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

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[111.] _Theor_. VI.
[112.] FINIS.
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          <pb o="100" file="0118" n="118" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s6666" xml:space="preserve">_XI._ </s>
            <s xml:id="echoid-s6667" xml:space="preserve">Ad lentem convexo-convexam diverg.</s>
            <s xml:id="echoid-s6668" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 158,
            <lb/>
          159.</note>
          <p style="it">
            <s xml:id="echoid-s6669" xml:space="preserve">_XII._ </s>
            <s xml:id="echoid-s6670" xml:space="preserve">Ad lentem concavo-concavam converg.</s>
            <s xml:id="echoid-s6671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6672" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6673" xml:space="preserve">Si AB &</s>
            <s xml:id="echoid-s6674" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6675" xml:space="preserve">{R/I} AC, facto AB - {R/I} AC. </s>
            <s xml:id="echoid-s6676" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6677" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6678" xml:space="preserve">BZ;
              <lb/>
            </s>
            <s xml:id="echoid-s6679" xml:space="preserve">& </s>
            <s xml:id="echoid-s6680" xml:space="preserve">{I/R} KZ - DZ :</s>
            <s xml:id="echoid-s6681" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6682" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6683" xml:space="preserve">puncta Z, Y adverſus Acadunt.</s>
            <s xml:id="echoid-s6684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6685" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6686" xml:space="preserve">Si AB = {R/I} AC, fac I - R. </s>
            <s xml:id="echoid-s6687" xml:space="preserve">R :</s>
            <s xml:id="echoid-s6688" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6689" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6690" xml:space="preserve">& </s>
            <s xml:id="echoid-s6691" xml:space="preserve">cape DY
              <lb/>
            adverſus A.</s>
            <s xml:id="echoid-s6692" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6693" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6694" xml:space="preserve">Si AB &</s>
            <s xml:id="echoid-s6695" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6696" xml:space="preserve">{R/I} AC; </s>
            <s xml:id="echoid-s6697" xml:space="preserve">fac {R/I} AC - AB. </s>
            <s xml:id="echoid-s6698" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6699" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6700" xml:space="preserve">BZ;
              <lb/>
            </s>
            <s xml:id="echoid-s6701" xml:space="preserve">& </s>
            <s xml:id="echoid-s6702" xml:space="preserve">ſume BZ verſus A. </s>
            <s xml:id="echoid-s6703" xml:space="preserve">Jam cùm Z cadit extra DK, ſi primò ſit
              <lb/>
            {I/R} KZ &</s>
            <s xml:id="echoid-s6704" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6705" xml:space="preserve">DZ, fac {I/R} KZ - DZ. </s>
            <s xml:id="echoid-s6706" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6707" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6709" xml:space="preserve">& </s>
            <s xml:id="echoid-s6710" xml:space="preserve">ſume
              <lb/>
            DY adverſus A</s>
          </p>
          <p>
            <s xml:id="echoid-s6711" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6712" xml:space="preserve">Secundò, ſi {I/R} KZ = DZ, imago diſtabit infini è.</s>
            <s xml:id="echoid-s6713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6714" xml:space="preserve">5. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">Tertiò, ſi {I/R} KZ &</s>
            <s xml:id="echoid-s6716" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6717" xml:space="preserve">DZ, fac DZ - {I/R} KZ. </s>
            <s xml:id="echoid-s6718" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6719" xml:space="preserve">: DK.
              <lb/>
            </s>
            <s xml:id="echoid-s6720" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6721" xml:space="preserve">& </s>
            <s xml:id="echoid-s6722" xml:space="preserve">ſume DY verſus A.</s>
            <s xml:id="echoid-s6723" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6724" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6725" xml:space="preserve">Quum denuò cadit Z inter D, & </s>
            <s xml:id="echoid-s6726" xml:space="preserve">K, fiat DZ + {I/R} KZ. </s>
            <s xml:id="echoid-s6727" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6728" xml:space="preserve">:
              <lb/>
            DK. </s>
            <s xml:id="echoid-s6729" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6730" xml:space="preserve">ſumatúrque DY verſus A.</s>
            <s xml:id="echoid-s6731" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6732" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s6733" xml:space="preserve">Ad in regram Sphæram diυerg.</s>
            <s xml:id="echoid-s6734" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6735" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6736" xml:space="preserve">Si AB + AC &</s>
            <s xml:id="echoid-s6737" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6738" xml:space="preserve">{2R/I} AC; </s>
            <s xml:id="echoid-s6739" xml:space="preserve">fiat AB + AC - {2R/I} AC.
              <lb/>
            </s>
            <s xml:id="echoid-s6740" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s6741" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6742" xml:space="preserve">CY; </s>
            <s xml:id="echoid-s6743" xml:space="preserve">& </s>
            <s xml:id="echoid-s6744" xml:space="preserve">cape CY adverſus A.</s>
            <s xml:id="echoid-s6745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6746" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6747" xml:space="preserve">Si AB + AC = {2R/I} AC; </s>
            <s xml:id="echoid-s6748" xml:space="preserve">imago in infinitum abit.</s>
            <s xml:id="echoid-s6749" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6750" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6751" xml:space="preserve">Si AB + AC &</s>
            <s xml:id="echoid-s6752" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6753" xml:space="preserve">{2R/I} AC; </s>
            <s xml:id="echoid-s6754" xml:space="preserve">fiat {2R/I} AC - AC - AB.
              <lb/>
            </s>
            <s xml:id="echoid-s6755" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s6756" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6757" xml:space="preserve">CY; </s>
            <s xml:id="echoid-s6758" xml:space="preserve">capiatúrque CY verſus A.</s>
            <s xml:id="echoid-s6759" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6760" xml:space="preserve">_XIII._ </s>
            <s xml:id="echoid-s6761" xml:space="preserve">Ad lentem concavc-concavam diverg.</s>
            <s xml:id="echoid-s6762" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 159.</note>
          <p style="it">
            <s xml:id="echoid-s6763" xml:space="preserve">_XIV._ </s>
            <s xml:id="echoid-s6764" xml:space="preserve">Ad lentem convexo-convexam converg.</s>
            <s xml:id="echoid-s6765" xml:space="preserve"/>
          </p>
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