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-s1806" xml:space="preserve">
              <pb o="35" file="0053" n="53" rhead=""/>
            tervallum IK minus ipſo KL ; </s>
            <s xml:id="echoid-s1807" xml:space="preserve">ſeu generalius efferendo, libere ſum-
              <lb/>
            ptis ipſis MN, NO ; </s>
            <s xml:id="echoid-s1808" xml:space="preserve">erit IK. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">KL &</s>
            <s xml:id="echoid-s1810" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1811" xml:space="preserve">MN. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">NO. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">hoc verò non
              <lb/>
            aliter, opinor, elegantius quam ex adjunctis uno, vel altero Theore-
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">Fig. 43.</note>
            mate conſtabit.</s>
            <s xml:id="echoid-s1814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1815" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s1816" xml:space="preserve">In primo caſu; </s>
            <s xml:id="echoid-s1817" xml:space="preserve">ſit (ut antehac) ZB. </s>
            <s xml:id="echoid-s1818" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s1819" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1820" xml:space="preserve">R; </s>
            <s xml:id="echoid-s1821" xml:space="preserve">ſuper-
              <lb/>
            que diametro ZB conſtituatur ſemicirculus; </s>
            <s xml:id="echoid-s1822" xml:space="preserve">cui à puncto B adapte-
              <lb/>
            tur BD = BA ; </s>
            <s xml:id="echoid-s1823" xml:space="preserve">& </s>
            <s xml:id="echoid-s1824" xml:space="preserve">per puncta Z, D ducta recta refringenti occur-
              <lb/>
            rat in Y ; </s>
            <s xml:id="echoid-s1825" xml:space="preserve">tum ad ſemiaxes BZ, BY (centro nempe B, vertice Z) de-
              <lb/>
            ſcribatur Hyperbole HZG; </s>
            <s xml:id="echoid-s1826" xml:space="preserve">in hac autem ſumpto quolibet puncto S
              <lb/>
            ducantur SN ad AB, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">SK ad EF parallelæ. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">Denique ducantur
              <lb/>
              <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">Fig. 44.</note>
            A N, KN _a_ erit KM _a_ incidentis AN refractus.</s>
            <s xml:id="echoid-s1829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1830" xml:space="preserve">Nam ex _Hyperbolæ_ natura eſt KBq - ZBq. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">BNq :</s>
            <s xml:id="echoid-s1832" xml:space="preserve">: BZq.
              <lb/>
            </s>
            <s xml:id="echoid-s1833" xml:space="preserve">BYq :</s>
            <s xml:id="echoid-s1834" xml:space="preserve">: ZDq. </s>
            <s xml:id="echoid-s1835" xml:space="preserve">BDq (hoc eſt) :</s>
            <s xml:id="echoid-s1836" xml:space="preserve">: ZBq - ABq. </s>
            <s xml:id="echoid-s1837" xml:space="preserve">ABq. </s>
            <s xml:id="echoid-s1838" xml:space="preserve">quare
              <lb/>
            componendo KBq - ZBq + BNq. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">BNq :</s>
            <s xml:id="echoid-s1840" xml:space="preserve">: ZBq. </s>
            <s xml:id="echoid-s1841" xml:space="preserve">ABq hoc
              <lb/>
            eſt KNq - ZBq. </s>
            <s xml:id="echoid-s1842" xml:space="preserve">BNq :</s>
            <s xml:id="echoid-s1843" xml:space="preserve">: ZBq. </s>
            <s xml:id="echoid-s1844" xml:space="preserve">ABq. </s>
            <s xml:id="echoid-s1845" xml:space="preserve">permutandóque KNq
              <lb/>
            - ZBq. </s>
            <s xml:id="echoid-s1846" xml:space="preserve">ZBq :</s>
            <s xml:id="echoid-s1847" xml:space="preserve">: BNq. </s>
            <s xml:id="echoid-s1848" xml:space="preserve">ABq rurſuſque componendo KNq. </s>
            <s xml:id="echoid-s1849" xml:space="preserve">
              <lb/>
            ZBq :</s>
            <s xml:id="echoid-s1850" xml:space="preserve">: ANq . </s>
            <s xml:id="echoid-s1851" xml:space="preserve">ABq. </s>
            <s xml:id="echoid-s1852" xml:space="preserve">denuóque permutando KNq. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">ANq :</s>
            <s xml:id="echoid-s1854" xml:space="preserve">:
              <lb/>
            ZBq. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">ABq :</s>
            <s xml:id="echoid-s1856" xml:space="preserve">: Iq . </s>
            <s xml:id="echoid-s1857" xml:space="preserve">Rq. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">quare KN. </s>
            <s xml:id="echoid-s1859" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s1860" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1861" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1862" xml:space="preserve">ergo KN ip-
              <lb/>
            ſius AN reſractus erit: </s>
            <s xml:id="echoid-s1863" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1864" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1865" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1866" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1867" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Hinc refractorum cum axe concurſus (puta I, K, L) à ſe
              <lb/>
            diſtant intervallis ordinatim applicatarum ad _Hyperbolam_, puta recta-
              <lb/>
            rum, BZ, MR, NS, OT ; </s>
            <s xml:id="echoid-s1869" xml:space="preserve">vel ipſarum O, ZI, ZK, ZL. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">Hæ ve-
              <lb/>
            rò (ceu paſſim notum, & </s>
            <s xml:id="echoid-s1871" xml:space="preserve">à nobis aliquando generatim circa cunctas
              <lb/>
            hujuſmodi curvas oſtenſum eſt) in majori ratione creſcunt, quam ipſæ
              <lb/>
            BM, BN, BO ; </s>
            <s xml:id="echoid-s1872" xml:space="preserve">nempe ZL . </s>
            <s xml:id="echoid-s1873" xml:space="preserve">ZK &</s>
            <s xml:id="echoid-s1874" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1875" xml:space="preserve">LT . </s>
            <s xml:id="echoid-s1876" xml:space="preserve">KS. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">& </s>
            <s xml:id="echoid-s1878" xml:space="preserve">ZK. </s>
            <s xml:id="echoid-s1879" xml:space="preserve">ZI &</s>
            <s xml:id="echoid-s1880" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s1881" xml:space="preserve">KS.
              <lb/>
            </s>
            <s xml:id="echoid-s1882" xml:space="preserve">IR. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">quare ſatìs liquet propoſitum. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">Enimverò prope verticem Z
              <lb/>
            ordinatarum differentiæ perquam exiguæ ſunt; </s>
            <s xml:id="echoid-s1885" xml:space="preserve">ut bene multorum
              <lb/>
            perpendiculari AB adjacentium radiorum refracti velut è puncto
              <lb/>
            Z manare videantur ; </s>
            <s xml:id="echoid-s1886" xml:space="preserve">utcunque circa ipſum præcipuè conſtipantur.</s>
            <s xml:id="echoid-s1887" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1888" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s1889" xml:space="preserve">Haud abſimiliter, in ſecundo caſu, ſuper ipſa AB deſcriba-
              <lb/>
            tur ſemicirculus; </s>
            <s xml:id="echoid-s1890" xml:space="preserve">& </s>
            <s xml:id="echoid-s1891" xml:space="preserve">huic accommodetur BD = BZ; </s>
            <s xml:id="echoid-s1892" xml:space="preserve">& </s>
            <s xml:id="echoid-s1893" xml:space="preserve">connexa
              <lb/>
            protractáque AD refringenti occurrat ad Y ; </s>
            <s xml:id="echoid-s1894" xml:space="preserve">tum centro B ſemiaxi-
              <lb/>
            bus BZ, BY deſcribatur ellipſis HZG; </s>
            <s xml:id="echoid-s1895" xml:space="preserve">& </s>
            <s xml:id="echoid-s1896" xml:space="preserve">in hac accepto quocunque
              <lb/>
              <note position="right" xlink:label="note-0053-03" xlink:href="note-0053-03a" xml:space="preserve">Fig. 45.</note>
            puncto S ducantur SN ad ZB, & </s>
            <s xml:id="echoid-s1897" xml:space="preserve">SK ad EF parallela; </s>
            <s xml:id="echoid-s1898" xml:space="preserve">connectan-
              <lb/>
            tur denique rectæ AN , KN; </s>
            <s xml:id="echoid-s1899" xml:space="preserve">erit KN incidentis AN refractus.
              <lb/>
            </s>
            <s xml:id="echoid-s1900" xml:space="preserve">Etenim ex ellipſis natura eſt KSq. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">ZBq - SNq :</s>
            <s xml:id="echoid-s1902" xml:space="preserve">: BYq. </s>
            <s xml:id="echoid-s1903" xml:space="preserve">BZq
              <lb/>
            :</s>
            <s xml:id="echoid-s1904" xml:space="preserve">: BYq. </s>
            <s xml:id="echoid-s1905" xml:space="preserve">BDq :</s>
            <s xml:id="echoid-s1906" xml:space="preserve">: BAq. </s>
            <s xml:id="echoid-s1907" xml:space="preserve">ADq:</s>
            <s xml:id="echoid-s1908" xml:space="preserve">: BAq. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">BAq - BZq. </s>
            <s xml:id="echoid-s1910" xml:space="preserve">& </s>
            <s xml:id="echoid-s1911" xml:space="preserve">per </s>
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