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-div99" type="section" level="1" n="18">
          <pb o="69" file="0087" n="87"/>
        </div>
        <div xml:id="echoid-div113" type="section" level="1" n="19">
          <head xml:id="echoid-head22" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          X.</head>
          <p>
            <s xml:id="echoid-s4235" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4236" xml:space="preserve">IN poſtrema Lectione quod ſpectavimus punctum circuli convexo
              <lb/>
            alluxit; </s>
            <s xml:id="echoid-s4237" xml:space="preserve">nunc parte@ concavas irradians aliud, at magìs @ π’ π ω,
              <lb/>
            contemplabimur. </s>
            <s xml:id="echoid-s4238" xml:space="preserve">& </s>
            <s xml:id="echoid-s4239" xml:space="preserve">quidem caſuum præcipuorum diverſitatem im-
              <lb/>
            primìs diſtinguemus. </s>
            <s xml:id="echoid-s4240" xml:space="preserve">Nempe radiet punctum A in circulum re-
              <lb/>
            flectentem, cujus centrum C; </s>
            <s xml:id="echoid-s4241" xml:space="preserve">connexaque recta AC protendatur in-
              <lb/>
            definitè; </s>
            <s xml:id="echoid-s4242" xml:space="preserve">quo poſito.</s>
            <s xml:id="echoid-s4243" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4244" xml:space="preserve">II. </s>
            <s xml:id="echoid-s4245" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4246" xml:space="preserve">Incidat radius AN; </s>
            <s xml:id="echoid-s4247" xml:space="preserve">& </s>
            <s xml:id="echoid-s4248" xml:space="preserve">ſit AN = AC; </s>
            <s xml:id="echoid-s4249" xml:space="preserve">erit ipſius AN
              <lb/>
            reflexus, puta N _a_, ad AC parallelus.</s>
            <s xml:id="echoid-s4250" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 97.</note>
          <p>
            <s xml:id="echoid-s4251" xml:space="preserve">Hoc è ſuprà generatim oſtenſis conſtat; </s>
            <s xml:id="echoid-s4252" xml:space="preserve">& </s>
            <s xml:id="echoid-s4253" xml:space="preserve">facilè jam patet, con-
              <lb/>
            nexâ CA. </s>
            <s xml:id="echoid-s4254" xml:space="preserve">etenim eſt ang. </s>
            <s xml:id="echoid-s4255" xml:space="preserve">ACN = AN C; </s>
            <s xml:id="echoid-s4256" xml:space="preserve">ob AC, AN, ex
              <lb/>
            Hypotheſi pares; </s>
            <s xml:id="echoid-s4257" xml:space="preserve">& </s>
            <s xml:id="echoid-s4258" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s4259" xml:space="preserve">ANC = _a_ NC, propter reflectionem;
              <lb/>
            </s>
            <s xml:id="echoid-s4260" xml:space="preserve">adeóque ang. </s>
            <s xml:id="echoid-s4261" xml:space="preserve">ACN = _a_ NC; </s>
            <s xml:id="echoid-s4262" xml:space="preserve">unde ſunt AC, N _a_ ſibi paralle-
              <lb/>
            læ.</s>
            <s xml:id="echoid-s4263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4264" xml:space="preserve">III. </s>
            <s xml:id="echoid-s4265" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4266" xml:space="preserve">Incidat radius AM major ipsâ AC; </s>
            <s xml:id="echoid-s4267" xml:space="preserve">ejus reflexus (puta
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">Fig. 98.</note>
            M _a_) cum axe directè procedens conveniet ultra centrum, reſpectu
              <lb/>
            puncti A; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">(hoc eſt centrum C puncto radianti, concurſuique inter-
              <lb/>
            jacebit).</s>
            <s xml:id="echoid-s4269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4270" xml:space="preserve">Nam ob AM &</s>
            <s xml:id="echoid-s4271" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4272" xml:space="preserve">AC, erit ang. </s>
            <s xml:id="echoid-s4273" xml:space="preserve">ACM&</s>
            <s xml:id="echoid-s4274" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4275" xml:space="preserve">AMC = CM _a_.
              <lb/>
            </s>
            <s xml:id="echoid-s4276" xml:space="preserve">ergo ang. </s>
            <s xml:id="echoid-s4277" xml:space="preserve">BCM+ CM _a_ &</s>
            <s xml:id="echoid-s4278" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">BCM+ ACM = 2 rect. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">
              <lb/>
            quare M _a_, CB convenient infra CM ad partes _a_ B; </s>
            <s xml:id="echoid-s4282" xml:space="preserve">velut
              <lb/>
            ad K.</s>
            <s xml:id="echoid-s4283" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4284" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s4285" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4286" xml:space="preserve">Incidat radius AR; </s>
            <s xml:id="echoid-s4287" xml:space="preserve">& </s>
            <s xml:id="echoid-s4288" xml:space="preserve">ſit AR minor ipsâ AC; </s>
            <s xml:id="echoid-s4289" xml:space="preserve">ejus
              <lb/>
              <note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">Fig. 99.</note>
            reflexus, puta R _a_, axi retrò protractus occurret. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">(hoceſt ut radians
              <lb/>
            centro, concurſuíque ſit interjectum).</s>
            <s xml:id="echoid-s4291" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4292" xml:space="preserve">Nam hîc ob AR &</s>
            <s xml:id="echoid-s4293" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4294" xml:space="preserve">AC; </s>
            <s xml:id="echoid-s4295" xml:space="preserve">erit ang. </s>
            <s xml:id="echoid-s4296" xml:space="preserve">ACR&</s>
            <s xml:id="echoid-s4297" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4298" xml:space="preserve">ang ARC = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s4299" xml:space="preserve">_a_ RC. </s>
            <s xml:id="echoid-s4300" xml:space="preserve">quapropter ang. </s>
            <s xml:id="echoid-s4301" xml:space="preserve">DCR+ _a_ RC &</s>
            <s xml:id="echoid-s4302" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4303" xml:space="preserve">2 rect. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">unde patet ipſas
              <lb/>
            D C, _a_ R portractas infra CR concurrere.</s>
            <s xml:id="echoid-s4305" xml:space="preserve"/>
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