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-s10258" xml:space="preserve">
              <pb o="53" file="0231" n="246" rhead=""/>
            = x; </s>
            <s xml:id="echoid-s10259" xml:space="preserve">GN = y. </s>
            <s xml:id="echoid-s10260" xml:space="preserve">ergò BE = {by/x}; </s>
            <s xml:id="echoid-s10261" xml:space="preserve">& </s>
            <s xml:id="echoid-s10262" xml:space="preserve">OF = g + y; </s>
            <s xml:id="echoid-s10263" xml:space="preserve">ergò {by/x}.
              <lb/>
            </s>
            <s xml:id="echoid-s10264" xml:space="preserve">g + y :</s>
            <s xml:id="echoid-s10265" xml:space="preserve">: b. </s>
            <s xml:id="echoid-s10266" xml:space="preserve">r; </s>
            <s xml:id="echoid-s10267" xml:space="preserve">hinc autem æquatio ry - yx = gx. </s>
            <s xml:id="echoid-s10268" xml:space="preserve">unde DNN
              <lb/>
            eſt _hyperbola_ ſuprà mox determinata.</s>
            <s xml:id="echoid-s10269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10270" xml:space="preserve">Quòd ſi punctum O ſumatur infra D B; </s>
            <s xml:id="echoid-s10271" xml:space="preserve">ſiet æquatio _yx_ - _ry_ =
              <lb/>
            _g x_. </s>
            <s xml:id="echoid-s10272" xml:space="preserve">unde rurſus conſtat.</s>
            <s xml:id="echoid-s10273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10274" xml:space="preserve">XXI. </s>
            <s xml:id="echoid-s10275" xml:space="preserve">Quinetiam, reliquis ſimiliter poſitis, recta FX non jam
              <lb/>
            ipſi D B, ſed alteri DH feratur parallela; </s>
            <s xml:id="echoid-s10276" xml:space="preserve">ità ut aſſumpto in B A
              <lb/>
              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">Fig. 54.</note>
            puncto habeat ſemper BE ad OF rationem aſſignatam (DB ad _m_)
              <lb/>
            erunt interſectiones N itidem ad _hyperbolam._</s>
            <s xml:id="echoid-s10277" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10278" xml:space="preserve">Nam ducatur NG ad AB parallela; </s>
            <s xml:id="echoid-s10279" xml:space="preserve">vocentúrque DB = b; </s>
            <s xml:id="echoid-s10280" xml:space="preserve">HB
              <lb/>
            = f; </s>
            <s xml:id="echoid-s10281" xml:space="preserve">HO = g; </s>
            <s xml:id="echoid-s10282" xml:space="preserve">DG = x; </s>
            <s xml:id="echoid-s10283" xml:space="preserve">GN = y; </s>
            <s xml:id="echoid-s10284" xml:space="preserve">eſt ergò x. </s>
            <s xml:id="echoid-s10285" xml:space="preserve">y :</s>
            <s xml:id="echoid-s10286" xml:space="preserve">: b. </s>
            <s xml:id="echoid-s10287" xml:space="preserve">{by/x}
              <lb/>
            = BE; </s>
            <s xml:id="echoid-s10288" xml:space="preserve">& </s>
            <s xml:id="echoid-s10289" xml:space="preserve">b. </s>
            <s xml:id="echoid-s10290" xml:space="preserve">f :</s>
            <s xml:id="echoid-s10291" xml:space="preserve">: x. </s>
            <s xml:id="echoid-s10292" xml:space="preserve">{fx/b} = GK; </s>
            <s xml:id="echoid-s10293" xml:space="preserve">quare NK (FH) = y + {fx/b}
              <lb/>
            & </s>
            <s xml:id="echoid-s10294" xml:space="preserve">OF = y + {fx/b} - g. </s>
            <s xml:id="echoid-s10295" xml:space="preserve">Eſt ergò{by/x}. </s>
            <s xml:id="echoid-s10296" xml:space="preserve">y + {fx/b} - g :</s>
            <s xml:id="echoid-s10297" xml:space="preserve">: b. </s>
            <s xml:id="echoid-s10298" xml:space="preserve">m.
              <lb/>
            </s>
            <s xml:id="echoid-s10299" xml:space="preserve">unde reſultat æquatio my + gx - yx = {f/b}xx. </s>
            <s xml:id="echoid-s10300" xml:space="preserve">vel facto f. </s>
            <s xml:id="echoid-s10301" xml:space="preserve">b :</s>
            <s xml:id="echoid-s10302" xml:space="preserve">:
              <lb/>
            m. </s>
            <s xml:id="echoid-s10303" xml:space="preserve">r; </s>
            <s xml:id="echoid-s10304" xml:space="preserve">eſt my + gx - yx = {m/r}x x. </s>
            <s xml:id="echoid-s10305" xml:space="preserve">Conſtat igitur lineam DNN
              <lb/>
            eſſe _hyperbolam_; </s>
            <s xml:id="echoid-s10306" xml:space="preserve">qualis ſuperjùs habetur determinata.</s>
            <s xml:id="echoid-s10307" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10308" xml:space="preserve">Notetur, Si computatio ab ipſo puncto H. </s>
            <s xml:id="echoid-s10309" xml:space="preserve">initium ſumat, (hoc eſt
              <lb/>
            ſit BE. </s>
            <s xml:id="echoid-s10310" xml:space="preserve">HF :</s>
            <s xml:id="echoid-s10311" xml:space="preserve">: DB. </s>
            <s xml:id="echoid-s10312" xml:space="preserve">m) evaneſcente tunc termino g; </s>
            <s xml:id="echoid-s10313" xml:space="preserve">erit my - yx
              <lb/>
            = {m/r}x x; </s>
            <s xml:id="echoid-s10314" xml:space="preserve">unde quoque ſuprà habetur alìa determinatio ſimpli-
              <lb/>
            cior.</s>
            <s xml:id="echoid-s10315" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10316" xml:space="preserve">XXII. </s>
            <s xml:id="echoid-s10317" xml:space="preserve">Eſto triangulum ADB, & </s>
            <s xml:id="echoid-s10318" xml:space="preserve">linea DYY talis, ut ductâ ut-
              <lb/>
            cunque PM ad DB parallelâ, ſit perpetuò PY = √: </s>
            <s xml:id="echoid-s10319" xml:space="preserve">PMq -
              <lb/>
            DBq; </s>
            <s xml:id="echoid-s10320" xml:space="preserve">erit linea DYY _hyperbola_; </s>
            <s xml:id="echoid-s10321" xml:space="preserve">cujus utique Centrum eſt A, ſe-
              <lb/>
            _midiameter_ AD, (vel _aſymptotos_ AB) _ſemiparameter_ autem P ; </s>
            <s xml:id="echoid-s10322" xml:space="preserve">faci-
              <lb/>
              <note position="right" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">Fig. 55.</note>
            endo AD. </s>
            <s xml:id="echoid-s10323" xml:space="preserve">DB :</s>
            <s xml:id="echoid-s10324" xml:space="preserve">: DB.</s>
            <s xml:id="echoid-s10325" xml:space="preserve">P.</s>
            <s xml:id="echoid-s10326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10327" xml:space="preserve">Sit enim TD = 2AD. </s>
            <s xml:id="echoid-s10328" xml:space="preserve">Eſtque ADP :</s>
            <s xml:id="echoid-s10329" xml:space="preserve">: (ADq. </s>
            <s xml:id="echoid-s10330" xml:space="preserve">DBq :</s>
            <s xml:id="echoid-s10331" xml:space="preserve">:
              <lb/>
              <note position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">* 6, 2. El@@.</note>
            APq. </s>
            <s xml:id="echoid-s10332" xml:space="preserve">PMq :</s>
            <s xml:id="echoid-s10333" xml:space="preserve">: *TP x DP + ADq. </s>
            <s xml:id="echoid-s10334" xml:space="preserve">PMq :</s>
            <s xml:id="echoid-s10335" xml:space="preserve">: TP x DP.
              <lb/>
            </s>
            <s xml:id="echoid-s10336" xml:space="preserve">PMq - DBq :</s>
            <s xml:id="echoid-s10337" xml:space="preserve">:) TP x DP. </s>
            <s xml:id="echoid-s10338" xml:space="preserve">PYq. </s>
            <s xml:id="echoid-s10339" xml:space="preserve">vel TD. </s>
            <s xml:id="echoid-s10340" xml:space="preserve">2P; </s>
            <s xml:id="echoid-s10341" xml:space="preserve">TP x DP. </s>
            <s xml:id="echoid-s10342" xml:space="preserve">
              <lb/>
            PYq. </s>
            <s xml:id="echoid-s10343" xml:space="preserve">unde liquet Propoſitum.</s>
            <s xml:id="echoid-s10344" xml:space="preserve"/>
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