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-s1668" xml:space="preserve">XI _corol_. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Hinc ſi duo reſracti M _a_, N _a_ cum Axe AB conve-
              <lb/>
            niant in I, K; </s>
            <s xml:id="echoid-s1671" xml:space="preserve">& </s>
            <s xml:id="echoid-s1672" xml:space="preserve">à puncto Y ad incidentias ducantur rectæ YM, YN;
              <lb/>
            </s>
            <s xml:id="echoid-s1673" xml:space="preserve">erit KB. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">IB :</s>
            <s xml:id="echoid-s1675" xml:space="preserve">: YN. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">YM. </s>
            <s xml:id="echoid-s1677" xml:space="preserve">Nam KBq. </s>
            <s xml:id="echoid-s1678" xml:space="preserve">YNq :</s>
            <s xml:id="echoid-s1679" xml:space="preserve">: Iq - Rq. </s>
            <s xml:id="echoid-s1680" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">Fig. 40.</note>
            Rq :</s>
            <s xml:id="echoid-s1681" xml:space="preserve">: IBq. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">YMq. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">quare permutatim KBq. </s>
            <s xml:id="echoid-s1684" xml:space="preserve">IBq :</s>
            <s xml:id="echoid-s1685" xml:space="preserve">: YNq.
              <lb/>
            </s>
            <s xml:id="echoid-s1686" xml:space="preserve">YM q.</s>
            <s xml:id="echoid-s1687" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1688" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s1689" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1690" xml:space="preserve">Hinc etiam ſi refracti M I, NK conveniant in X; </s>
            <s xml:id="echoid-s1691" xml:space="preserve">& </s>
            <s xml:id="echoid-s1692" xml:space="preserve">de-
              <lb/>
            mìttatur XP ad AB parallela; </s>
            <s xml:id="echoid-s1693" xml:space="preserve">& </s>
            <s xml:id="echoid-s1694" xml:space="preserve">huic protractæ MY, NY occur-
              <lb/>
            rant in R, S; </s>
            <s xml:id="echoid-s1695" xml:space="preserve">erit NS = MR Nam X P. </s>
            <s xml:id="echoid-s1696" xml:space="preserve">SN :</s>
            <s xml:id="echoid-s1697" xml:space="preserve">: KB. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">YN :</s>
            <s xml:id="echoid-s1699" xml:space="preserve">:
              <lb/>
            IB. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">YM :</s>
            <s xml:id="echoid-s1701" xml:space="preserve">: XP. </s>
            <s xml:id="echoid-s1702" xml:space="preserve">RM. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">cum itaque ſit X P. </s>
            <s xml:id="echoid-s1704" xml:space="preserve">SN :</s>
            <s xml:id="echoid-s1705" xml:space="preserve">: XP . </s>
            <s xml:id="echoid-s1706" xml:space="preserve">RM;
              <lb/>
            </s>
            <s xml:id="echoid-s1707" xml:space="preserve">erìt SN = RM.</s>
            <s xml:id="echoid-s1708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1709" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">In ſecundo caſu ; </s>
            <s xml:id="echoid-s1712" xml:space="preserve">ſit cujuſvis incidentis AN refractus
              <lb/>
            KN _a_ & </s>
            <s xml:id="echoid-s1713" xml:space="preserve">fiat YBq. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">KBq :</s>
            <s xml:id="echoid-s1715" xml:space="preserve">: Rq. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">Rq - Iq; </s>
            <s xml:id="echoid-s1717" xml:space="preserve">& </s>
            <s xml:id="echoid-s1718" xml:space="preserve">connectatur YN;
              <lb/>
            </s>
            <s xml:id="echoid-s1719" xml:space="preserve">erit ABq. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">YNq :</s>
            <s xml:id="echoid-s1721" xml:space="preserve">: Rq - Iq. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">Iq.</s>
            <s xml:id="echoid-s1723" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1724" xml:space="preserve">Nam quia KBq = KNq - BNq = KNq - YNq + YBq; </s>
            <s xml:id="echoid-s1725" xml:space="preserve">erit
              <lb/>
            (hypotheſin perſequendo) YBq. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">KNq + YBq - YNq :</s>
            <s xml:id="echoid-s1727" xml:space="preserve">: Rq.
              <lb/>
            </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Rq - Iq :</s>
            <s xml:id="echoid-s1729" xml:space="preserve">: ANq. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">ANq - KNq. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">& </s>
            <s xml:id="echoid-s1732" xml:space="preserve">per rationis converſionem
              <lb/>
            YBq. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">YNq - KNq :</s>
            <s xml:id="echoid-s1734" xml:space="preserve">: ANq. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">KNq. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">(eſt autem YBq =
              <lb/>
              <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">Fig. 41.</note>
            YNq - BNq = YNq - ANq + ABq) ergò YNq - ANq
              <lb/>
            + ABq. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">YNq - KNq :</s>
            <s xml:id="echoid-s1738" xml:space="preserve">: ANq. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">KNq (hoc eſt, anteceden-
              <lb/>
            tes & </s>
            <s xml:id="echoid-s1740" xml:space="preserve">conſequentes adjungendo) :</s>
            <s xml:id="echoid-s1741" xml:space="preserve">: YNq + ABq. </s>
            <s xml:id="echoid-s1742" xml:space="preserve">YNq. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">quare
              <lb/>
            dividendo ANq - KNq. </s>
            <s xml:id="echoid-s1744" xml:space="preserve">KNq :</s>
            <s xml:id="echoid-s1745" xml:space="preserve">: ABq. </s>
            <s xml:id="echoid-s1746" xml:space="preserve">YNq hoc eſt Rq -
              <lb/>
            Iq. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">Iq :</s>
            <s xml:id="echoid-s1748" xml:space="preserve">: ABq. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">YNq: </s>
            <s xml:id="echoid-s1750" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1752" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1754" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">_Corol_. </s>
            <s xml:id="echoid-s1756" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">Hinc rurſus, ſi duo reſracti M _a_, N _a_ ſecent axem punctis
              <lb/>
            I, K; </s>
            <s xml:id="echoid-s1758" xml:space="preserve">ipſos autem ſe decuſſent puncto X; </s>
            <s xml:id="echoid-s1759" xml:space="preserve">& </s>
            <s xml:id="echoid-s1760" xml:space="preserve">ſiat YP. </s>
            <s xml:id="echoid-s1761" xml:space="preserve">XP :</s>
            <s xml:id="echoid-s1762" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">√
              <lb/>
            Rq - Iq. </s>
            <s xml:id="echoid-s1764" xml:space="preserve">& </s>
            <s xml:id="echoid-s1765" xml:space="preserve">per Y ducantur MY R, NY S; </s>
            <s xml:id="echoid-s1766" xml:space="preserve">erit NS = MR.</s>
            <s xml:id="echoid-s1767" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1768" xml:space="preserve">Nam SB. </s>
            <s xml:id="echoid-s1769" xml:space="preserve">KB :</s>
            <s xml:id="echoid-s1770" xml:space="preserve">: YP. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">XP :</s>
            <s xml:id="echoid-s1772" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s1773" xml:space="preserve">√ Rq - Iq. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">quare AB.
              <lb/>
            </s>
            <s xml:id="echoid-s1775" xml:space="preserve">SN :</s>
            <s xml:id="echoid-s1776" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1778" xml:space="preserve">item RB. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">IB :</s>
            <s xml:id="echoid-s1780" xml:space="preserve">: YP. </s>
            <s xml:id="echoid-s1781" xml:space="preserve">XP :</s>
            <s xml:id="echoid-s1782" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">√ Rq -
              <lb/>
              <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">Fig. 42.</note>
            Iq. </s>
            <s xml:id="echoid-s1784" xml:space="preserve">quare AB. </s>
            <s xml:id="echoid-s1785" xml:space="preserve">RM :</s>
            <s xml:id="echoid-s1786" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">ergò AB. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">SN :</s>
            <s xml:id="echoid-s1790" xml:space="preserve">: AB.
              <lb/>
            </s>
            <s xml:id="echoid-s1791" xml:space="preserve">RM. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">quare SN = RM.</s>
            <s xml:id="echoid-s1793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1794" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1795" xml:space="preserve">Hinc SB. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">RB :</s>
            <s xml:id="echoid-s1797" xml:space="preserve">: KB. </s>
            <s xml:id="echoid-s1798" xml:space="preserve">IB.</s>
            <s xml:id="echoid-s1799" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1800" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">Porrò, notandum eſt quò radii ab A manantes axi viciniores
              <lb/>
            f
              <unsure/>
            unt eò refractos ipſorum ſpiſſiùs incedere; </s>
            <s xml:id="echoid-s1802" xml:space="preserve">ſeu minora fore concur-
              <lb/>
            ſuum interſtitia; </s>
            <s xml:id="echoid-s1803" xml:space="preserve">ut nempe ſi in refringente EF ſumantur æqualia
              <lb/>
            intervalla MN, NO; </s>
            <s xml:id="echoid-s1804" xml:space="preserve">& </s>
            <s xml:id="echoid-s1805" xml:space="preserve">radiorum punctis M, N, O incidentium
              <lb/>
            refracti M _a_, N _a_, O_a_ cum axe concurrant punctis I, K, L ; </s>
            <s xml:id="echoid-s1806" xml:space="preserve">erit </s>
          </p>
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