Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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            <s xml:id="echoid-s2050" xml:space="preserve">
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            AN refractus. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">Hæc autem è ſupra poſitis Theorematis abunde
              <lb/>
            conſtant.</s>
            <s xml:id="echoid-s2052" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">_10 & 13 Lect. 4._</note>
          <p>
            <s xml:id="echoid-s2053" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s2054" xml:space="preserve">Verum extra caſum hunc, & </s>
            <s xml:id="echoid-s2055" xml:space="preserve">particulares alios nonnullos (quos
              <lb/>
            hìc certè nil attinet commemorare) generatim & </s>
            <s xml:id="echoid-s2056" xml:space="preserve">illimitatè conceptum
              <lb/>
            Problema ſolidum eſt, plureſque duabus ſolutiones admittit; </s>
            <s xml:id="echoid-s2057" xml:space="preserve">id quod
              <lb/>
            facilè perſpicietur concipiendo punctum datum (puta X) in primo ca-
              <lb/>
            ſu extra angulum AB F jacere (vel intra eundem, in ſecundo) quo po-
              <lb/>
            ſito liquet è præcedentibus obtingere poſſe nonnunquam, ut duorum
              <lb/>
              <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">Fig. 50.</note>
            ad partes BF incidentium refractì concurrant ad X; </s>
            <s xml:id="echoid-s2058" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s2059" xml:space="preserve">alterius
              <lb/>
            unius ad partes BE incidentis reſractum etiam per idem X tranſire
              <lb/>
            quod cùm ſubinde, dico, contingere poſſit, indè certo conſequetur
              <lb/>
            _Problema_ ſolidum eſſe.</s>
            <s xml:id="echoid-s2060" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2061" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2062" xml:space="preserve">Pro cujus ſolutione, primùm adnoto vix ullum _Problema_ dari
              <lb/>
            (præſertim è difficilioribus) quod non peculiarem lineam naturâ ſibi-
              <lb/>
            met appropriatam habeat, cujus deſcriptione quàm expeditè conſtrua-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s2063" xml:space="preserve">& </s>
            <s xml:id="echoid-s2064" xml:space="preserve">quidem ità, ut ſimul indolem ſuam prodat ; </s>
            <s xml:id="echoid-s2065" xml:space="preserve">poſſibilitatem,
              <lb/>
            inquam, & </s>
            <s xml:id="echoid-s2066" xml:space="preserve">impoſſibilitatem ſuam; </s>
            <s xml:id="echoid-s2067" xml:space="preserve">determinationes, & </s>
            <s xml:id="echoid-s2068" xml:space="preserve">limitationes
              <lb/>
            neceſſarias; </s>
            <s xml:id="echoid-s2069" xml:space="preserve">caſuum & </s>
            <s xml:id="echoid-s2070" xml:space="preserve">ſolutionum varietatem apertè monſtret, & </s>
            <s xml:id="echoid-s2071" xml:space="preserve">ve-
              <lb/>
            lut ob oculos repreſentet. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">In cujus qualis qualis obſervationis ſpeci-
              <lb/>
            men (alia quædam poſtmodùm exhibituri) imprimis lineam propone-
              <lb/>
            mus hujuſce Problematis executioni peculiariter accommodatam, hoc
              <lb/>
            modo promptè deſcribendam.</s>
            <s xml:id="echoid-s2073" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2074" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s2075" xml:space="preserve">Per radians punctum A ducatur ARS refringenti parallela;
              <lb/>
            </s>
            <s xml:id="echoid-s2076" xml:space="preserve">
              <note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">Fig. 51.</note>
            eidémque perpendicularis AB utrinque protendatur indefinitè. </s>
            <s xml:id="echoid-s2077" xml:space="preserve">Item
              <lb/>
            per datum alterum punctum X protendatur XR ad AB parallela:
              <lb/>
            </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Quinetiam facto AS. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">AR :</s>
            <s xml:id="echoid-s2080" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">R; </s>
            <s xml:id="echoid-s2082" xml:space="preserve">per S extendatur SU ad AB pa-
              <lb/>
            rallela. </s>
            <s xml:id="echoid-s2083" xml:space="preserve">Quibus ſtantibus per A quotcunque tranſeant rectæ ſecantes
              <lb/>
            ipſam SU punctis H; </s>
            <s xml:id="echoid-s2084" xml:space="preserve">& </s>
            <s xml:id="echoid-s2085" xml:space="preserve">centro X, intervallis ipſas AH exæquanti-
              <lb/>
            bus, deſcribantur circuli ſecantes perpendicularem AB punctis K; </s>
            <s xml:id="echoid-s2086" xml:space="preserve">
              <lb/>
            demum per X, K ductæ lineæ cum ipſis HA conveniant in N. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">Per
              <lb/>
            ejuſmodi quæ cunque puncta tranſibit propoſito noſtro deſerviens linea
              <lb/>
            (AN N) quam ſuſcepimus deſcribendam; </s>
            <s xml:id="echoid-s2088" xml:space="preserve">cujuſce nimirum cum re-
              <lb/>
            fringente FF interſectiones ipſiſſima ſunt incidentiæ puncta, quæ in-
              <lb/>
            dagamus (hæ autem ad unas rectæ AB partes (veluti ad F ) aliquando
              <lb/>
            duæ erunt; </s>
            <s xml:id="echoid-s2089" xml:space="preserve">ſubinde tantùm una, cù EF ſic effectam curvam tangit; </s>
            <s xml:id="echoid-s2090" xml:space="preserve">
              <lb/>
            quandoque nulla, cùm EF ultra tangentem dictam jacet; </s>
            <s xml:id="echoid-s2091" xml:space="preserve">ad alteras
              <lb/>
            ſaltem una erit; </s>
            <s xml:id="echoid-s2092" xml:space="preserve">quæ ſatis attendenti manifeſta futura ſubnoto </s>
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