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-s1347" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Hinc punctum Z erit ipſius A (reſpectu oculi uspiam conſti-
              <lb/>
            tuti) imago perfectiſſima. </s>
            <s xml:id="echoid-s1349" xml:space="preserve">Siquidem imaginis vocabulo nil aliud in-
              <lb/>
            telligo, quàm locum à quo plures radii (quot ſcilicet afficiendo viſui
              <lb/>
            ſufficiunt) ſimiliter divergere, ſeu dimanare videntur, atque cùm à
              <lb/>
            primariis objectis diffunduntur. </s>
            <s xml:id="echoid-s1350" xml:space="preserve">Proinde cujuſvis hoc modo radiantis
              <lb/>
            objecti locus apparens, vel imago facilimè determinatur.</s>
            <s xml:id="echoid-s1351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1352" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s1353" xml:space="preserve">Exhinc etiam eâdem operâ, viſùs imaginem adſpectantis axis,
              <lb/>
            ſeu reflexus principalis (iſte nimirum qui per oculi centrum (puta O)
              <lb/>
            tranſit,) & </s>
            <s xml:id="echoid-s1354" xml:space="preserve">reflectionis (quod vocant) punctum determinantur. </s>
            <s xml:id="echoid-s1355" xml:space="preserve">Con-
              <lb/>
            nexa nempe recta OZ@erit axis iſte; </s>
            <s xml:id="echoid-s1356" xml:space="preserve">nec non ejus cum EF interſectio
              <lb/>
            N, punctum reflectionis.</s>
            <s xml:id="echoid-s1357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1358" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Quoad hoc reflectionis punctum unicam ſubjiciemus anno-
              <lb/>
            tatiunculam. </s>
            <s xml:id="echoid-s1360" xml:space="preserve">Radiante puncto A, & </s>
            <s xml:id="echoid-s1361" xml:space="preserve">oculi centro O fixis manentibus
              <lb/>
            recta Catoptrica EF ponatur rectæ cuidam OP parallela, ſed alioquin
              <lb/>
            ſitu indeterminata; </s>
            <s xml:id="echoid-s1362" xml:space="preserve">erunt omnia reflectionis puncta in _Hyperbolæ_.
              <lb/>
            </s>
            <s xml:id="echoid-s1363" xml:space="preserve">Sit, inquam, AP ad OP perpendicularis, & </s>
            <s xml:id="echoid-s1364" xml:space="preserve">biſecentur AP in X, at-
              <lb/>
            que PO in Y; </s>
            <s xml:id="echoid-s1365" xml:space="preserve">& </s>
            <s xml:id="echoid-s1366" xml:space="preserve">per X ducatur XG ad PO parallela, item per Y
              <lb/>
              <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">Fig. 30.</note>
            ducatur YH ad AP parallela; </s>
            <s xml:id="echoid-s1367" xml:space="preserve">& </s>
            <s xml:id="echoid-s1368" xml:space="preserve">XG, YH concurrant in C; </s>
            <s xml:id="echoid-s1369" xml:space="preserve">tum
              <lb/>
            Aſymptotis CG, CH per ipſum O deſcripta concipiatur _Hyperbole_
              <lb/>
            ROS; </s>
            <s xml:id="echoid-s1370" xml:space="preserve">hæc per omnia reflectionum dictarum puncta tranſibit. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Nam
              <lb/>
            utcunque ducta EF ad PO parallela _Hyperbolæ_ ROS occurrat ad N;
              <lb/>
            </s>
            <s xml:id="echoid-s1372" xml:space="preserve">& </s>
            <s xml:id="echoid-s1373" xml:space="preserve">ducantur rectæ AN, ON; </s>
            <s xml:id="echoid-s1374" xml:space="preserve">dico angulnm ANE angulo ONF
              <lb/>
            æquari. </s>
            <s xml:id="echoid-s1375" xml:space="preserve">Secet enim AP ipſam EF in B; </s>
            <s xml:id="echoid-s1376" xml:space="preserve">& </s>
            <s xml:id="echoid-s1377" xml:space="preserve">ducatur OQ ad AB
              <lb/>
            parallela. </s>
            <s xml:id="echoid-s1378" xml:space="preserve">Et, ex _Hyperbolæ_ natura, eſt CD. </s>
            <s xml:id="echoid-s1379" xml:space="preserve">CY :</s>
            <s xml:id="echoid-s1380" xml:space="preserve">: YODN. </s>
            <s xml:id="echoid-s1381" xml:space="preserve">
              <lb/>
            quare dividendo erit YD. </s>
            <s xml:id="echoid-s1382" xml:space="preserve">CY :</s>
            <s xml:id="echoid-s1383" xml:space="preserve">: YO-DNDN; </s>
            <s xml:id="echoid-s1384" xml:space="preserve">hoc eſt OQ. </s>
            <s xml:id="echoid-s1385" xml:space="preserve">
              <lb/>
            CY :</s>
            <s xml:id="echoid-s1386" xml:space="preserve">: NQDN. </s>
            <s xml:id="echoid-s1387" xml:space="preserve">& </s>
            <s xml:id="echoid-s1388" xml:space="preserve">permutatim OQNQ :</s>
            <s xml:id="echoid-s1389" xml:space="preserve">: CY. </s>
            <s xml:id="echoid-s1390" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s1391" xml:space="preserve">item
              <lb/>
            rurſus ob CD. </s>
            <s xml:id="echoid-s1392" xml:space="preserve">CY :</s>
            <s xml:id="echoid-s1393" xml:space="preserve">: YO. </s>
            <s xml:id="echoid-s1394" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s1395" xml:space="preserve">erit componendo CD + CY. </s>
            <s xml:id="echoid-s1396" xml:space="preserve">
              <lb/>
            CY :</s>
            <s xml:id="echoid-s1397" xml:space="preserve">: YO + DN. </s>
            <s xml:id="echoid-s1398" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s1399" xml:space="preserve">hoc eſt AB. </s>
            <s xml:id="echoid-s1400" xml:space="preserve">CY :</s>
            <s xml:id="echoid-s1401" xml:space="preserve">: BN. </s>
            <s xml:id="echoid-s1402" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s1403" xml:space="preserve">vel
              <lb/>
            permutando AB. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">BN :</s>
            <s xml:id="echoid-s1405" xml:space="preserve">: CY. </s>
            <s xml:id="echoid-s1406" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s1407" xml:space="preserve">quare eſt OQ. </s>
            <s xml:id="echoid-s1408" xml:space="preserve">NQ :</s>
            <s xml:id="echoid-s1409" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">
              <lb/>
            BN. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">ergò rectangula triangula, OQN, ABN ſimilia ſunt; </s>
            <s xml:id="echoid-s1412" xml:space="preserve">& </s>
            <s xml:id="echoid-s1413" xml:space="preserve">patet
              <lb/>
            angulum ONQ angulo ANB æquari: </s>
            <s xml:id="echoid-s1414" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1415" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1416" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1418" xml:space="preserve">Mereri ſaltem vel _Hyperbolæ gratiâ_ videbatur hæc ejuſce proprietas
              <lb/>
            adnotari; </s>
            <s xml:id="echoid-s1419" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s1420" xml:space="preserve">Analogiæ cauſà verſus ea quæ ſequentur. </s>
            <s xml:id="echoid-s1421" xml:space="preserve">Neque
              <lb/>
            de reflectionibus ad plana quicquam prætereà. </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Ad refractiones
              <lb/>
            tranſeo.</s>
            <s xml:id="echoid-s1423" xml:space="preserve"/>
          </p>
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