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

Page concordance

< >
Scan Original
41 23
42 24
43 25
44 26
45 27
46 28
47 29
48 30
49 31
50 32
51 33
52 34
53 35
54 36
55 37
56 38
57 39
58 40
59 41
60 42
61 43
62 44
63 45
64 46
65 47
66 48
67 49
68 50
69 51
70 52
< >
page |< < (32) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div41" type="section" level="1" n="13">
          <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>
          </p>
        </div>
      </text>
    </echo>
Impressum