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-s10989" xml:space="preserve">
              <pb o="62" file="0240" n="255" rhead=""/>
            niam jam eſt KF &</s>
            <s xml:id="echoid-s10990" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10991" xml:space="preserve">NF; </s>
            <s xml:id="echoid-s10992" xml:space="preserve">& </s>
            <s xml:id="echoid-s10993" xml:space="preserve">KE * &</s>
            <s xml:id="echoid-s10994" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s10995" xml:space="preserve">MF; </s>
            <s xml:id="echoid-s10996" xml:space="preserve">perſpicuum
              <note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve"> (b) _Conſtr._</note>
            reſtare FE &</s>
            <s xml:id="echoid-s10997" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10998" xml:space="preserve">NM.</s>
            <s xml:id="echoid-s10999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11000" xml:space="preserve">Ità quidem ab una rectæ BQ parte recta BR duci poteſt, quæ mi-
              <lb/>
            nores ipſis MN intercipiat; </s>
            <s xml:id="echoid-s11001" xml:space="preserve"> poteſt autem ab altera parte recta quoque duci, quæ minores intercipiat ipſis F E; </s>
            <s xml:id="echoid-s11002" xml:space="preserve">unde totum liquet
              <lb/>
            Propoſitum.</s>
            <s xml:id="echoid-s11003" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11004" xml:space="preserve">XX. </s>
            <s xml:id="echoid-s11005" xml:space="preserve">In recta DZ ſint tria puncta D, E, F; </s>
            <s xml:id="echoid-s11006" xml:space="preserve">& </s>
            <s xml:id="echoid-s11007" xml:space="preserve">in F ſit vertex an-
              <lb/>
              <note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">Fig. 73.</note>
            guli rectilinei BFC, cujus latera ſecet recta DBC; </s>
            <s xml:id="echoid-s11008" xml:space="preserve">per E vero
              <lb/>
            ducta ſit recta EG; </s>
            <s xml:id="echoid-s11009" xml:space="preserve">poteſt ab E recta duci (ceu EH) talis, ut à
              <lb/>
            puncto D projectâ utcunque rectâ DK ſit in hac à rectis EG, EH in-
              <lb/>
            tercepta minor à rectis FC, FB interceptâ.</s>
            <s xml:id="echoid-s11010" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11011" xml:space="preserve">Ducantur ES ad FC, & </s>
            <s xml:id="echoid-s11012" xml:space="preserve">ER ad FB parallelæ; </s>
            <s xml:id="echoid-s11013" xml:space="preserve">& </s>
            <s xml:id="echoid-s11014" xml:space="preserve">in primo caſu,
              <lb/>
            ubi punctum E puncto D vicinius eſt, (ob ſimilitudinem triangulorum
              <lb/>
            ENM, FKI) manifeſtum eſt fore MN &</s>
            <s xml:id="echoid-s11015" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11016" xml:space="preserve">IK; </s>
            <s xml:id="echoid-s11017" xml:space="preserve"> poteſt
              <note position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">(a) _19. bujus._</note>
            tem ab E duci recta (puta EH) talis, ut interceptæ PO minores ſint
              <lb/>
            interceptis MN; </s>
            <s xml:id="echoid-s11018" xml:space="preserve">ergò liquet.</s>
            <s xml:id="echoid-s11019" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11020" xml:space="preserve">In altero caſu, ubi punctum F ipſi D propius, ſumatur SL æqualis
              <lb/>
            ipſi CB; </s>
            <s xml:id="echoid-s11021" xml:space="preserve">& </s>
            <s xml:id="echoid-s11022" xml:space="preserve">connectatur EL; </s>
            <s xml:id="echoid-s11023" xml:space="preserve">Eſtque jam IK. </s>
            <s xml:id="echoid-s11024" xml:space="preserve">MN :</s>
            <s xml:id="echoid-s11025" xml:space="preserve">: FK. </s>
            <s xml:id="echoid-s11026" xml:space="preserve">EN :</s>
            <s xml:id="echoid-s11027" xml:space="preserve">:
              <lb/>
              <note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">Fig. 74.</note>
            DF. </s>
            <s xml:id="echoid-s11028" xml:space="preserve">DE :</s>
            <s xml:id="echoid-s11029" xml:space="preserve">: FC. </s>
            <s xml:id="echoid-s11030" xml:space="preserve">ES :</s>
            <s xml:id="echoid-s11031" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s11032" xml:space="preserve">RS :</s>
            <s xml:id="echoid-s11033" xml:space="preserve">: LS. </s>
            <s xml:id="echoid-s11034" xml:space="preserve">RS &</s>
            <s xml:id="echoid-s11035" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11036" xml:space="preserve">QN.</s>
            <s xml:id="echoid-s11037" xml:space="preserve">
              <note position="left" xlink:label="note-0240-05" xlink:href="note-0240-05a" xml:space="preserve">(_c_) _Conſtr_.</note>
            MN. </s>
            <s xml:id="echoid-s11038" xml:space="preserve">quapropter eſt IK &</s>
            <s xml:id="echoid-s11039" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11040" xml:space="preserve">QN. </s>
            <s xml:id="echoid-s11041" xml:space="preserve"> poteſt autem ab E recta
              <note position="left" xlink:label="note-0240-06" xlink:href="note-0240-06a" xml:space="preserve">(_d_)6. Lect. VI.</note>
            ceu E H, ſic ut ab EG, EH interceptæ OP minores ſint interceptis
              <lb/>
            QN. </s>
            <s xml:id="echoid-s11042" xml:space="preserve">quamobrem abundè conſtat Propoſitum.</s>
            <s xml:id="echoid-s11043" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11044" xml:space="preserve">XXI Curvam BA tangat recta BO in B; </s>
            <s xml:id="echoid-s11045" xml:space="preserve">ſitque recta BO æ-
              <lb/>
            qualis curvæ B A; </s>
            <s xml:id="echoid-s11046" xml:space="preserve">ſumpto tunc in curva puncto quopiam K conne-
              <lb/>
              <note position="left" xlink:label="note-0240-07" xlink:href="note-0240-07a" xml:space="preserve">Fig. 75.</note>
            ctatur recta KO; </s>
            <s xml:id="echoid-s11047" xml:space="preserve">erit KO major arcu KA.</s>
            <s xml:id="echoid-s11048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11049" xml:space="preserve">Nam, quoniam recta minimum eſt inter bina puncta intervallum,
              <lb/>
            eſt BK + KO &</s>
            <s xml:id="echoid-s11050" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11051" xml:space="preserve">BO = BK + KA. </s>
            <s xml:id="echoid-s11052" xml:space="preserve">ergò KA &</s>
            <s xml:id="echoid-s11053" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11054" xml:space="preserve">KO.</s>
            <s xml:id="echoid-s11055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11056" xml:space="preserve">XXII. </s>
            <s xml:id="echoid-s11057" xml:space="preserve">Hinc, utcunque ſumptis (ad eaſdem contactûs partes) duobus
              <lb/>
            punctis K, L, connexâque rectâ KL; </s>
            <s xml:id="echoid-s11058" xml:space="preserve">erit KL + LO &</s>
            <s xml:id="echoid-s11059" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11060" xml:space="preserve">KA.</s>
            <s xml:id="echoid-s11061" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11062" xml:space="preserve">Nam, ſupra contactum verſus A, eſt KL + LO &</s>
            <s xml:id="echoid-s11063" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11064" xml:space="preserve">KO &</s>
            <s xml:id="echoid-s11065" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11066" xml:space="preserve">KA.</s>
            <s xml:id="echoid-s11067" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11068" xml:space="preserve">Infra verò, eſt KL + LB &</s>
            <s xml:id="echoid-s11069" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11070" xml:space="preserve">KB (ex hypotheſibus _Archime-_
              <lb/>
            _dæis_) adeóque KL + LO &</s>
            <s xml:id="echoid-s11071" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11072" xml:space="preserve">KA.</s>
            <s xml:id="echoid-s11073" xml:space="preserve"/>
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