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-s10345" xml:space="preserve">_Corol_. </s>
            <s xml:id="echoid-s10346" xml:space="preserve">Si YS tangat _hyperbolam_ DYY; </s>
            <s xml:id="echoid-s10347" xml:space="preserve">erit PMq. </s>
            <s xml:id="echoid-s10348" xml:space="preserve">PYq :</s>
            <s xml:id="echoid-s10349" xml:space="preserve">:
              <lb/>
            PA. </s>
            <s xml:id="echoid-s10350" xml:space="preserve">PS.</s>
            <s xml:id="echoid-s10351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10352" xml:space="preserve">Nam eſt PMq. </s>
            <s xml:id="echoid-s10353" xml:space="preserve">DBq :</s>
            <s xml:id="echoid-s10354" xml:space="preserve">: PAq. </s>
            <s xml:id="echoid-s10355" xml:space="preserve">ADq :</s>
            <s xml:id="echoid-s10356" xml:space="preserve">: PA. </s>
            <s xml:id="echoid-s10357" xml:space="preserve">AS. </s>
            <s xml:id="echoid-s10358" xml:space="preserve">ergò per
              <lb/>
            rationis converſionem eſt PMq. </s>
            <s xml:id="echoid-s10359" xml:space="preserve">PYq :</s>
            <s xml:id="echoid-s10360" xml:space="preserve">: PA. </s>
            <s xml:id="echoid-s10361" xml:space="preserve">PS.</s>
            <s xml:id="echoid-s10362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10363" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s10364" xml:space="preserve">Quòd ſi reliquis ſimiliter poſitis; </s>
            <s xml:id="echoid-s10365" xml:space="preserve">ſit jam PY = √ PMq
              <lb/>
              <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">Fig. 56.</note>
            + DBq; </s>
            <s xml:id="echoid-s10366" xml:space="preserve">erit etiam linea YYY _hyperbola_; </s>
            <s xml:id="echoid-s10367" xml:space="preserve">cujus nempe Cen-
              <lb/>
            trum A; </s>
            <s xml:id="echoid-s10368" xml:space="preserve">_Semidiameter_ AF (parallela & </s>
            <s xml:id="echoid-s10369" xml:space="preserve">æqualis ipſi DB) _Semi_-
              <lb/>
            _parameter_ autem P, ſi ſiat AF. </s>
            <s xml:id="echoid-s10370" xml:space="preserve">AD :</s>
            <s xml:id="echoid-s10371" xml:space="preserve">: AD.</s>
            <s xml:id="echoid-s10372" xml:space="preserve">P.</s>
            <s xml:id="echoid-s10373" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10374" xml:space="preserve">Nam ducatur YK ipſi AP parallela cum AF conveniens in K;
              <lb/>
            </s>
            <s xml:id="echoid-s10375" xml:space="preserve">Sítque FT = 2 FA; </s>
            <s xml:id="echoid-s10376" xml:space="preserve">éſtque AF. </s>
            <s xml:id="echoid-s10377" xml:space="preserve">P :</s>
            <s xml:id="echoid-s10378" xml:space="preserve">: (AFq. </s>
            <s xml:id="echoid-s10379" xml:space="preserve">ADq :</s>
            <s xml:id="echoid-s10380" xml:space="preserve">: DBq. </s>
            <s xml:id="echoid-s10381" xml:space="preserve">
              <lb/>
            ADq :</s>
            <s xml:id="echoid-s10382" xml:space="preserve">: PMq. </s>
            <s xml:id="echoid-s10383" xml:space="preserve">APq :</s>
            <s xml:id="echoid-s10384" xml:space="preserve">: PYq - DBq. </s>
            <s xml:id="echoid-s10385" xml:space="preserve">APq :</s>
            <s xml:id="echoid-s10386" xml:space="preserve">: AKq - AFq. </s>
            <s xml:id="echoid-s10387" xml:space="preserve">
              <lb/>
            KYq :</s>
            <s xml:id="echoid-s10388" xml:space="preserve">:) TK x FK. </s>
            <s xml:id="echoid-s10389" xml:space="preserve">KYq :</s>
            <s xml:id="echoid-s10390" xml:space="preserve">: AF.</s>
            <s xml:id="echoid-s10391" xml:space="preserve">P. </s>
            <s xml:id="echoid-s10392" xml:space="preserve">unde conſtat Propoſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s10393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10394" xml:space="preserve">_Corol_. </s>
            <s xml:id="echoid-s10395" xml:space="preserve">Rurſus, Si recta YS _hyperbolam_ FYY tangat, erit PMq.
              <lb/>
            </s>
            <s xml:id="echoid-s10396" xml:space="preserve">PYq :</s>
            <s xml:id="echoid-s10397" xml:space="preserve">: PA. </s>
            <s xml:id="echoid-s10398" xml:space="preserve">PS.</s>
            <s xml:id="echoid-s10399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10400" xml:space="preserve">Nam AD eſt _Semidiameter_ ipſi AF conjugata. </s>
            <s xml:id="echoid-s10401" xml:space="preserve">unde PA. </s>
            <s xml:id="echoid-s10402" xml:space="preserve">AS :</s>
            <s xml:id="echoid-s10403" xml:space="preserve">:
              <lb/>
            PAq. </s>
            <s xml:id="echoid-s10404" xml:space="preserve">ADq :</s>
            <s xml:id="echoid-s10405" xml:space="preserve">: PMq. </s>
            <s xml:id="echoid-s10406" xml:space="preserve">DBq. </s>
            <s xml:id="echoid-s10407" xml:space="preserve">ergò PA. </s>
            <s xml:id="echoid-s10408" xml:space="preserve">PS :</s>
            <s xml:id="echoid-s10409" xml:space="preserve">: PMq. </s>
            <s xml:id="echoid-s10410" xml:space="preserve">PMq
              <lb/>
            + DBq :</s>
            <s xml:id="echoid-s10411" xml:space="preserve">: PMq. </s>
            <s xml:id="echoid-s10412" xml:space="preserve">PYq.</s>
            <s xml:id="echoid-s10413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10414" xml:space="preserve">XXIV. </s>
            <s xml:id="echoid-s10415" xml:space="preserve">Sit triangulum ADB, rectum habens angulum ADB;
              <lb/>
            </s>
            <s xml:id="echoid-s10416" xml:space="preserve">
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">Fig. 57.</note>
            & </s>
            <s xml:id="echoid-s10417" xml:space="preserve">curva CGD talis, ut ductâ quâcunque rectâ FEG ad DB paral-
              <lb/>
            lelâ (quæ lineas expoſitas ſecet ut vides) ſit aggregatum quadrato-
              <lb/>
            rum ex EF, EG æquale quadrato ex DB; </s>
            <s xml:id="echoid-s10418" xml:space="preserve">erit curva CGD _εllip_-
              <lb/>
            _ſis_ cujus ſemiaxes AD, AC.</s>
            <s xml:id="echoid-s10419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10420" xml:space="preserve">Nam ſit AV = AD. </s>
            <s xml:id="echoid-s10421" xml:space="preserve">Eſtque ADq. </s>
            <s xml:id="echoid-s10422" xml:space="preserve">DBq (ACq) :</s>
            <s xml:id="echoid-s10423" xml:space="preserve">: AEq.
              <lb/>
            </s>
            <s xml:id="echoid-s10424" xml:space="preserve">EFq :</s>
            <s xml:id="echoid-s10425" xml:space="preserve">: ADq - AEq. </s>
            <s xml:id="echoid-s10426" xml:space="preserve">DBq - EFq. </s>
            <s xml:id="echoid-s10427" xml:space="preserve">Hoc eſt ADq. </s>
            <s xml:id="echoid-s10428" xml:space="preserve">ACq :</s>
            <s xml:id="echoid-s10429" xml:space="preserve">:
              <lb/>
            VE x ED. </s>
            <s xml:id="echoid-s10430" xml:space="preserve">EGq. </s>
            <s xml:id="echoid-s10431" xml:space="preserve">unde liquet Propoſitum.</s>
            <s xml:id="echoid-s10432" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10433" xml:space="preserve">_Nota_, Tangat GT _ellipſin_ CGD; </s>
            <s xml:id="echoid-s10434" xml:space="preserve">eſt EFq. </s>
            <s xml:id="echoid-s10435" xml:space="preserve">EGq :</s>
            <s xml:id="echoid-s10436" xml:space="preserve">: EA.
              <lb/>
            </s>
            <s xml:id="echoid-s10437" xml:space="preserve">ET.</s>
            <s xml:id="echoid-s10438" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10439" xml:space="preserve">Nam ob AE. </s>
            <s xml:id="echoid-s10440" xml:space="preserve">AD :</s>
            <s xml:id="echoid-s10441" xml:space="preserve">: AD. </s>
            <s xml:id="echoid-s10442" xml:space="preserve">AT. </s>
            <s xml:id="echoid-s10443" xml:space="preserve">eſt AEq. </s>
            <s xml:id="echoid-s10444" xml:space="preserve">ADq :</s>
            <s xml:id="echoid-s10445" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s10446" xml:space="preserve">AT.
              <lb/>
            </s>
            <s xml:id="echoid-s10447" xml:space="preserve">unde AEq. </s>
            <s xml:id="echoid-s10448" xml:space="preserve">ADq - AEq :</s>
            <s xml:id="echoid-s10449" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s10450" xml:space="preserve">AT - AE. </s>
            <s xml:id="echoid-s10451" xml:space="preserve">Hoc eſt EFq. </s>
            <s xml:id="echoid-s10452" xml:space="preserve">
              <lb/>
            DBq - EFq :</s>
            <s xml:id="echoid-s10453" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s10454" xml:space="preserve">ET. </s>
            <s xml:id="echoid-s10455" xml:space="preserve">hoc eſt EFq. </s>
            <s xml:id="echoid-s10456" xml:space="preserve">EGq :</s>
            <s xml:id="echoid-s10457" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s10458" xml:space="preserve">ET.</s>
            <s xml:id="echoid-s10459" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10460" xml:space="preserve">Sit _Angulus rectilineus_ DTH, in cujus latere TD ſignetur pun-
              <lb/>
            ctum A. </s>
            <s xml:id="echoid-s10461" xml:space="preserve">Sit item curva VGG proprietate talis, ut ductâ rectâ quâ-
              <lb/>
              <note position="left" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">Fig. 58.</note>
            piam EFG ad TD perpendiculari (quæ lineas TD, TH, VGG
              <lb/>
            ſecet punctis E, F, G,) connexáque rectâ AF, ſit EG = AF;
              <lb/>
            </s>
            <s xml:id="echoid-s10462" xml:space="preserve">erit linea VGG _hyperbola_.</s>
            <s xml:id="echoid-s10463" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10464" xml:space="preserve">Nam ducantur AP ad TH & </s>
            <s xml:id="echoid-s10465" xml:space="preserve">VPC ad TD perpendiculares;</s>
            <s xml:id="echoid-s10466" xml:space="preserve"/>
          </p>
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