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-s11784" xml:space="preserve">
              <pb o="74" file="0252" n="267" rhead=""/>
            M x TP:</s>
            <s xml:id="echoid-s11785" xml:space="preserve">: RP. </s>
            <s xml:id="echoid-s11786" xml:space="preserve">SP; </s>
            <s xml:id="echoid-s11787" xml:space="preserve">& </s>
            <s xml:id="echoid-s11788" xml:space="preserve">connectatur SF; </s>
            <s xml:id="echoid-s11789" xml:space="preserve">hæc curvam
              <lb/>
            FBF tanget; </s>
            <s xml:id="echoid-s11790" xml:space="preserve">id quod omnino ſimili diſcurſu demonſtratur, quo ter-
              <lb/>
            tia hujus; </s>
            <s xml:id="echoid-s11791" xml:space="preserve">tantùm hîc (non per E ad VD parallela ducitur, at) con-
              <lb/>
            nectitur ET; </s>
            <s xml:id="echoid-s11792" xml:space="preserve">& </s>
            <s xml:id="echoid-s11793" xml:space="preserve">loco ſeptimæ allegatur octava ſeptimæ Lectionis.
              <lb/>
            </s>
            <s xml:id="echoid-s11794" xml:space="preserve">quid plura?</s>
            <s xml:id="echoid-s11795" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11796" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s11797" xml:space="preserve">Adnotetur, ſi linea EBE ſit recta, (rectæ nempe BR coin-
              <lb/>
            cidens) eſſe lineam FBF ex _infinitis hyperbolis_ (vel _hyperboliformi-_
              <lb/>
            _bus_) aliquam; </s>
            <s xml:id="echoid-s11798" xml:space="preserve">quarum igitur (unà cùm aliarum infinities diverſi ge-
              <lb/>
            neris plurium) _Tangentes_ determinandi modum uno _Tbeorem
              <unsure/>
            ate_ com-
              <lb/>
            plexi ſumus.</s>
            <s xml:id="echoid-s11799" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11800" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s11801" xml:space="preserve">Quòd ſi puncta T, R non ad eaſdem partes puncti D (vel P)
              <lb/>
            cadant; </s>
            <s xml:id="echoid-s11802" xml:space="preserve">curvæ FBF tangens (BS) deſignatur faciendo N x RD-:
              <lb/>
            </s>
            <s xml:id="echoid-s11803" xml:space="preserve">
              <note position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">Fig. 102.</note>
            M \\ - N} x TD. </s>
            <s xml:id="echoid-s11804" xml:space="preserve">M x TD:</s>
            <s xml:id="echoid-s11805" xml:space="preserve">: RD. </s>
            <s xml:id="echoid-s11806" xml:space="preserve">SD.</s>
            <s xml:id="echoid-s11807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11808" xml:space="preserve">Simili planè diſcurſu conſtat hoc, tantùm (quartæ loco) ſeptimæ
              <lb/>
            Lectionis quintam adhibendo.</s>
            <s xml:id="echoid-s11809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11810" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s11811" xml:space="preserve">Hinc autem nedum _Ellipſoidum_ omnium (poſito nempe line-
              <lb/>
            am EBE rectam eſſe, lineæ BR coincidentem) aſt aliarum alterius
              <lb/>
            generis _linearnm innumer abilium Taxgentes_ unâ operâ determinan-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s11812" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11813" xml:space="preserve">_Exemplum._ </s>
            <s xml:id="echoid-s11814" xml:space="preserve">Si PF ſit è quatuor mediis quarta, ſeu M = 5; </s>
            <s xml:id="echoid-s11815" xml:space="preserve">& </s>
            <s xml:id="echoid-s11816" xml:space="preserve">N
              <lb/>
            = 4; </s>
            <s xml:id="echoid-s11817" xml:space="preserve">erit SD = {5 TD x RD/4 RD - TD.</s>
            <s xml:id="echoid-s11818" xml:space="preserve">}</s>
          </p>
          <p>
            <s xml:id="echoid-s11819" xml:space="preserve">_Notetur_; </s>
            <s xml:id="echoid-s11820" xml:space="preserve">Si contigerit eſſe ND x RD = M/- N} x TD, eſſe DS
              <lb/>
            infinitam; </s>
            <s xml:id="echoid-s11821" xml:space="preserve">ſeu BS ipſi VD parallelam. </s>
            <s xml:id="echoid-s11822" xml:space="preserve">Alia poſſent adnotari; </s>
            <s xml:id="echoid-s11823" xml:space="preserve">ſed
              <lb/>
            relinquo.</s>
            <s xml:id="echoid-s11824" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11825" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s11826" xml:space="preserve">Inter alias curvas innumeras, etiam hâc methodo _Ciſſois_ & </s>
            <s xml:id="echoid-s11827" xml:space="preserve">
              <lb/>
            _Ciſſoidaliam_ omne genus comprehenditur: </s>
            <s xml:id="echoid-s11828" xml:space="preserve">Sit utique ſemirectus an-
              <lb/>
              <note position="left" xlink:label="note-0252-02" xlink:href="note-0252-02a" xml:space="preserve">Fig. 103.</note>
            gulus DSB; </s>
            <s xml:id="echoid-s11829" xml:space="preserve">curvæque duæ SGB, SEE ſic ad ſe referantur, ut
              <lb/>
            ductâ liberè rectâ GE ad BD parallelâ, (quæ lineas expoſitas, ut
              <lb/>
            conſpicis, ſecet) ſint PG, PF, PE continuè proportionales; </s>
            <s xml:id="echoid-s11830" xml:space="preserve">tangat
              <lb/>
            autem recta GT curvam SGB in G, reperietur quæ ad E lineam SEB
              <lb/>
            tangit, faciendo 2 TP - SP. </s>
            <s xml:id="echoid-s11831" xml:space="preserve">TP:</s>
            <s xml:id="echoid-s11832" xml:space="preserve">: SP. </s>
            <s xml:id="echoid-s11833" xml:space="preserve">RP; </s>
            <s xml:id="echoid-s11834" xml:space="preserve">utique connexa
              <lb/>
            RE curvam SEE tanget. </s>
            <s xml:id="echoid-s11835" xml:space="preserve">Id quod è præmiſſis facilè colligitur.
              <lb/>
            </s>
            <s xml:id="echoid-s11836" xml:space="preserve">Quòd ſi jam curva SGB ſit circulus, & </s>
            <s xml:id="echoid-s11837" xml:space="preserve">applicationis angulus </s>
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