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-s11230" xml:space="preserve">
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            eans, ut vides. </s>
            <s xml:id="echoid-s11231" xml:space="preserve">Eſtque T P. </s>
            <s xml:id="echoid-s11232" xml:space="preserve">PM &</s>
            <s xml:id="echoid-s11233" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11234" xml:space="preserve">( TP. </s>
            <s xml:id="echoid-s11235" xml:space="preserve">PI :</s>
            <s xml:id="echoid-s11236" xml:space="preserve">:) TD. </s>
            <s xml:id="echoid-s11237" xml:space="preserve">DE
              <lb/>
            item SP. </s>
            <s xml:id="echoid-s11238" xml:space="preserve">PK :</s>
            <s xml:id="echoid-s11239" xml:space="preserve">: SD. </s>
            <s xml:id="echoid-s11240" xml:space="preserve">DF. </s>
            <s xml:id="echoid-s11241" xml:space="preserve">ergò TP x SP. </s>
            <s xml:id="echoid-s11242" xml:space="preserve">PM x PK &</s>
            <s xml:id="echoid-s11243" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11244" xml:space="preserve">TD
              <lb/>
            x SD. </s>
            <s xml:id="echoid-s11245" xml:space="preserve">DE xDF :</s>
            <s xml:id="echoid-s11246" xml:space="preserve">: TD x SD. </s>
            <s xml:id="echoid-s11247" xml:space="preserve">PM xPN. </s>
            <s xml:id="echoid-s11248" xml:space="preserve">Verum TD x
              <lb/>
            SD &</s>
            <s xml:id="echoid-s11249" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11250" xml:space="preserve">TP xSP; </s>
            <s xml:id="echoid-s11251" xml:space="preserve">ac indè magís TD x SD. </s>
            <s xml:id="echoid-s11252" xml:space="preserve">PM x PK &</s>
            <s xml:id="echoid-s11253" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11254" xml:space="preserve">TD x
              <lb/>
            SD. </s>
            <s xml:id="echoid-s11255" xml:space="preserve">PM x PN. </s>
            <s xml:id="echoid-s11256" xml:space="preserve">quare PM x PK &</s>
            <s xml:id="echoid-s11257" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11258" xml:space="preserve">PM x PN; </s>
            <s xml:id="echoid-s11259" xml:space="preserve">vel PK &</s>
            <s xml:id="echoid-s11260" xml:space="preserve">lt;
              <lb/>
            </s>
            <s xml:id="echoid-s11261" xml:space="preserve">PN. </s>
            <s xml:id="echoid-s11262" xml:space="preserve">Itaque recta FS extra curvam YFN tota jacet.</s>
            <s xml:id="echoid-s11263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11264" xml:space="preserve">_Not_. </s>
            <s xml:id="echoid-s11265" xml:space="preserve">Si linea XEM recta fuerit ( utique ipſi TE I coincidens) erit
              <lb/>
            YFN _hyperbola_ vulgaris, cujus centrum T, _aſymptotos_ una TS, al-
              <lb/>
            tera TZ ad EF parallela.</s>
            <s xml:id="echoid-s11266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11267" xml:space="preserve">X. </s>
            <s xml:id="echoid-s11268" xml:space="preserve">Quinetiam ſit punctum D; </s>
            <s xml:id="echoid-s11269" xml:space="preserve">curvæque duæ XEM, YFN ità
              <lb/>
            relatæ, ut per D ductâ quacunque rectâ EF; </s>
            <s xml:id="echoid-s11270" xml:space="preserve">ſit perpetuo rectangu-
              <lb/>
            lum ex DE, DF æquale cuidam quadrato _(_ex Z puta); </s>
            <s xml:id="echoid-s11271" xml:space="preserve">unam verò
              <lb/>
            curvam XEM tangat recta ER; </s>
            <s xml:id="echoid-s11272" xml:space="preserve">alterius ad F tangens ita determina-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s11273" xml:space="preserve">Ducatur DP ad ER perpendicularis: </s>
            <s xml:id="echoid-s11274" xml:space="preserve">factóque DP. </s>
            <s xml:id="echoid-s11275" xml:space="preserve">Z :</s>
            <s xml:id="echoid-s11276" xml:space="preserve">: Z.
              <lb/>
            </s>
            <s xml:id="echoid-s11277" xml:space="preserve">
              <note position="left" xlink:label="note-0244-01" xlink:href="note-0244-01a" xml:space="preserve">Fig. 84.</note>
            DB; </s>
            <s xml:id="echoid-s11278" xml:space="preserve">biſecetur DB in C; </s>
            <s xml:id="echoid-s11279" xml:space="preserve">connexâque CF, ducatur FS ad CF nor-
              <lb/>
            malis; </s>
            <s xml:id="echoid-s11280" xml:space="preserve">hæc curvam YFN tanget.</s>
            <s xml:id="echoid-s11281" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11282" xml:space="preserve">Nam centro C per F deſcribatur _Circulus_ DO B; </s>
            <s xml:id="echoid-s11283" xml:space="preserve">& </s>
            <s xml:id="echoid-s11284" xml:space="preserve">per B traji-
              <lb/>
            ciatur utcunque recta IN lineas interſecans, ut vides; </s>
            <s xml:id="echoid-s11285" xml:space="preserve">eſtque DO x
              <lb/>
            DI = DP x DB = Zq = DM x DN vel DO. </s>
            <s xml:id="echoid-s11286" xml:space="preserve">
              <note position="left" xlink:label="note-0244-02" xlink:href="note-0244-02a" xml:space="preserve">(_a_) 27 Lect.
                <lb/>
              VI.</note>
            :</s>
            <s xml:id="echoid-s11287" xml:space="preserve">: DN. </s>
            <s xml:id="echoid-s11288" xml:space="preserve">DI. </s>
            <s xml:id="echoid-s11289" xml:space="preserve">ergò quum ſit DM (_c_) &</s>
            <s xml:id="echoid-s11290" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11291" xml:space="preserve">DI; </s>
            <s xml:id="echoid-s11292" xml:space="preserve">erit DO &</s>
            <s xml:id="echoid-s11293" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11294" xml:space="preserve">DN;
              <lb/>
            </s>
            <s xml:id="echoid-s11295" xml:space="preserve">itaque circulus DOB curvam YFN tanget. </s>
            <s xml:id="echoid-s11296" xml:space="preserve">Quare recta FS eandem
              <lb/>
              <note position="left" xlink:label="note-0244-03" xlink:href="note-0244-03a" xml:space="preserve">(_b_) _Conſtr_.</note>
              <note position="left" xlink:label="note-0244-04" xlink:href="note-0244-04a" xml:space="preserve">(_c_)_Hyp._</note>
            YF N tanget.</s>
            <s xml:id="echoid-s11297" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11298" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s11299" xml:space="preserve">Curvæ XEM, YFN tales ſint, ut ductâ quâpiam FE ad poſi-
              <lb/>
            tione datam parallelâ, ſit ſemper hæc æqualis eidem alicui; </s>
            <s xml:id="echoid-s11300" xml:space="preserve">curvàm
              <lb/>
            autem YFN tangat recta SF; </s>
            <s xml:id="echoid-s11301" xml:space="preserve">huic parallela RE alteram XEM
              <lb/>
              <note position="left" xlink:label="note-0244-05" xlink:href="note-0244-05a" xml:space="preserve">Fig. 85.</note>
            continget.</s>
            <s xml:id="echoid-s11302" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11303" xml:space="preserve">Nam utcunque ductâ MK ad FE parallelâ eſt NI &</s>
            <s xml:id="echoid-s11304" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11305" xml:space="preserve">( KI = FE
              <lb/>
            = ) NM. </s>
            <s xml:id="echoid-s11306" xml:space="preserve">Quare punctum I extra curvam XEM jacet, _& </s>
            <s xml:id="echoid-s11307" xml:space="preserve">c_.</s>
            <s xml:id="echoid-s11308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11309" xml:space="preserve">Reverà linea XEM nil aliud eſt, quàm ipſa YFN _tranſlocata_.
              <lb/>
            </s>
            <s xml:id="echoid-s11310" xml:space="preserve">Levius hoc, & </s>
            <s xml:id="echoid-s11311" xml:space="preserve">methoditantùm gratiâ Propoſitum.</s>
            <s xml:id="echoid-s11312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11313" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s11314" xml:space="preserve">Sit curva quæpiam XEM, quam tangat recta ER ad E; </s>
            <s xml:id="echoid-s11315" xml:space="preserve">ſit
              <lb/>
            item alia curva YF N ad alteram ità relata, ut ab aſſignato puncto D
              <lb/>
              <note position="left" xlink:label="note-0244-06" xlink:href="note-0244-06a" xml:space="preserve">Fig. 86.</note>
            utcunque ductâ rectâ DEF, ſit ſemper intercepta EF æqualis alicui
              <lb/>
            determinatæ Z; </s>
            <s xml:id="echoid-s11316" xml:space="preserve">curvæ YFN tangens (ad F) ità deſignatur: </s>
            <s xml:id="echoid-s11317" xml:space="preserve">Su-
              <lb/>
            matur DH = Z; </s>
            <s xml:id="echoid-s11318" xml:space="preserve">& </s>
            <s xml:id="echoid-s11319" xml:space="preserve">per H ducatur AH ad DH perpendicularis,
              <lb/>
            ipſi ER occurrens in B, & </s>
            <s xml:id="echoid-s11320" xml:space="preserve">per F ducatur FG ad AB parallela; </s>
            <s xml:id="echoid-s11321" xml:space="preserve">ſuma-
              <lb/>
            túrque GL = GB; </s>
            <s xml:id="echoid-s11322" xml:space="preserve">erit connexa LFS curvæ YFN tangens.</s>
            <s xml:id="echoid-s11323" xml:space="preserve"/>
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