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-s11324" xml:space="preserve">Nam _aſymptotis_ ER, AB per F deſcripta concipiatur _hyperbol@_
              <lb/>
            OFO; </s>
            <s xml:id="echoid-s11325" xml:space="preserve">cui occurrat à D projecta quæpiam DO, lineas expoſitas
              <lb/>
              <note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">(_a_) Conver ſ 9@
                <lb/>
              Lect. VI.</note>
            ſecans, utì cernis. </s>
            <s xml:id="echoid-s11326" xml:space="preserve">Eſtque QO = DP; </s>
            <s xml:id="echoid-s11327" xml:space="preserve"> quare MO &</s>
            <s xml:id="echoid-s11328" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11329" xml:space="preserve">
              <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">(_b_)_Hyp_.</note>
              <note position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">(_c_)_Elem_.</note>
            &</s>
            <s xml:id="echoid-s11330" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11331" xml:space="preserve">DH = MN. </s>
            <s xml:id="echoid-s11332" xml:space="preserve">ergò _hyperbola_ OFO curvam YFN git.</s>
            <s xml:id="echoid-s11333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11334" xml:space="preserve">Verùm recta LS _hyperbolam_ OFO tangit; </s>
            <s xml:id="echoid-s11335" xml:space="preserve">hæc itaque
              <note position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">(_d_)_9. hujues_</note>
            YF N quoque tanget.</s>
            <s xml:id="echoid-s11336" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11337" xml:space="preserve">_Not_. </s>
            <s xml:id="echoid-s11338" xml:space="preserve">Si XEM ponatur linea recta ( vel ipſi ER coincidat) erit
              <lb/>
            YF N _Conchois_ prima vulgaris, ſeu _Nicomedea_; </s>
            <s xml:id="echoid-s11339" xml:space="preserve">hujus igitur tangens
              <lb/>
            è generali ratione quâdam habetur determinata.</s>
            <s xml:id="echoid-s11340" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11341" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s11342" xml:space="preserve">Sit recta LA, curváque quæpiam BEI; </s>
            <s xml:id="echoid-s11343" xml:space="preserve">cum alia curva
              <lb/>
            DFG talis, ut ductâ liberè rectâ PFE ad p@itione datâm quandam
              <lb/>
              <note position="right" xlink:label="note-0245-05" xlink:href="note-0245-05a" xml:space="preserve">Fig. 87.</note>
            parallelâ, poſſit recta PE quadratum ex PF unà cum quadrato ex da-
              <lb/>
            tâ Z; </s>
            <s xml:id="echoid-s11344" xml:space="preserve">item curvam BE I tangat recta ET; </s>
            <s xml:id="echoid-s11345" xml:space="preserve">tum fiat PEq. </s>
            <s xml:id="echoid-s11346" xml:space="preserve">PFq :</s>
            <s xml:id="echoid-s11347" xml:space="preserve">:
              <lb/>
            PT. </s>
            <s xml:id="echoid-s11348" xml:space="preserve">PS; </s>
            <s xml:id="echoid-s11349" xml:space="preserve">connexa SF curvam DFG tanget.</s>
            <s xml:id="echoid-s11350" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11351" xml:space="preserve">Nam concipiatur curva VFH talis, ut liberè ductâ QK ad PE
              <lb/>
            parallelâ (quæ lineas expoſitas ſecet ut vides) ſit perpetuò QKq =
              <lb/>
            QHq + Zq; </s>
            <s xml:id="echoid-s11352" xml:space="preserve">unde quoniam eſt QK &</s>
            <s xml:id="echoid-s11353" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11354" xml:space="preserve">Q I; </s>
            <s xml:id="echoid-s11355" xml:space="preserve">erit QKq
              <note position="right" xlink:label="note-0245-06" xlink:href="note-0245-06a" xml:space="preserve">(_a_)_Hyp_.</note>
            Zq &</s>
            <s xml:id="echoid-s11356" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11357" xml:space="preserve">Q Iq-- Zq; </s>
            <s xml:id="echoid-s11358" xml:space="preserve">hoc eſt QHq &</s>
            <s xml:id="echoid-s11359" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11360" xml:space="preserve">QGq; </s>
            <s xml:id="echoid-s11361" xml:space="preserve">ergò curva VFH
              <lb/>
              <note position="right" xlink:label="note-0245-07" xlink:href="note-0245-07a" xml:space="preserve">(_b_) 22. _Lect. 6._</note>
            curvam DFG tanget ad F ; </s>
            <s xml:id="echoid-s11362" xml:space="preserve">eſt autem curva VF H _hyperbola_,
              <note position="right" xlink:label="note-0245-08" xlink:href="note-0245-08a" xml:space="preserve">(_c_)_Cor. 22._
                <lb/>
              Lect. _I_.</note>
            tangit recta SF. </s>
            <s xml:id="echoid-s11363" xml:space="preserve">hæc itaque curvam DFG quoque get.</s>
            <s xml:id="echoid-s11364" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11365" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s11366" xml:space="preserve">Cætera ponantur eadem; </s>
            <s xml:id="echoid-s11367" xml:space="preserve">at jam PE unà cum quadrato ex
              <lb/>
            data Z poſſit quadratum ex PF; </s>
            <s xml:id="echoid-s11368" xml:space="preserve">fiátque PEq. </s>
            <s xml:id="echoid-s11369" xml:space="preserve">PFq :</s>
            <s xml:id="echoid-s11370" xml:space="preserve">: PT. </s>
            <s xml:id="echoid-s11371" xml:space="preserve">PS;
              <lb/>
            </s>
            <s xml:id="echoid-s11372" xml:space="preserve">
              <note position="right" xlink:label="note-0245-09" xlink:href="note-0245-09a" xml:space="preserve">Fig. 88.</note>
            & </s>
            <s xml:id="echoid-s11373" xml:space="preserve">connectatur FS; </s>
            <s xml:id="echoid-s11374" xml:space="preserve">hæc rurſus ipſam GFG continget.</s>
            <s xml:id="echoid-s11375" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11376" xml:space="preserve">Similis eſt demonſtratio; </s>
            <s xml:id="echoid-s11377" xml:space="preserve">ſed adhibe 23 am primæ Lectionis.</s>
            <s xml:id="echoid-s11378" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11379" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s11380" xml:space="preserve">Sint curvæ duæ AFB, CGD, communem habentes _axe@@_
              <lb/>
            AD, ac ità verſus ſerelatæ, ut ductâ quâcunque rectâ FEG ad AD
              <lb/>
            perpendiculari ( quæ rectas expoſitas ſecet ut vides ) ſit ſumma qua-
              <lb/>
            dratorum ex ipſis EF, EG æqualis quadrato ex determinata recta Z;
              <lb/>
            </s>
            <s xml:id="echoid-s11381" xml:space="preserve">
              <note position="right" xlink:label="note-0245-10" xlink:href="note-0245-10a" xml:space="preserve">Fig. 89.</note>
            tangat autem recta FR ex his curvis unam AFB; </s>
            <s xml:id="echoid-s11382" xml:space="preserve">& </s>
            <s xml:id="echoid-s11383" xml:space="preserve">fiat EFq.
              <lb/>
            </s>
            <s xml:id="echoid-s11384" xml:space="preserve">EGq :</s>
            <s xml:id="echoid-s11385" xml:space="preserve">: ER. </s>
            <s xml:id="echoid-s11386" xml:space="preserve">ET; </s>
            <s xml:id="echoid-s11387" xml:space="preserve">connexa GT curvam CGD quoque tanget.</s>
            <s xml:id="echoid-s11388" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11389" xml:space="preserve">Concipiatur enim curva OGO talis, ut ductâ rectâ KQO (quæ
              <lb/>
            rectas FR, ER ſecet punctis K, Q, curvam OGO in O ) ſit QKq
              <lb/>
            + QO = Zq; </s>
            <s xml:id="echoid-s11390" xml:space="preserve">erit ideò QKq + QOq = QIq + QLq;
              <lb/>
            </s>
            <s xml:id="echoid-s11391" xml:space="preserve">& </s>
            <s xml:id="echoid-s11392" xml:space="preserve">cùm ſit QKq &</s>
            <s xml:id="echoid-s11393" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11394" xml:space="preserve">QIq, erit ideò QOq &</s>
            <s xml:id="echoid-s11395" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11396" xml:space="preserve">QLq. </s>
            <s xml:id="echoid-s11397" xml:space="preserve">
              <note position="right" xlink:label="note-0245-11" xlink:href="note-0245-11a" xml:space="preserve">(_a_)_Hyp_.</note>
            curva OGO curvam CGD (introrſum) tangit. </s>
            <s xml:id="echoid-s11398" xml:space="preserve"> Eſt autem (
              <note position="right" xlink:label="note-0245-12" xlink:href="note-0245-12a" xml:space="preserve">(_b_) 24. lect.
                <lb/>
              VI.</note>
            </s>
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