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-s1280" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">Non abſimiliter in _Hyperbola_, (cujus itidem axis BD, foci H, K;
              <lb/>
            </s>
            <s xml:id="echoid-s1282" xml:space="preserve">reliquiſque velut anteà præparatis) oſtendetur fore perpetuò NK. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">Fig. 27.</note>
            CK :</s>
            <s xml:id="echoid-s1284" xml:space="preserve">: BD. </s>
            <s xml:id="echoid-s1285" xml:space="preserve">HK. </s>
            <s xml:id="echoid-s1286" xml:space="preserve">unde ſi fuerit (ex _Hyperbolæ_ conſtructione) BD.
              <lb/>
            </s>
            <s xml:id="echoid-s1287" xml:space="preserve">HK :</s>
            <s xml:id="echoid-s1288" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1289" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1290" xml:space="preserve">erit etiam NK. </s>
            <s xml:id="echoid-s1291" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s1292" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1293" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1294" xml:space="preserve">quòd ſi radius MN ad
              <lb/>
            CB parallelus refringatur in NK; </s>
            <s xml:id="echoid-s1295" xml:space="preserve">hoc idem accidet, ut nempe ſit
              <lb/>
            NK. </s>
            <s xml:id="echoid-s1296" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s1297" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">R. </s>
            <s xml:id="echoid-s1299" xml:space="preserve">quare radii MN refractus per _Hyperbolæ_ focum
              <lb/>
            tranſibit.</s>
            <s xml:id="echoid-s1300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1301" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1302" xml:space="preserve">Quòd verò ab _Ellipſis_ aut _Hyperbolæ_ cujuſvis focorum alterutro
              <lb/>
            quilibet curvæ incidens radieus in alterum reflectatur, admodum facilè
              <lb/>
            diluceſcit. </s>
            <s xml:id="echoid-s1303" xml:space="preserve">Nam in ellipſe, perpendicularis NC, in _Hyperbolæ_, tan-
              <lb/>
            gens. </s>
            <s xml:id="echoid-s1304" xml:space="preserve">NT biſecat angulum HNK. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">unde patet propoſitum, Hæc
              <lb/>
            extra noſtras oleas poſita curſim & </s>
            <s xml:id="echoid-s1306" xml:space="preserve">leviſſimè perſtringo; </s>
            <s xml:id="echoid-s1307" xml:space="preserve">nec tamen
              <lb/>
            ut eò multa putem deſiderari.</s>
            <s xml:id="echoid-s1308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1309" xml:space="preserve">Revertamur in orbitani; </s>
            <s xml:id="echoid-s1310" xml:space="preserve">& </s>
            <s xml:id="echoid-s1311" xml:space="preserve">quidem derelictis his generaliſſimis,
              <lb/>
            ac abſtractiſſimis, lemmatum vicem obituris, ad particularia deſcenda-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s1312" xml:space="preserve">Ad planas verò ſuperficies (vel earum loco propter inſinuatam
              <lb/>
            antehac cauſam ſubrogatas lineas rectas) inflexis obtingentia radiis pri-
              <lb/>
            mò contemplemur. </s>
            <s xml:id="echoid-s1313" xml:space="preserve">Etiam quoad has Catoptricis primum, utpote fa-
              <lb/>
            cillimis, breviſſimè defungemur.</s>
            <s xml:id="echoid-s1314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1315" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s1316" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1317" xml:space="preserve">Parallelorum ſibi radiorum (AB, MN) rectæ (EF) in-
              <lb/>
              <note position="right" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve">Fig. 28.</note>
            cidentium reflexi (B _α_, Nμ) ſunt etiam ſibi paralleli.</s>
            <s xml:id="echoid-s1318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1319" xml:space="preserve">Nam quoniam AB, MN ex hypotheſi ſunt pàralleli, erunt anguli
              <lb/>
            ABE, MNE pares. </s>
            <s xml:id="echoid-s1320" xml:space="preserve">Ergò ſunt anguli _α_ BF, μ NF etiam pares.
              <lb/>
            </s>
            <s xml:id="echoid-s1321" xml:space="preserve">Quare rectæ _α_ B, μ N ſunt parallelæ.</s>
            <s xml:id="echoid-s1322" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1323" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s1324" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1325" xml:space="preserve">Sit recta ABZ rectæ reflectenti EF perpendicularis; </s>
            <s xml:id="echoid-s1326" xml:space="preserve">cum
              <lb/>
            hacverò promanantis ab A cujuſvis radii AN reflexus _α_ N. </s>
            <s xml:id="echoid-s1327" xml:space="preserve">conveniat
              <lb/>
            in Z; </s>
            <s xml:id="echoid-s1328" xml:space="preserve">dico forè BZ = AB. </s>
            <s xml:id="echoid-s1329" xml:space="preserve">Nam ang. </s>
            <s xml:id="echoid-s1330" xml:space="preserve">ANB = ang. </s>
            <s xml:id="echoid-s1331" xml:space="preserve">_α_ NF =
              <lb/>
            ZNB. </s>
            <s xml:id="echoid-s1332" xml:space="preserve">quare liquet triangula BNA, BNZ ſibi mutuò æquilatera
              <lb/>
            fore; </s>
            <s xml:id="echoid-s1333" xml:space="preserve">& </s>
            <s xml:id="echoid-s1334" xml:space="preserve">eſſe AB = BZ: </s>
            <s xml:id="echoid-s1335" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1336" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1337" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1338" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1339" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s1340" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1341" xml:space="preserve">Hinc, omnes ab uno puncto, divergentium tanquam ab altero
              <lb/>
              <note position="right" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve">Fig. 29.</note>
            quodam uno prodeuntes.</s>
            <s xml:id="echoid-s1342" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1343" xml:space="preserve">Quoad punctum longè diſſitum (ſuo parallelos ad ſenſum radios eja-
              <lb/>
            @ulante) patet è penultima. </s>
            <s xml:id="echoid-s1344" xml:space="preserve">Quòad punctum è ſenſibiliter finita di-
              <lb/>
            ſtantia radians, ex ultima patet, quòd omnium ab A divergentium ra-
              <lb/>
            diorum reflexi protracti concurrunt in Z; </s>
            <s xml:id="echoid-s1345" xml:space="preserve">adeóque videbuntur ab eo
              <lb/>
            promanare.</s>
            <s xml:id="echoid-s1346" xml:space="preserve"/>
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