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

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          <p>
            <s xml:id="echoid-s1535" xml:space="preserve">
              <pb o="33" file="0051" n="51" rhead=""/>
            ipſius perpendicularis AB (quaſi) refractus in ipſum punctum Z ter-
              <lb/>
            minatur. </s>
            <s xml:id="echoid-s1536" xml:space="preserve">Porrò:</s>
            <s xml:id="echoid-s1537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1538" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s1539" xml:space="preserve">_Lemma_: </s>
            <s xml:id="echoid-s1540" xml:space="preserve">ſit AB ad EF normalis, & </s>
            <s xml:id="echoid-s1541" xml:space="preserve">à duobus in AB
              <lb/>
            ſumptis utcunque punctis A, I (quorum A proprius ipſi B) ad duo
              <lb/>
            puncta quæ vis M, N in ipſa EF acceptis (quorum verò M ſit ipſi B
              <lb/>
            vicinius) connectantur rectæ AM, AN ; </s>
            <s xml:id="echoid-s1542" xml:space="preserve">& </s>
            <s xml:id="echoid-s1543" xml:space="preserve">IM, IN; </s>
            <s xml:id="echoid-s1544" xml:space="preserve">dico fore A N.
              <lb/>
            </s>
            <s xml:id="echoid-s1545" xml:space="preserve">AM &</s>
            <s xml:id="echoid-s1546" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1547" xml:space="preserve">IN. </s>
            <s xml:id="echoid-s1548" xml:space="preserve">IM.</s>
            <s xml:id="echoid-s1549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1550" xml:space="preserve">Nam centro N per A deſcribatur circulus PA OR (rectas IM,
              <lb/>
            IN interſecans punctis O, R) & </s>
            <s xml:id="echoid-s1551" xml:space="preserve">per R ducatur RT ad EF parallela,
              <lb/>
            ſecans IM in S. </s>
            <s xml:id="echoid-s1552" xml:space="preserve">Et ob angulum NRT obtuſum, patet rectam RT
              <lb/>
            extra circulum totam excidere; </s>
            <s xml:id="echoid-s1553" xml:space="preserve">unde SM &</s>
            <s xml:id="echoid-s1554" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1555" xml:space="preserve">(OM &</s>
            <s xml:id="echoid-s1556" xml:space="preserve">gt;) </s>
            <s xml:id="echoid-s1557" xml:space="preserve">AM.
              <lb/>
            </s>
            <s xml:id="echoid-s1558" xml:space="preserve">adeóque AN. </s>
            <s xml:id="echoid-s1559" xml:space="preserve">AM &</s>
            <s xml:id="echoid-s1560" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1561" xml:space="preserve">AN : </s>
            <s xml:id="echoid-s1562" xml:space="preserve">SM :</s>
            <s xml:id="echoid-s1563" xml:space="preserve">: RN. </s>
            <s xml:id="echoid-s1564" xml:space="preserve">SM :</s>
            <s xml:id="echoid-s1565" xml:space="preserve">: IN. </s>
            <s xml:id="echoid-s1566" xml:space="preserve">IM. </s>
            <s xml:id="echoid-s1567" xml:space="preserve">li-
              <lb/>
            quet igitur eſſe AN . </s>
            <s xml:id="echoid-s1568" xml:space="preserve">AM &</s>
            <s xml:id="echoid-s1569" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1570" xml:space="preserve">IN. </s>
            <s xml:id="echoid-s1571" xml:space="preserve">IM : </s>
            <s xml:id="echoid-s1572" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s1573" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1574" xml:space="preserve">Hinc</s>
          </p>
          <p>
            <s xml:id="echoid-s1575" xml:space="preserve">Si duorum radiorum AM, AN (quorum hic obliquior) refracti
              <lb/>
            M _a_, N _a_ cum axe AB conveniant punctis I, K, erit in primo caſu IB
              <lb/>
            &</s>
            <s xml:id="echoid-s1576" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1577" xml:space="preserve">KB; </s>
            <s xml:id="echoid-s1578" xml:space="preserve">in ſecundo IB &</s>
            <s xml:id="echoid-s1579" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1580" xml:space="preserve">KB. </s>
            <s xml:id="echoid-s1581" xml:space="preserve">Etenim connexâ IN; </s>
            <s xml:id="echoid-s1582" xml:space="preserve">eſt in primo
              <lb/>
            caſu, NK. </s>
            <s xml:id="echoid-s1583" xml:space="preserve">MI :</s>
            <s xml:id="echoid-s1584" xml:space="preserve">: NA. </s>
            <s xml:id="echoid-s1585" xml:space="preserve">MA &</s>
            <s xml:id="echoid-s1586" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1587" xml:space="preserve">NI. </s>
            <s xml:id="echoid-s1588" xml:space="preserve">MI. </s>
            <s xml:id="echoid-s1589" xml:space="preserve">adeóque NK &</s>
            <s xml:id="echoid-s1590" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1591" xml:space="preserve">NI.
              <lb/>
            </s>
            <s xml:id="echoid-s1592" xml:space="preserve">unde BK &</s>
            <s xml:id="echoid-s1593" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1594" xml:space="preserve">BI. </s>
            <s xml:id="echoid-s1595" xml:space="preserve">aſt in ſecundo, NK. </s>
            <s xml:id="echoid-s1596" xml:space="preserve">MI :</s>
            <s xml:id="echoid-s1597" xml:space="preserve">: NA. </s>
            <s xml:id="echoid-s1598" xml:space="preserve">MA &</s>
            <s xml:id="echoid-s1599" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1600" xml:space="preserve">NI. </s>
            <s xml:id="echoid-s1601" xml:space="preserve">
              <lb/>
            MI quare NK &</s>
            <s xml:id="echoid-s1602" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1603" xml:space="preserve">NI; </s>
            <s xml:id="echoid-s1604" xml:space="preserve">& </s>
            <s xml:id="echoid-s1605" xml:space="preserve">indè BK &</s>
            <s xml:id="echoid-s1606" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1607" xml:space="preserve">BI.</s>
            <s xml:id="echoid-s1608" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 37.</note>
          <p>
            <s xml:id="echoid-s1609" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s1610" xml:space="preserve">_Coroll_. </s>
            <s xml:id="echoid-s1611" xml:space="preserve">Refractorum in primo caſu concurſus extra angulum
              <lb/>
            AB N verſantur; </s>
            <s xml:id="echoid-s1612" xml:space="preserve">in ſecundo, intra eundem. </s>
            <s xml:id="echoid-s1613" xml:space="preserve">Sed hæc eadem in decur-
              <lb/>
            ſu liquidius, ac multifariàm conſtabunt.</s>
            <s xml:id="echoid-s1614" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1615" xml:space="preserve">X. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Porrò, bina quoad hos caſus _Theoremata_ ſubjiciemus, uſus haud
              <lb/>
            contemnendi.</s>
            <s xml:id="echoid-s1617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1618" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">Si ſiat (in primo caſu) YB. </s>
            <s xml:id="echoid-s1620" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s1621" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1622" xml:space="preserve">√ Iq - Rq. </s>
            <s xml:id="echoid-s1623" xml:space="preserve">ſit autem cu-
              <lb/>
              <note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">Fig. 39.</note>
            juſvis incidentis AN reſractus KN _a_; </s>
            <s xml:id="echoid-s1624" xml:space="preserve">& </s>
            <s xml:id="echoid-s1625" xml:space="preserve">connectatur YN: </s>
            <s xml:id="echoid-s1626" xml:space="preserve">erit KB.
              <lb/>
            </s>
            <s xml:id="echoid-s1627" xml:space="preserve">YN :</s>
            <s xml:id="echoid-s1628" xml:space="preserve">: √ Iq - Rq. </s>
            <s xml:id="echoid-s1629" xml:space="preserve">R.</s>
            <s xml:id="echoid-s1630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1631" xml:space="preserve">Nam ob YBq. </s>
            <s xml:id="echoid-s1632" xml:space="preserve">ABq :</s>
            <s xml:id="echoid-s1633" xml:space="preserve">: (_a_) Iq. </s>
            <s xml:id="echoid-s1634" xml:space="preserve">Iq - Rq. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">erit per converſi-
              <lb/>
              <note position="right" xlink:label="note-0051-03" xlink:href="note-0051-03a" xml:space="preserve">_(a) Hypoib._</note>
            onem rationis YBq. </s>
            <s xml:id="echoid-s1636" xml:space="preserve">YBq - ABq :</s>
            <s xml:id="echoid-s1637" xml:space="preserve">: Iq. </s>
            <s xml:id="echoid-s1638" xml:space="preserve">Rq :</s>
            <s xml:id="echoid-s1639" xml:space="preserve">: _(b)_ KNq. </s>
            <s xml:id="echoid-s1640" xml:space="preserve">ANq.
              <lb/>
            </s>
            <s xml:id="echoid-s1641" xml:space="preserve">
              <note position="right" xlink:label="note-0051-04" xlink:href="note-0051-04a" xml:space="preserve">_(b) 4 hujus_</note>
            & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">permutando YBq. </s>
            <s xml:id="echoid-s1643" xml:space="preserve">KNq :</s>
            <s xml:id="echoid-s1644" xml:space="preserve">: YBq - ABq. </s>
            <s xml:id="echoid-s1645" xml:space="preserve">ANq . </s>
            <s xml:id="echoid-s1646" xml:space="preserve">componen-
              <lb/>
            dóque YBq + KNq. </s>
            <s xml:id="echoid-s1647" xml:space="preserve">KNq :</s>
            <s xml:id="echoid-s1648" xml:space="preserve">: YBq + BNq. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">ANq. </s>
            <s xml:id="echoid-s1650" xml:space="preserve">(nempe
              <lb/>
            YBq - ABq + ANq = YBq + BNq; </s>
            <s xml:id="echoid-s1651" xml:space="preserve">quoniam ANq -
              <lb/>
            ABq = BNq) Quarè runſus permutando eſt YBq + KNq.
              <lb/>
            </s>
            <s xml:id="echoid-s1652" xml:space="preserve">YBq. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">+ BNq :</s>
            <s xml:id="echoid-s1654" xml:space="preserve">: KNq. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">ANq. </s>
            <s xml:id="echoid-s1656" xml:space="preserve">dividendoque KNq - BNq. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">
              <lb/>
            YBq + BNq :</s>
            <s xml:id="echoid-s1658" xml:space="preserve">: KNq - ANq. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">ANq; </s>
            <s xml:id="echoid-s1660" xml:space="preserve">hoc eſt KBq. </s>
            <s xml:id="echoid-s1661" xml:space="preserve">YNq
              <lb/>
            :</s>
            <s xml:id="echoid-s1662" xml:space="preserve">: Iq - Rq. </s>
            <s xml:id="echoid-s1663" xml:space="preserve">Rq: </s>
            <s xml:id="echoid-s1664" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1667" xml:space="preserve"/>
          </p>
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