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

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        <div xml:id="echoid-div355" type="section" level="1" n="153">
          <head xml:id="echoid-head158" xml:space="preserve">PROBL. XXV. PROP. LXVII.</head>
          <p>
            <s xml:id="echoid-s3691" xml:space="preserve">Dato angulo rectilineo, per punctum intra ipſum datum MA-
              <lb/>
            XIMAM Parabolen inſcribere: </s>
            <s xml:id="echoid-s3692" xml:space="preserve">& </s>
            <s xml:id="echoid-s3693" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s3694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3695" xml:space="preserve">SIt datus angulus rectilineus ABC, & </s>
            <s xml:id="echoid-s3696" xml:space="preserve">datum, intra ipſum, punctum ſit D.
              <lb/>
            </s>
            <s xml:id="echoid-s3697" xml:space="preserve">Oportet per D _MAXIMAM_ Parabolen inſcribere.</s>
            <s xml:id="echoid-s3698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3699" xml:space="preserve">Sumatur DE æqualis DB, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">per E in angulo ABC applicetur,
              <note symbol="a" position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">66. h.</note>
            AEC, quæ à diametro AE ſit bifariam ſecta in E, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">per verticem D circa
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">57. h.</note>
            diametrum ED, & </s>
            <s xml:id="echoid-s3702" xml:space="preserve">applicatam AC magnitudine, & </s>
            <s xml:id="echoid-s3703" xml:space="preserve">poſitione datam de- ſcribatur Parabole ADC. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">Dico ipſam eſſe quæſitam.</s>
            <s xml:id="echoid-s3705" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3706" xml:space="preserve">Quoniam cum ſint DE, DB æquales, rectæ
              <lb/>
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                <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0134-01"/>
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              <note symbol="c" position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">2. huius.</note>
            AB, CB ſectionem contingent, vnde Parabo- le erit dato angulo inſcripta; </s>
            <s xml:id="echoid-s3707" xml:space="preserve">eritque _MAXIMA_
              <lb/>
            quoniam quælibet Parabole per D ipſi ADC
              <lb/>
            adſcripta cum recto, quod eius recto ſit minus
              <lb/>
            ipſa ADC minor eſt, quęlibet verò
              <note symbol="d" position="left" xlink:label="note-0134-04" xlink:href="note-0134-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            cum recto, quod prædictum excedat licet ea-
              <lb/>
            dem ſit maior, ſecat tamen latera dati anguli.</s>
            <s xml:id="echoid-s3708" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-0134-05" xlink:href="note-0134-05a" xml:space="preserve">ibidem.</note>
            Quare Parabole ADC eſt _MAXIMA_. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">Quod
              <lb/>
            primò, &</s>
            <s xml:id="echoid-s3710" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3712" xml:space="preserve">SI verò data ſit Parabole ADC, & </s>
            <s xml:id="echoid-s3713" xml:space="preserve">extra ip-
              <lb/>
            ſam datum ſit pũctum B, per quod ei opor-
              <lb/>
            teat _MINIMVM_ angulum rectilineum circum-
              <lb/>
            ſcribere. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Ducta BE parabolæ diametro, & </s>
            <s xml:id="echoid-s3715" xml:space="preserve">ſumpta DE æquali DB applica-
              <lb/>
            taque AEC, iunctiſque BA, BC, Erit angulus ABC _MINIMVS_ quæſitus,
              <lb/>
              <note symbol="f" position="left" xlink:label="note-0134-06" xlink:href="note-0134-06a" xml:space="preserve">2. huius.</note>
            vt ſatis perſpicuè patet. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Nam cum ipſæ BA, BC ſectionem contingant om- nes aliæ ex B ductæ minorem angulum dato ABC adſcriptum conſtituentes,
              <lb/>
            ſectionem ſecabunt, quare, &</s>
            <s xml:id="echoid-s3717" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3718" xml:space="preserve">Quod vltimò, &</s>
            <s xml:id="echoid-s3719" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3720" xml:space="preserve"/>
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        <div xml:id="echoid-div359" type="section" level="1" n="154">
          <head xml:id="echoid-head159" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s3721" xml:space="preserve">MOnendus hìc Lector eſt, quod dum in hoc, & </s>
            <s xml:id="echoid-s3722" xml:space="preserve">in ſequentibus
              <lb/>
            problematibus; </s>
            <s xml:id="echoid-s3723" xml:space="preserve">dato angulo, per datum punctum adſcribitur,
              <lb/>
            velinſcribi, aut circumſcribi proponitur, quæſita coni-ſectio,
              <lb/>
            vel circulus; </s>
            <s xml:id="echoid-s3724" xml:space="preserve">& </s>
            <s xml:id="echoid-s3725" xml:space="preserve">è contra, dum datæ com-ſectioni, vel circulo
              <lb/>
            per datum punctum adſcribitur, velinſcribitur, aut circumſcribitur quæſi-
              <lb/>
            tus angulus; </s>
            <s xml:id="echoid-s3726" xml:space="preserve">id ſemper à nobis accipi intelligitur in eodem ſenſu quintæ ſe-
              <lb/>
            cundarum definitionum huius, qua in præcedentibus hactenus vſi ſumus;
              <lb/>
            </s>
            <s xml:id="echoid-s3727" xml:space="preserve">nempe lineam, quæ per datum punctum educta diameter eſt datæ, vel quæſitæ
              <lb/>
            ſectionis, eſſe quoque diametrum dati, vel quæſiti anguli, ſiue eius verti-
              <lb/>
            ci occurrere; </s>
            <s xml:id="echoid-s3728" xml:space="preserve">ita vt quæ in angulo ducuntur æquidiſtantes ordinatim appli-
              <lb/>
            catis com-ſectionis, velcirculi, ſint quoque ab eadem ſectionis diametro </s>
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