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

Table of Notes

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          <p>
            <s xml:id="echoid-s1458" xml:space="preserve">
              <pb o="32" file="0050" n="50" rhead=""/>
            autem procedentis cujuſvis radii (ceu AN) refractus N _a_ cum ipſa AB
              <lb/>
              <note position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve">_lect. 3. num. 9_.</note>
            (protractus utique, vel retractus) conve@iat in K; </s>
            <s xml:id="echoid-s1459" xml:space="preserve">dico fore NK.
              <lb/>
            </s>
            <s xml:id="echoid-s1460" xml:space="preserve">NA :</s>
            <s xml:id="echoid-s1461" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1462" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1463" xml:space="preserve">(Neque non inverſè, ſi fuerit NK. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">NA :</s>
            <s xml:id="echoid-s1465" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">R; </s>
            <s xml:id="echoid-s1467" xml:space="preserve">
              <lb/>
            erit KN _a_ ipſius NA refractus.)</s>
            <s xml:id="echoid-s1468" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1469" xml:space="preserve">Hoc è ſuperiùs oſtenſis immediatè conſectatur. </s>
            <s xml:id="echoid-s1470" xml:space="preserve">Et hinc etiam ſatis
              <lb/>
            apparet, quoniam (id quod bene notetur, ut paſſim in ſequentibus aſ-
              <lb/>
            ſumendum) angulus NAB, æ quatur angulo incidentiæ (quippe cum
              <lb/>
            is complementum ſit anguli ANB;) </s>
            <s xml:id="echoid-s1471" xml:space="preserve">& </s>
            <s xml:id="echoid-s1472" xml:space="preserve">angulus NKB (comple-
              <lb/>
            mentum videlicet anguli KNB) æquatur angulo refracto. </s>
            <s xml:id="echoid-s1473" xml:space="preserve">Cùm ita-
              <lb/>
            que ſit hinc ſinus anguli NAB (vel anguli deinceps NAK) ad ſi-
              <lb/>
              <note position="left" xlink:label="note-0050-02" xlink:href="note-0050-02a" xml:space="preserve">Fig. 34, 35.</note>
            num anguli NKA, ut I ad R; </s>
            <s xml:id="echoid-s1474" xml:space="preserve">etiam in triangulo NAK latus NK ad
              <lb/>
            latus NA ſeſe habebit ut I ad R. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1477" xml:space="preserve">Quinetiam ſi latera
              <lb/>
            NK, NA ſe habeant ut I ad R; </s>
            <s xml:id="echoid-s1478" xml:space="preserve">etiam dictorum angulorum ſinus ità
              <lb/>
            ſe habebunt; </s>
            <s xml:id="echoid-s1479" xml:space="preserve">unde conſtabit ipſam KN _a_ ad AN pertinere.</s>
            <s xml:id="echoid-s1480" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1481" xml:space="preserve">V. </s>
            <s xml:id="echoid-s1482" xml:space="preserve">Hinc particularis emergit expeditiſſimus modus hujuſmodi quot-
              <lb/>
            cunque refractos deſignandi. </s>
            <s xml:id="echoid-s1483" xml:space="preserve">Nempe per radians punctum A ducatur
              <lb/>
            AB refringenti EF perpendicularis; </s>
            <s xml:id="echoid-s1484" xml:space="preserve">& </s>
            <s xml:id="echoid-s1485" xml:space="preserve">fiat AB. </s>
            <s xml:id="echoid-s1486" xml:space="preserve">ZB :</s>
            <s xml:id="echoid-s1487" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s1488" xml:space="preserve">I; </s>
            <s xml:id="echoid-s1489" xml:space="preserve">tum
              <lb/>
            per Z ducatur recta GH ad EF parallela, Proponatur jam quilibet
              <lb/>
            incidens AN, cui conveniens deſignandus eſt refractus. </s>
            <s xml:id="echoid-s1490" xml:space="preserve">Eum ſic de-
              <lb/>
            deſignaveris. </s>
            <s xml:id="echoid-s1491" xml:space="preserve">Protrahatur NA (ſi opus) ut cum GH conveniat in
              <lb/>
            S; </s>
            <s xml:id="echoid-s1492" xml:space="preserve">& </s>
            <s xml:id="echoid-s1493" xml:space="preserve">centro N per S deſcribatur circulus ipſam AB ſecans in K (ſe-
              <lb/>
            cabit utique ſi refractus aliquis ad incidentem AN pertineat) erit con-
              <lb/>
            nexa KN, protractáque radio AN debitus refractus. </s>
            <s xml:id="echoid-s1494" xml:space="preserve">Etenim eſt
              <lb/>
            KN. </s>
            <s xml:id="echoid-s1495" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s1496" xml:space="preserve">: SN. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s1498" xml:space="preserve">: ZB. </s>
            <s xml:id="echoid-s1499" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s1500" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">R :</s>
            <s xml:id="echoid-s1502" xml:space="preserve">: KN. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">AN. </s>
            <s xml:id="echoid-s1504" xml:space="preserve">unde
              <lb/>
            liquet (è præcedente) propoſitum.</s>
            <s xml:id="echoid-s1505" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1506" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">Exhinc etiam hujuſmodi refractionis præcipua ſymptomata
              <lb/>
            perfacili colliguntur Negotio; </s>
            <s xml:id="echoid-s1508" xml:space="preserve">quæſeorſim acceptis, & </s>
            <s xml:id="echoid-s1509" xml:space="preserve">quæ ſe-
              <lb/>
            cum mutuò collatis accidunt refractis; </s>
            <s xml:id="echoid-s1510" xml:space="preserve">hoc imprimis: </s>
            <s xml:id="echoid-s1511" xml:space="preserve">In primo caſu
              <lb/>
            (quum nempe refractio fit è rariori in denſius, ſeu quum I&</s>
            <s xml:id="echoid-s1512" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s1513" xml:space="preserve">R)
              <lb/>
            concurſus refractorum cum recta AB (quam ſubinde radiationis hujus
              <lb/>
            axem appellare licebit) ſupra punctum Z exiſtit. </s>
            <s xml:id="echoid-s1514" xml:space="preserve">Nam connexâ NZ;
              <lb/>
            </s>
            <s xml:id="echoid-s1515" xml:space="preserve">quoniam ang. </s>
            <s xml:id="echoid-s1516" xml:space="preserve">NZS recto BZS major eſt, erit NS (vel NK) &</s>
            <s xml:id="echoid-s1517" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1518" xml:space="preserve">
              <lb/>
            NZ; </s>
            <s xml:id="echoid-s1519" xml:space="preserve">adeoque BK&</s>
            <s xml:id="echoid-s1520" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s1521" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s1522" xml:space="preserve">Item, in ſecundo caſu (quum media
              <lb/>
            contrariè ſe habent) dictus concurſus infra punctum Z exiſtit. </s>
            <s xml:id="echoid-s1523" xml:space="preserve">Ete-
              <lb/>
            nim rurſus connexâ NZ; </s>
            <s xml:id="echoid-s1524" xml:space="preserve">eſt ang. </s>
            <s xml:id="echoid-s1525" xml:space="preserve">NSZ recto AZS (interno) ma-
              <lb/>
            jor, adeóque NZ &</s>
            <s xml:id="echoid-s1526" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1527" xml:space="preserve">NS, vel NK; </s>
            <s xml:id="echoid-s1528" xml:space="preserve">& </s>
            <s xml:id="echoid-s1529" xml:space="preserve">ideò BZ &</s>
            <s xml:id="echoid-s1530" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1531" xml:space="preserve">BK.</s>
            <s xml:id="echoid-s1532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1533" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s1534" xml:space="preserve">Hinc liquet punctum Z eſſe limitem ultra vel citra quem (re-
              <lb/>
            ſpectivè) omnes refracti cum axe AB concurrunt. </s>
            <s xml:id="echoid-s1535" xml:space="preserve">Quinimò quòd
              <lb/>
              <note position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">Fig. 35.</note>
            </s>
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