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

Table of Notes

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          <p>
            <s xml:id="echoid-s11398" xml:space="preserve">
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            oſtenſis) curva OGO _Ellipſis_, quam recta GT tangit. </s>
            <s xml:id="echoid-s11399" xml:space="preserve">ergò recta
              <lb/>
            GT curvam CGD quoque tanget.</s>
            <s xml:id="echoid-s11400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11401" xml:space="preserve">XVI Sit curva quæpiam AFB (cujus axis AD, & </s>
            <s xml:id="echoid-s11402" xml:space="preserve">ad hunc ap-
              <lb/>
              <note position="left" xlink:label="note-0246-01" xlink:href="note-0246-01a" xml:space="preserve">Fig. 90.</note>
            plicata DB) ſit etiam alia curva VGC ad iſtam ſic relata, ut a deſig-
              <lb/>
            nato quodam in axe AD puncto Z ad curvam AFB utcunque ductâ
              <lb/>
            rectâ ZF, & </s>
            <s xml:id="echoid-s11403" xml:space="preserve">per F ductâ rectâ EFG ad DBC parallelâ, ſit EG
              <lb/>
            æqualis ipſi ZF; </s>
            <s xml:id="echoid-s11404" xml:space="preserve">ſit autem PQ perpendicularis curvæ AFB; </s>
            <s xml:id="echoid-s11405" xml:space="preserve">ſu-
              <lb/>
            matúruqe QR æqualis ipſi ZE; </s>
            <s xml:id="echoid-s11406" xml:space="preserve">connexa recta GR ipſi curvæ VGC
              <lb/>
            perpendicularis erit.</s>
            <s xml:id="echoid-s11407" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11408" xml:space="preserve">Nam ducatur FT ad ipſam FQ perpendicularis, ſeu curvam AFB
              <lb/>
            tangens; </s>
            <s xml:id="echoid-s11409" xml:space="preserve">& </s>
            <s xml:id="echoid-s11410" xml:space="preserve">concipiatur curva OGO talis, ut ductâ quâcunq; </s>
            <s xml:id="echoid-s11411" xml:space="preserve">rectâ
              <lb/>
            HKO ad EFG parallelâ ( quæ rectas TE, TF, & </s>
            <s xml:id="echoid-s11412" xml:space="preserve">curvam OGO
              <lb/>
            ſecet punctis H, K, O) connexâque ZK, ſit HO = ZK; </s>
            <s xml:id="echoid-s11413" xml:space="preserve">tum du-
              <lb/>
              <note position="left" xlink:label="note-0246-02" xlink:href="note-0246-02a" xml:space="preserve">(_a_)_Hyp_.</note>
            ctâ Z I, quoniam HK &</s>
            <s xml:id="echoid-s11414" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11415" xml:space="preserve">HI, erit ZK &</s>
            <s xml:id="echoid-s11416" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11417" xml:space="preserve">ZI, vel HO &</s>
            <s xml:id="echoid-s11418" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11419" xml:space="preserve">HL;</s>
            <s xml:id="echoid-s11420" xml:space="preserve">
              <note position="left" xlink:label="note-0246-03" xlink:href="note-0246-03a" xml:space="preserve">(_b_)25 Lect. VI</note>
            quare curva OGO curvam VGC tangit. </s>
            <s xml:id="echoid-s11421" xml:space="preserve"> Eſt autem OGO (ex oſtenſis) _Hyperbola_, cui perpendicularis eſt recta GR; </s>
            <s xml:id="echoid-s11422" xml:space="preserve">eadem
              <lb/>
            itaque GR curvæ VGC quoque perpendicularis erit: </s>
            <s xml:id="echoid-s11423" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s11424" xml:space="preserve">D.</s>
            <s xml:id="echoid-s11425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11426" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s11427" xml:space="preserve">Sint recta DQ, duæque curvæ DRS, DYX ità relatæ,
              <lb/>
              <note position="left" xlink:label="note-0246-04" xlink:href="note-0246-04a" xml:space="preserve">Fig. 91.</note>
            ut ductâ utcunque rectâ REY ad poſitione datam DB parallelâ (quæ
              <lb/>
            dictas lineas ſecet, ut perſpicis) connexâque rectâ DY, ſit ſemper
              <lb/>
            RY. </s>
            <s xml:id="echoid-s11428" xml:space="preserve">DY :</s>
            <s xml:id="echoid-s11429" xml:space="preserve">: DY. </s>
            <s xml:id="echoid-s11430" xml:space="preserve">EY; </s>
            <s xml:id="echoid-s11431" xml:space="preserve">tangat autem recta RF curvam DRS ad R;
              <lb/>
            </s>
            <s xml:id="echoid-s11432" xml:space="preserve">oporter curvæ DYX tangentem ad Y rectam deſignare.</s>
            <s xml:id="echoid-s11433" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11434" xml:space="preserve">Concipiatur linea DYO talis, ut ductâ utcunque GO ad DB pa-
              <lb/>
            rallelâ ( quæ lineas FR, FP, DYO ſecet punctis G, P, O) connexâ-
              <lb/>
            que DO ſit ſemper GO. </s>
            <s xml:id="echoid-s11435" xml:space="preserve">DO_:_</s>
            <s xml:id="echoid-s11436" xml:space="preserve">: </s>
            <s xml:id="echoid-s11437" xml:space="preserve">DO. </s>
            <s xml:id="echoid-s11438" xml:space="preserve">PO; </s>
            <s xml:id="echoid-s11439" xml:space="preserve">tanget curva DYO
              <lb/>
            curvam DYX ad Y; </s>
            <s xml:id="echoid-s11440" xml:space="preserve">Nam ſecet recta GO curvas DRS, DYX
              <lb/>
            punctis S, X; </s>
            <s xml:id="echoid-s11441" xml:space="preserve">& </s>
            <s xml:id="echoid-s11442" xml:space="preserve">connectantur rectæ DG, DS, DX; </s>
            <s xml:id="echoid-s11443" xml:space="preserve">patet (è cur-
              <lb/>
            varum natura) angulos XDP, DSP; </s>
            <s xml:id="echoid-s11444" xml:space="preserve">nec non angulos ODP, DGP
              <lb/>
            æquari; </s>
            <s xml:id="echoid-s11445" xml:space="preserve">quare cùm angulus DSP major ſit angulo DGP; </s>
            <s xml:id="echoid-s11446" xml:space="preserve">erit an-
              <lb/>
            gulus XDP angulo ODP major, adeóque PX major erit quàm PO;
              <lb/>
            </s>
            <s xml:id="echoid-s11447" xml:space="preserve">
              <note position="left" xlink:label="note-0246-05" xlink:href="note-0246-05a" xml:space="preserve">(_a_) Y2 Lect.
                <lb/>
              VI.</note>
            hinc curva DYO curvam DYX tanget ad Y; </s>
            <s xml:id="echoid-s11448" xml:space="preserve">eſt autem curva DYO
              <lb/>
            _hyperbolæ_ ſuperiùs determinata; </s>
            <s xml:id="echoid-s11449" xml:space="preserve">hanc tangat YS; </s>
            <s xml:id="echoid-s11450" xml:space="preserve">hæc igitur curvam DYX quoque tanget.</s>
            <s xml:id="echoid-s11451" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s11452" xml:space="preserve">_Not_. </s>
            <s xml:id="echoid-s11453" xml:space="preserve">Si curva DRS ſit circulus, & </s>
            <s xml:id="echoid-s11454" xml:space="preserve">angulus QDB rectus, erit cur-
              <lb/>
            va DYX _ciſſois_ vulgaris; </s>
            <s xml:id="echoid-s11455" xml:space="preserve">hujus itaque ( cum innumeris aliis ſimiliter
              <lb/>
            genitis) tangens hîc deſinitur.</s>
            <s xml:id="echoid-s11456" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11457" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s11458" xml:space="preserve">Poſitione datæ ſint rectæ DB, BK; </s>
            <s xml:id="echoid-s11459" xml:space="preserve">ſitque curva DYX
              <lb/>
              <note position="left" xlink:label="note-0246-06" xlink:href="note-0246-06a" xml:space="preserve">Fig. 92.</note>
            </s>
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