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

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            <s xml:id="echoid-s11459" xml:space="preserve">
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            talis; </s>
            <s xml:id="echoid-s11460" xml:space="preserve">ut à puncto D ductâ quâvis rectâ DYH (quæ rectam BK ſe-
              <lb/>
            cet in H, curvam DYX in Y) ſit perpetuò ſubtenſa DY æqualis re-
              <lb/>
            ctæ BH; </s>
            <s xml:id="echoid-s11461" xml:space="preserve">oportet curvæ DYX tangentem ad Y rectam determi-
              <lb/>
            nare.</s>
            <s xml:id="echoid-s11462" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11463" xml:space="preserve">Centro D per B ducatur circulus BRS; </s>
            <s xml:id="echoid-s11464" xml:space="preserve">cui occurrat recta YER
              <lb/>
            ad BK parallela; </s>
            <s xml:id="echoid-s11465" xml:space="preserve">& </s>
            <s xml:id="echoid-s11466" xml:space="preserve">connectatur DR; </s>
            <s xml:id="echoid-s11467" xml:space="preserve">eſtque (propter ang. </s>
            <s xml:id="echoid-s11468" xml:space="preserve">DYE
              <lb/>
            = ang. </s>
            <s xml:id="echoid-s11469" xml:space="preserve">DHB; </s>
            <s xml:id="echoid-s11470" xml:space="preserve">& </s>
            <s xml:id="echoid-s11471" xml:space="preserve">DY = BH, ac DR = DB) triangulum RDY
              <lb/>
            triangulo DBH ſimile ac æquale; </s>
            <s xml:id="echoid-s11472" xml:space="preserve">quare RY. </s>
            <s xml:id="echoid-s11473" xml:space="preserve">YD :</s>
            <s xml:id="echoid-s11474" xml:space="preserve">: (DH. </s>
            <s xml:id="echoid-s11475" xml:space="preserve">HB)
              <lb/>
            :</s>
            <s xml:id="echoid-s11476" xml:space="preserve">: YD. </s>
            <s xml:id="echoid-s11477" xml:space="preserve">YE. </s>
            <s xml:id="echoid-s11478" xml:space="preserve">unde ex præcedente determinabilis eſt recta curvam
              <lb/>
            DYX tangens in Y.</s>
            <s xml:id="echoid-s11479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11480" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s11481" xml:space="preserve">Sint itidem rectæ DB, BK poſitione datæ; </s>
            <s xml:id="echoid-s11482" xml:space="preserve">nec non curva
              <lb/>
            BXX talis, ut à puncto Dprojectâ quâcunque rectâ DX (quæ re-
              <lb/>
              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">Fig. 93.</note>
            ctam BK ſecet in H, curvámque BXX in X) ſit perpetuò HX ipſi
              <lb/>
            BH æqualis; </s>
            <s xml:id="echoid-s11483" xml:space="preserve">deſignetur oportet recta curvam BMX tangens in X.</s>
            <s xml:id="echoid-s11484" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11485" xml:space="preserve">Concipiatur curva DYY talis, ut perpetuò ſit DY = BH (talis
              <lb/>
            nempe, qualem attigimus in præcedente) hanc verò tangat recta YT
              <lb/>
            in Y, ipſi BK occurrens in R; </s>
            <s xml:id="echoid-s11486" xml:space="preserve">tum _aſymptotis_ RB, RT per X de-
              <lb/>
            ſcripta cenſeatur _hyperbola_ NXN; </s>
            <s xml:id="echoid-s11487" xml:space="preserve">ad quam utcunque projiciatur re-
              <lb/>
              <note position="right" xlink:label="note-0247-02" xlink:href="note-0247-02a" xml:space="preserve">_a_) _Couſtr_.</note>
            cta DN (lineas expoſitas ſecans, ut vides) Eſtque jam OM
              <note position="right" xlink:label="note-0247-03" xlink:href="note-0247-03a" xml:space="preserve">(_b_) _Converſ_
                <lb/>
              9. Lect. VI</note>
            D I) &</s>
            <s xml:id="echoid-s11488" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11489" xml:space="preserve"> (DL = ) ON; </s>
            <s xml:id="echoid-s11490" xml:space="preserve">ergò _hyperbola_ NXN curvam BXX tangit ad X. </s>
            <s xml:id="echoid-s11491" xml:space="preserve">Ducatur itaque recta XS _hyperbolam_ NXN contin-
              <lb/>
            gens, hæc ipſam curvam BXX quoque continget.</s>
            <s xml:id="echoid-s11492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11493" xml:space="preserve">Cæterùm ſatìs pro hac vice nugati videmur; </s>
            <s xml:id="echoid-s11494" xml:space="preserve">ceſſemus aliquantiſper.</s>
            <s xml:id="echoid-s11495" xml:space="preserve"/>
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