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

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        <div xml:id="echoid-div222" type="section" level="1" n="31">
          <p>
            <s xml:id="echoid-s10466" xml:space="preserve">
              <pb o="55" file="0233" n="248" rhead=""/>
            item PO ad TE parallela. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">Eſtque EFq = EOq (CPq) + OFq
              <lb/>
            + 2 EO x OF (+ 2 CP x OF). </s>
            <s xml:id="echoid-s10468" xml:space="preserve">Verùm ob CP. </s>
            <s xml:id="echoid-s10469" xml:space="preserve">CA :</s>
            <s xml:id="echoid-s10470" xml:space="preserve">: OP.
              <lb/>
            </s>
            <s xml:id="echoid-s10471" xml:space="preserve">OF :</s>
            <s xml:id="echoid-s10472" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s10473" xml:space="preserve">OF; </s>
            <s xml:id="echoid-s10474" xml:space="preserve">eſt CP x OF = CA x CE; </s>
            <s xml:id="echoid-s10475" xml:space="preserve">ergò EFq =
              <lb/>
            CPq + OFq + 2 CA x CE. </s>
            <s xml:id="echoid-s10476" xml:space="preserve">item eſt AEq = CEq +
              <lb/>
            CAq - 2 CA x CE; </s>
            <s xml:id="echoid-s10477" xml:space="preserve">quapropter eſt EFq + AEq = CPq +
              <lb/>
            CAq + OFq + CEq. </s>
            <s xml:id="echoid-s10478" xml:space="preserve">hoc eſt EGq = (APq + PFq = )
              <lb/>
            CVq + PFq. </s>
            <s xml:id="echoid-s10479" xml:space="preserve">vel EGq - PFq = CVq. </s>
            <s xml:id="echoid-s10480" xml:space="preserve">Verùm eſt CE. </s>
            <s xml:id="echoid-s10481" xml:space="preserve">
              <lb/>
            (PO). </s>
            <s xml:id="echoid-s10482" xml:space="preserve">PF :</s>
            <s xml:id="echoid-s10483" xml:space="preserve">: CP.</s>
            <s xml:id="echoid-s10484" xml:space="preserve">AP :</s>
            <s xml:id="echoid-s10485" xml:space="preserve">: CP.</s>
            <s xml:id="echoid-s10486" xml:space="preserve">CV; </s>
            <s xml:id="echoid-s10487" xml:space="preserve">unde EGq - {CVq/CPq} CEq
              <lb/>
            = CVq; </s>
            <s xml:id="echoid-s10488" xml:space="preserve">adeóque linea GVG eſt _hyperbola_, cujus centrum C; </s>
            <s xml:id="echoid-s10489" xml:space="preserve">ſe-
              <lb/>
            miaxes CV, CP.</s>
            <s xml:id="echoid-s10490" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10491" xml:space="preserve">Not. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">Ductà rectâ FQ ad TH perpendiculari, ſumptáque QR =
              <lb/>
            AE; </s>
            <s xml:id="echoid-s10493" xml:space="preserve">& </s>
            <s xml:id="echoid-s10494" xml:space="preserve">connexâ GR; </s>
            <s xml:id="echoid-s10495" xml:space="preserve">erit GR _hyperbolæ_ VGG perpendicularis;
              <lb/>
            </s>
            <s xml:id="echoid-s10496" xml:space="preserve">mihi præſta sîs ſidem; </s>
            <s xml:id="echoid-s10497" xml:space="preserve">aut ipſe rem ad Calculum exige; </s>
            <s xml:id="echoid-s10498" xml:space="preserve">eò verba
              <lb/>
            non proſundam.</s>
            <s xml:id="echoid-s10499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10500" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s10501" xml:space="preserve">Poſitione datæ ſint rectæ AC, BD (ſe interſecantes in X)
              <lb/>
              <note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" xml:space="preserve">Fig. 59.</note>
            qnas decuſſet recta A B; </s>
            <s xml:id="echoid-s10502" xml:space="preserve">tum ductâ utcunque rectâ PKL ad AB
              <lb/>
            parallelâ, (quæ rectas AC, BD ſecet punctis P, K) ſit PL æqua-
              <lb/>
            lis ipſi BK; </s>
            <s xml:id="echoid-s10503" xml:space="preserve">erit linea ALL recta.</s>
            <s xml:id="echoid-s10504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10505" xml:space="preserve">Nam, (ductâ XQ ad BA parallelâ, eſt AQ. </s>
            <s xml:id="echoid-s10506" xml:space="preserve">AP :</s>
            <s xml:id="echoid-s10507" xml:space="preserve">: (BX.
              <lb/>
            </s>
            <s xml:id="echoid-s10508" xml:space="preserve">BK :</s>
            <s xml:id="echoid-s10509" xml:space="preserve">: ) QX. </s>
            <s xml:id="echoid-s10510" xml:space="preserve">PL: </s>
            <s xml:id="echoid-s10511" xml:space="preserve">ergo linea ALL eſt recta.</s>
            <s xml:id="echoid-s10512" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10513" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s10514" xml:space="preserve">Poſitione data ſit recta A X, & </s>
            <s xml:id="echoid-s10515" xml:space="preserve">punctum D; </s>
            <s xml:id="echoid-s10516" xml:space="preserve">neque non
              <lb/>
            linea DNN talis; </s>
            <s xml:id="echoid-s10517" xml:space="preserve">ut per D ductâ quâcunque rectâ MN (quæ re-
              <lb/>
              <note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">Fig. 60.</note>
            ctam AX ſecet in M, & </s>
            <s xml:id="echoid-s10518" xml:space="preserve">lineam DNN in N) ſit perpetim rectangu-
              <lb/>
            lum ex DM, DN æquale dato (puta quadrato ex Z); </s>
            <s xml:id="echoid-s10519" xml:space="preserve">erit linea
              <lb/>
            DNN circularis.</s>
            <s xml:id="echoid-s10520" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10521" xml:space="preserve">Nam ducatur DB ad AX perpendicularis; </s>
            <s xml:id="echoid-s10522" xml:space="preserve">ſitque DB. </s>
            <s xml:id="echoid-s10523" xml:space="preserve">Z :</s>
            <s xml:id="echoid-s10524" xml:space="preserve">: Z.
              <lb/>
            </s>
            <s xml:id="echoid-s10525" xml:space="preserve">DE; </s>
            <s xml:id="echoid-s10526" xml:space="preserve">& </s>
            <s xml:id="echoid-s10527" xml:space="preserve">connectatur NE; </s>
            <s xml:id="echoid-s10528" xml:space="preserve">Eſt jam DM x DN = Zq = DB x
              <lb/>
            DE; </s>
            <s xml:id="echoid-s10529" xml:space="preserve">quare DM. </s>
            <s xml:id="echoid-s10530" xml:space="preserve">DB :</s>
            <s xml:id="echoid-s10531" xml:space="preserve">: DE. </s>
            <s xml:id="echoid-s10532" xml:space="preserve">DN. </s>
            <s xml:id="echoid-s10533" xml:space="preserve">ergò triangula DBM, DNE
              <lb/>
            ſimilia ſunt; </s>
            <s xml:id="echoid-s10534" xml:space="preserve">quapropter angulus DNE rectus eſt; </s>
            <s xml:id="echoid-s10535" xml:space="preserve">itaque linea DNN
              <lb/>
            eſt circularis: </s>
            <s xml:id="echoid-s10536" xml:space="preserve">(ad circulum pertinens, _c@jus Diameter_ DE).</s>
            <s xml:id="echoid-s10537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10538" xml:space="preserve">Vides nedum rectam & </s>
            <s xml:id="echoid-s10539" xml:space="preserve">_hyperbolam_; </s>
            <s xml:id="echoid-s10540" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s10541" xml:space="preserve">ſuo modo rectam ac
              <lb/>
            _circulum_ ſibi lineas eſſe reciprocas. </s>
            <s xml:id="echoid-s10542" xml:space="preserve">Verùm hîc, etſi præludiis no-
              <lb/>
            ſtris nondum abſolutis, paulùm ſubſiſtamus.</s>
            <s xml:id="echoid-s10543" xml:space="preserve"/>
          </p>
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