum, & </s>
            <s xml:id="echoid-s3162" xml:space="preserve">centrum ſectionis
              <lb/>
            ducta non eſſet eius diameter, cum nunquam ſectioni occurreret, ac
              <note symbol="a" position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">Monit.
                <lb/>
              poſt 11. h.</note>
            problema, iuxta quintam ſecundarum definitionum inſolubile eſſet: </s>
            <s xml:id="echoid-s3163" xml:space="preserve">& </s>
            <s xml:id="echoid-s3164" xml:space="preserve">cum
              <lb/>
            fuerit in angulo ad verticem, vt in ſecunda, niſi diſtantia ED minor ſit ſemi-
              <lb/>
            tranſuerſo DB, Hyperbole ad regulam datæ adſcribi minimè poſſet, vt ſatis
              <lb/>
            patet) oportet per E _MINIMAM_ Hyperbolen circumſcribere, cuius regula
              <lb/>
            eadem ſit cum regula datæ ſectionis.</s>
            <s xml:id="echoid-s3165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3166" xml:space="preserve">Iungatur ED, & </s>
            <s xml:id="echoid-s3167" xml:space="preserve">ad partes ſectionis producatur donec ei occurrat in B,
              <lb/>
            ſumptaq; </s>
            <s xml:id="echoid-s3168" xml:space="preserve">in directum DH æquali DB, erit HB tranſuerſum ſectionis
              <note symbol="b" position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">47. pri-
                <lb/>
              mi conic.</note>
            cuius vertex B: </s>
            <s xml:id="echoid-s3169" xml:space="preserve">ſit ergo BI eius rectum latus, & </s>
            <s xml:id="echoid-s3170" xml:space="preserve">regula HI; </s>
            <s xml:id="echoid-s3171" xml:space="preserve">ſitque EK æqui-
              <lb/>
            diſtans BI, & </s>
            <s xml:id="echoid-s3172" xml:space="preserve">per verticem B, cum tranſuerſo EH, & </s>
            <s xml:id="echoid-s3173" xml:space="preserve">recto EK, ſiue ad ean-
              <lb/>
            dem regulam HI adſcribatur Hyperbole LEM: </s>
            <s xml:id="echoid-s3174" xml:space="preserve">patet ipſam datæ ABC eſſe
              <lb/>
            inſcriptam, cum ſimul ſint nun quam coeuntes.</s>
            <s xml:id="echoid-s3175" xml:space="preserve"/>
          </p>
          <note symbol="c" position="left" xml:space="preserve">45. h.</note>
          <figure number="83">
            <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0118-01"/>
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          <p>
            <s xml:id="echoid-s3176" xml:space="preserve">Dico ampliùs ipſam LEM eſſe _MINIMAM_ quæſitam. </s>
            <s xml:id="echoid-s3177" xml:space="preserve">Quoniam quęlibet
              <lb/>
            alia adſcripta per verticem E, cum eodem verſo HE, ſed cum recto, quod
              <lb/>
            excedat EK, maior eſt ipſa LEM; </s>
            <s xml:id="echoid-s3178" xml:space="preserve">quæ verò cum recto EN, quod minus
              <note symbol="d" position="left" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            EK, qualis OEQ, eſt quidem minor eadem LEM, ſed omnino ſecat
              <note symbol="e" position="left" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">ibidem.</note>
            ABC. </s>
            <s xml:id="echoid-s3179" xml:space="preserve">Nam ad productam regulam HN, ſecan@ BI in R adſcribatur per B
              <lb/>
            Hyperbole SBT; </s>
            <s xml:id="echoid-s3180" xml:space="preserve">hæc tota cadet intra ABC, eruntque SBT, OEQ duæ
              <note symbol="f" position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">ibidem.</note>
            miles Hyperbolæ per diuerſos vertices adſcriptæ ad eandem regulam HR,
              <lb/>
            eſtque ABC ipſi SBT, per eundem verticem, & </s>
            <s xml:id="echoid-s3181" xml:space="preserve">cum maiori recto latere BI
              <lb/>
            adſcripta, quare per præce dentem ſectiones ABC, OEQ ſe mutuò
              <note symbol="g" position="left" xlink:label="note-0118-07" xlink:href="note-0118-07a" xml:space="preserve">52. h.</note>
            bunt: </s>
            <s xml:id="echoid-s3182" xml:space="preserve">Vnde Hyperbole LEM eſt _MINIMA_ circumſcripta quæſita. </s>
            <s xml:id="echoid-s3183" xml:space="preserve">Quod
              <lb/>
            faciendum, & </s>
            <s xml:id="echoid-s3184" xml:space="preserve">demonſtrandum erat.</s>
            <s xml:id="echoid-s3185" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div300" type="section" level="1" n="131">
          <head xml:id="echoid-head136" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s3186" xml:space="preserve">SEcetur EH bifariam in X: </s>
            <s xml:id="echoid-s3187" xml:space="preserve">erit X centrum vtriuſque LEM, OEQ: </s>
            <s xml:id="echoid-s3188" xml:space="preserve">ſi ergo
              <lb/>
            ex centris X, D, ducantur XY, XZ, DF ſectionum LEM, OEQ, ABC
              <lb/>
            aſymptoti, hoc eſt XY circumſcriptæ LEM; </s>
            <s xml:id="echoid-s3189" xml:space="preserve">XZ inſcriptæ OEQ, quæ infra
              <lb/>
            XY cadet; </s>
            <s xml:id="echoid-s3190" xml:space="preserve">& </s>
            <s xml:id="echoid-s3191" xml:space="preserve">DF ſectionis ABC, quæ ipſi XY æquidiſtabit; </s>
            <s xml:id="echoid-s3192" xml:space="preserve">cum XZ
              <note symbol="h" position="left" xlink:label="note-0118-08" xlink:href="note-0118-08a" xml:space="preserve">Ex vlti-
                <lb/>
              ma partre
                <lb/>
              37. huius.</note>
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