Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div222" type="section" level="1" n="31">
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          <p>
            <s xml:id="echoid-s9548" xml:space="preserve">Ducatur enim quævis HO; </s>
            <s xml:id="echoid-s9549" xml:space="preserve">hæc tangenti priùs occurret, puta ad
              <lb/>
            R. </s>
            <s xml:id="echoid-s9550" xml:space="preserve">liquet HR majorem eſſe quàm HM; </s>
            <s xml:id="echoid-s9551" xml:space="preserve">multóq; </s>
            <s xml:id="echoid-s9552" xml:space="preserve">magìs eſſe HO
              <lb/>
            &</s>
            <s xml:id="echoid-s9553" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9554" xml:space="preserve">HM,</s>
          </p>
          <p>
            <s xml:id="echoid-s9555" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s9556" xml:space="preserve">Hinc _Circulus Centro_ H per M deſcriptus _curvam_ contin-
              <lb/>
            get.</s>
            <s xml:id="echoid-s9557" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9558" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s9559" xml:space="preserve">Etiam inversè, ſi HM minima ſit omnium quæ ab H ad
              <lb/>
            curvam duci poſſunt, erit HM curvæ perpendicularis.</s>
            <s xml:id="echoid-s9560" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9561" xml:space="preserve">Nam quoniam HM minima ponitur, circulus centro H, intervallo
              <lb/>
            quovis HS, majori quàm HM, curvam ſecabit, & </s>
            <s xml:id="echoid-s9562" xml:space="preserve">proinde tangentem
              <lb/>
            MT, hanc puta in R. </s>
            <s xml:id="echoid-s9563" xml:space="preserve">ergò quum ſit HR &</s>
            <s xml:id="echoid-s9564" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9565" xml:space="preserve">HM, non erit angu-
              <lb/>
            lus HRM rectus. </s>
            <s xml:id="echoid-s9566" xml:space="preserve">idem de punctis omnibus in recta TM evidens eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s9567" xml:space="preserve">ergò tangenti perpendicularis non alibi quàm in punctum M cadit.</s>
            <s xml:id="echoid-s9568" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9569" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s9570" xml:space="preserve">Quinetiam ſi recta HM minima ſit omnium quæ ab H
              <lb/>
              <note position="left" xlink:label="note-0220-01" xlink:href="note-0220-01a" xml:space="preserve">Fig. 31.</note>
            duci poſſunt, eíq; </s>
            <s xml:id="echoid-s9571" xml:space="preserve">perpendicularis ſit recta TM; </s>
            <s xml:id="echoid-s9572" xml:space="preserve">hæc curvam tan-
              <lb/>
            get.</s>
            <s xml:id="echoid-s9573" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9574" xml:space="preserve">Nam tangat alia, (ſi fieri poteſt) XM; </s>
            <s xml:id="echoid-s9575" xml:space="preserve">erit igitur XM ad HM
              <lb/>
            perpendicularis. </s>
            <s xml:id="echoid-s9576" xml:space="preserve">Unde pares erunt anguli HMX, HMT; </s>
            <s xml:id="echoid-s9577" xml:space="preserve">totum
              <lb/>
            & </s>
            <s xml:id="echoid-s9578" xml:space="preserve">pars Q: </s>
            <s xml:id="echoid-s9579" xml:space="preserve">E.</s>
            <s xml:id="echoid-s9580" xml:space="preserve">A.</s>
            <s xml:id="echoid-s9581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9582" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s9583" xml:space="preserve">Dico porrò minimæ HM propiorem HN remotiore HO
              <lb/>
              <note position="left" xlink:label="note-0220-02" xlink:href="note-0220-02a" xml:space="preserve">Fig. 32.</note>
            minorem eſſe.</s>
            <s xml:id="echoid-s9584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9585" xml:space="preserve">Nam ducatur ſubtenſa MN; </s>
            <s xml:id="echoid-s9586" xml:space="preserve">hæc producta curvam tranſgredietur,
              <lb/>
            & </s>
            <s xml:id="echoid-s9587" xml:space="preserve">ipſam HO ſecabit, puta in R. </s>
            <s xml:id="echoid-s9588" xml:space="preserve">& </s>
            <s xml:id="echoid-s9589" xml:space="preserve">quoniam Angulus HMR obtu-
              <lb/>
            ſus eſt (major illo nempe, quem tangens cum HM conſtituit ad M)
              <lb/>
            erit HNR magìs obtuſus; </s>
            <s xml:id="echoid-s9590" xml:space="preserve">adeôq; </s>
            <s xml:id="echoid-s9591" xml:space="preserve">recta HR &</s>
            <s xml:id="echoid-s9592" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9593" xml:space="preserve">HN & </s>
            <s xml:id="echoid-s9594" xml:space="preserve">magis HO &</s>
            <s xml:id="echoid-s9595" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9596" xml:space="preserve">HN.</s>
            <s xml:id="echoid-s9597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9598" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s9599" xml:space="preserve">Hinc perſpicuum eſt Circulum quemvis Centro H deſcri-
              <lb/>
            ptum, uno tantùm ad eaſdem puncti M partes puncto curvæ occurrere;
              <lb/>
            </s>
            <s xml:id="echoid-s9600" xml:space="preserve">nec omnino pluries igitur, quàm in duobus punctis.</s>
            <s xml:id="echoid-s9601" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9602" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s9603" xml:space="preserve">Perpendiculari HM parallelæ, ſint rectæ IN, KO; </s>
            <s xml:id="echoid-s9604" xml:space="preserve">ha-
              <lb/>
              <note position="left" xlink:label="note-0220-03" xlink:href="note-0220-03a" xml:space="preserve">Fig. 33.</note>
            rum propior IN remotiore KO rectiùs incidet.</s>
            <s xml:id="echoid-s9605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9606" xml:space="preserve">Nam per N, O ducantur ipſi curvæ perpendiculares EN, FO; </s>
            <s xml:id="echoid-s9607" xml:space="preserve">hæ
              <lb/>
            cum ipſa HM intra curvam convenient, puta ad R, & </s>
            <s xml:id="echoid-s9608" xml:space="preserve">P; </s>
            <s xml:id="echoid-s9609" xml:space="preserve">ſibi verò
              <lb/>
            ipſis in Q.</s>
            <s xml:id="echoid-s9610" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9611" xml:space="preserve">Liquet jam eſſe ang. </s>
            <s xml:id="echoid-s9612" xml:space="preserve">FOK = ang, FPH &</s>
            <s xml:id="echoid-s9613" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9614" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9615" xml:space="preserve">PRQ = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s9616" xml:space="preserve">NRH = ang ENJ. </s>
            <s xml:id="echoid-s9617" xml:space="preserve">Cùm ergò ſit ang. </s>
            <s xml:id="echoid-s9618" xml:space="preserve">FOK major angulo ENJ,
              <lb/>
            liquet propoſitum.</s>
            <s xml:id="echoid-s9619" xml:space="preserve"/>
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