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

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        <div xml:id="echoid-div359" type="section" level="1" n="154">
          <p style="it">
            <s xml:id="echoid-s3728" xml:space="preserve">
              <pb o="111" file="0135" n="135" rhead=""/>
            datum punctum tranſeunte bifariam ſectæ, quod à lineis ad anguli verticem
              <lb/>
            non collimantibus conſequi minimè poſſet. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">Si verò inſcriptio, ac circumſcri-
              <lb/>
            ptio alijs conditionibus confici iubeatur, aliæ item defintiones, & </s>
            <s xml:id="echoid-s3730" xml:space="preserve">conſtru-
              <lb/>
            ctiones diuerſæ ad problematum ſolutiones requirerentur, quas omnes, licet
              <lb/>
            nobis fortuitò datum ſit Geometriæ legibus ſubijcere, temporis tamen angu-
              <lb/>
            ſtijs obſequentes, hic
              <gap/>
            omittere neceſſe fuit; </s>
            <s xml:id="echoid-s3731" xml:space="preserve">ſed aliàs forſan, Deo dante, ſi
              <lb/>
            quid vnquam ocij nacti fuerimus, hanc ipſam de MAXIMIS, & </s>
            <s xml:id="echoid-s3732" xml:space="preserve">MI-
              <lb/>
            NIMIS doctrinam, & </s>
            <s xml:id="echoid-s3733" xml:space="preserve">duplò, & </s>
            <s xml:id="echoid-s3734" xml:space="preserve">triplò auctiorem denuò proferemus: </s>
            <s xml:id="echoid-s3735" xml:space="preserve">inte-
              <lb/>
            rim varijs ſtimulis, qui ad hæc edenda nos vrgent, obtemperantes, præſens
              <lb/>
            argumentum abſoluere properemus, vt citius (alteram huius tractationis
              <lb/>
            partem aggrediendo) ad noua pariter, & </s>
            <s xml:id="echoid-s3736" xml:space="preserve">apprimè iucunda in conicis acciden-
              <lb/>
            tia deueniamus, & </s>
            <s xml:id="echoid-s3737" xml:space="preserve">quod pluris eſt, præcipuè vtilitatis fundamenta iacien-
              <lb/>
            do, abſtruſionis doctrinæ myſteria perſpicacioribus ingenijs aperiamus.</s>
            <s xml:id="echoid-s3738" xml:space="preserve"/>
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        <div xml:id="echoid-div360" type="section" level="1" n="155">
          <head xml:id="echoid-head160" xml:space="preserve">PROBL. XXVI. PROP. LXVIII.</head>
          <p>
            <s xml:id="echoid-s3739" xml:space="preserve">Dato angulo rectilineo, per punctum intra ipſum datum, cum
              <lb/>
            dato ſemi-tranſuerſo latere, MAXIMAM Hyperbolen inſcribere.
              <lb/>
            </s>
            <s xml:id="echoid-s3740" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s3741" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3742" xml:space="preserve">Datę Hyperbolæ, per punctum extra ipſam datum, MINIMVM
              <lb/>
            angulum rectilineum circumſcribere.</s>
            <s xml:id="echoid-s3743" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3744" xml:space="preserve">Oportet autem, ad hoc vt anguli circumſcriptio fiat iuxta alla-
              <lb/>
            tam definitionem, ac præcedens monitum, datum punctum, vel
              <lb/>
            eſſe in centro, vel intra angulos, ab aſymptotis conſtitutos.</s>
            <s xml:id="echoid-s3745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3746" xml:space="preserve">SIt, in tribus primis figuris, datus angulus rectilineus ABC, & </s>
            <s xml:id="echoid-s3747" xml:space="preserve">datum in-
              <lb/>
            tra ipſum punctum ſit D: </s>
            <s xml:id="echoid-s3748" xml:space="preserve">oportet per D _MAXIMAM_ Hyperbolen inſcri-
              <lb/>
            bere, cuius ſemi-tranſuerſum latus æquale ſit dato E.</s>
            <s xml:id="echoid-s3749" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3750" xml:space="preserve">Iungatur DB, & </s>
            <s xml:id="echoid-s3751" xml:space="preserve">ſe-
              <lb/>
              <figure xlink:label="fig-0135-01" xlink:href="fig-0135-01a" number="101">
                <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0135-01"/>
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            cetur ex ipſa, DO ęqua
              <lb/>
            lis E. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">Iam, vel DO æ-
              <lb/>
            qualis eſt DB, vt in pri-
              <lb/>
            ma figura, vel minor vt
              <lb/>
            in ſecunda, vel maior
              <lb/>
            vt in tertia. </s>
            <s xml:id="echoid-s3753" xml:space="preserve">Si primùm,
              <lb/>
            deſcribatur per D,
              <note symbol="a" position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">4. ſec.
                <lb/>
              conic.</note>
            aſymptotis BA, BC
              <lb/>
            Hyperbole FDG: </s>
            <s xml:id="echoid-s3754" xml:space="preserve">& </s>
            <s xml:id="echoid-s3755" xml:space="preserve">
              <lb/>
            ipſa erit _MAXIMA_
              <lb/>
            quæſita.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3757" xml:space="preserve">Nam, quæ cum eo-
              <lb/>
            dem tranſuerſo, eidem angulo per D adſcribitur, cum recto, quod minus </s>
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