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-s11552" xml:space="preserve">
              <pb o="71" file="0249" n="264" rhead=""/>
            M :</s>
            <s xml:id="echoid-s11553" xml:space="preserve">: PX. </s>
            <s xml:id="echoid-s11554" xml:space="preserve">PY; </s>
            <s xml:id="echoid-s11555" xml:space="preserve">connectatúrque recta FY; </s>
            <s xml:id="echoid-s11556" xml:space="preserve">hæc curvam FBF continget.</s>
            <s xml:id="echoid-s11557" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11558" xml:space="preserve">Nam per E ducatur recta CE ad AB (vel VD) parallela; </s>
            <s xml:id="echoid-s11559" xml:space="preserve">conci-
              <lb/>
            piatúrque @@@ E tranſiens curva HEH talis, ut ductâ quâpiam QL
              <lb/>
            ad DE parallelâ (curvas EBE, HEH in L, & </s>
            <s xml:id="echoid-s11560" xml:space="preserve">H; </s>
            <s xml:id="echoid-s11561" xml:space="preserve">rectáſque CE,
              <lb/>
            VP in I ac Q ſecante ) ſit ſemper QH inter QI, QL eodem ordine
              <lb/>
            media, quo PF inter PG, PE; </s>
            <s xml:id="echoid-s11562" xml:space="preserve">è præcedente jam conſtat rectam
              <lb/>
            connexam EY curvam HEH contingere; </s>
            <s xml:id="echoid-s11563" xml:space="preserve">verùm curvæ HEH analoga eſt curva FBF; </s>
            <s xml:id="echoid-s11564" xml:space="preserve"> ergò recta FY curvam FBF
              <note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">_a_ 7. Lect. 7.</note>
            continget.</s>
            <s xml:id="echoid-s11565" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">_b_ 5. Lect. 8.</note>
          <p>
            <s xml:id="echoid-s11566" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s11567" xml:space="preserve">Adnotetur, poſito lineam EBE rectam eſſe, quòd linea FBF
              <lb/>
            parabolarum ſeu paraboliſormium aliqua ſit. </s>
            <s xml:id="echoid-s11568" xml:space="preserve">quare quod de his paſ-
              <lb/>
            ſim obſervatum habetur _(_ex calculo deduc@um, & </s>
            <s xml:id="echoid-s11569" xml:space="preserve">inductione quâdam
              <lb/>
            comprobatum, neſcio tamen an uſpiam Geometricè oſtenſum ) ex im-
              <lb/>
            mensùm uberiore fonte manat, ad iunumeras aliorum generum curvas
              <lb/>
            ſe diffundente.</s>
            <s xml:id="echoid-s11570" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11571" xml:space="preserve">V. </s>
            <s xml:id="echoid-s11572" xml:space="preserve">Hinc apertè conſectatur; </s>
            <s xml:id="echoid-s11573" xml:space="preserve">ſi TD ſit recta, síntque duæ quæ-
              <lb/>
            dam curvæ EEE, FFF ità ad ſe relatæ, ut ductis rectis PEF ad
              <lb/>
              <note position="right" xlink:label="note-0249-03" xlink:href="note-0249-03a" xml:space="preserve">Fig. 96.</note>
            poſitione datam BD parallelis, ſint ordinatæ PE ſemper ut quadrata
              <lb/>
            ex ordinatis PF; </s>
            <s xml:id="echoid-s11574" xml:space="preserve">rectæ verò ES, FT ( ex ejuſdem communis ordi-
              <lb/>
            natæ terminatis ductæ) curvas haſce contingant; </s>
            <s xml:id="echoid-s11575" xml:space="preserve">erit TP = 2 SP;
              <lb/>
            </s>
            <s xml:id="echoid-s11576" xml:space="preserve">Quòd ſi ordinatæ PE ſe habeant ut ipſarum PF cubi, erit TP = 3 SP; </s>
            <s xml:id="echoid-s11577" xml:space="preserve">
              <lb/>
            ſi PE ſint ut quadrato quadrata ipſarum PF, erit TP = 4 SP; </s>
            <s xml:id="echoid-s11578" xml:space="preserve">ac
              <lb/>
            ſic eodem ad infinitum continuo tenore.</s>
            <s xml:id="echoid-s11579" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11580" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s11581" xml:space="preserve">Sit porrò Circulus ABC, cujus Centrum D, radius DB,
              <lb/>
            item lineæ EBE, FBF per B tranſeuntes, ac ità relatæ, ut ductâ
              <lb/>
              <note position="right" xlink:label="note-0249-04" xlink:href="note-0249-04a" xml:space="preserve">Fig. 97.</note>
            per D rectâ quâpiam DG, ſit ſemper DF eodem ordine media Arith-
              <lb/>
            meticè inter DG, DE; </s>
            <s xml:id="echoid-s11582" xml:space="preserve">tangat autem recta BO curvam EBE in B;
              <lb/>
            </s>
            <s xml:id="echoid-s11583" xml:space="preserve">oportet curvæ FBF tangentem (ad B) deſignare.</s>
            <s xml:id="echoid-s11584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11585" xml:space="preserve">Hoc (certè generatim quadantenus præſtitum) è re fuerit
              <note position="right" xlink:label="note-0249-05" xlink:href="note-0249-05a" xml:space="preserve">a 8. Lect. 8.</note>
            ſpeciatim apertiùs atque plenius exequi: </s>
            <s xml:id="echoid-s11586" xml:space="preserve">Quorſum ſit DQ ad DB
              <lb/>
            perpendicularis, quam ſecet BO in S; </s>
            <s xml:id="echoid-s11587" xml:space="preserve">fiat verò N. </s>
            <s xml:id="echoid-s11588" xml:space="preserve">M :</s>
            <s xml:id="echoid-s11589" xml:space="preserve">: DS. </s>
            <s xml:id="echoid-s11590" xml:space="preserve">DT;
              <lb/>
            </s>
            <s xml:id="echoid-s11591" xml:space="preserve">connectatúrque recta TB; </s>
            <s xml:id="echoid-s11592" xml:space="preserve">hæc curvam FBF tanget.</s>
            <s xml:id="echoid-s11593" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11594" xml:space="preserve">Tangat enim recta PB _circulum_ AB G; </s>
            <s xml:id="echoid-s11595" xml:space="preserve">ſecentúrque rectæ D S
              <lb/>
              <note position="right" xlink:label="note-0249-06" xlink:href="note-0249-06a" xml:space="preserve">Fig. 97.</note>
            in X, & </s>
            <s xml:id="echoid-s11596" xml:space="preserve">BS in Y, ità ut ſit DS. </s>
            <s xml:id="echoid-s11597" xml:space="preserve">D X :</s>
            <s xml:id="echoid-s11598" xml:space="preserve">: M. </s>
            <s xml:id="echoid-s11599" xml:space="preserve">N :</s>
            <s xml:id="echoid-s11600" xml:space="preserve">: BS. </s>
            <s xml:id="echoid-s11601" xml:space="preserve">BY; </s>
            <s xml:id="echoid-s11602" xml:space="preserve">perque
              <lb/>
            puncta X, Y ducantur XZ ad BS, & </s>
            <s xml:id="echoid-s11603" xml:space="preserve">YV ad DS parallelæ, concur-
              <lb/>
            rentes in C; </s>
            <s xml:id="echoid-s11604" xml:space="preserve">tum _aſymptotis_ YCZ per B traducta concipiatur _hyper_-
              <lb/>
            _bola_ LB L; </s>
            <s xml:id="echoid-s11605" xml:space="preserve">porrò ex D projiciatur utcunque recta DP dictas </s>
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