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-div283" type="section" level="1" n="32">
          <p>
            <s xml:id="echoid-s10692" xml:space="preserve">
              <pb o="58" file="0236" n="251" rhead=""/>
            eodem ſemper ordine media inter QL, QI (eodem inquam illo, quo
              <lb/>
            PF media fuerat inter PG, PE) : </s>
            <s xml:id="echoid-s10693" xml:space="preserve">dico lineas FBF, KEK analo-
              <lb/>
              <note position="left" xlink:label="note-0236-01" xlink:href="note-0236-01a" xml:space="preserve">Fig. 65.</note>
            gas eſſe; </s>
            <s xml:id="echoid-s10694" xml:space="preserve">hoc eſt ordinatas (quales QR, QK) eandem perpetuò in-
              <lb/>
            ter ſe rationem habere; </s>
            <s xml:id="echoid-s10695" xml:space="preserve">eandem ſcilicet illi quam habet PF ad PE.</s>
            <s xml:id="echoid-s10696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10697" xml:space="preserve">Hoc è Lemmate proximè præmiſſo conſectatur, utì patebit, ad ſub-
              <lb/>
            jectum Schema mentem advertendo.</s>
            <s xml:id="echoid-s10698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10699" xml:space="preserve">QS* QR* QI. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">\\ QL* QK* QI. </s>
            <s xml:id="echoid-s10701" xml:space="preserve">\\ PG* PF* PE. </s>
            <s xml:id="echoid-s10702" xml:space="preserve">\\ PE* PE* PE.</s>
            <s xml:id="echoid-s10703" xml:space="preserve">} Sunt {.</s>
            <s xml:id="echoid-s10704" xml:space="preserve">./.</s>
            <s xml:id="echoid-s10705" xml:space="preserve">.}. </s>
            <s xml:id="echoid-s10706" xml:space="preserve">unde QR. </s>
            <s xml:id="echoid-s10707" xml:space="preserve">QK:</s>
            <s xml:id="echoid-s10708" xml:space="preserve">:
              <lb/>
            PF. </s>
            <s xml:id="echoid-s10709" xml:space="preserve">PE.</s>
            <s xml:id="echoid-s10710" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10711" xml:space="preserve">Not. </s>
            <s xml:id="echoid-s10712" xml:space="preserve">Pro lineis rectis AB, HE, CD ſubſtitui poſſent quælibet,
              <lb/>
            etiam curvæ, parallelæ.</s>
            <s xml:id="echoid-s10713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10714" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s10715" xml:space="preserve">Sint rurſus, in A concurrentes duæ rectæ AB, AD, rectaq;
              <lb/>
            </s>
            <s xml:id="echoid-s10716" xml:space="preserve">
              <note position="left" xlink:label="note-0236-02" xlink:href="note-0236-02a" xml:space="preserve">Fig. 66.</note>
            BD poſitione data; </s>
            <s xml:id="echoid-s10717" xml:space="preserve">item duæ curvæ EBE, FBF ſic relatæ, ut ductâ
              <lb/>
            utcunque PG ad DB parallelâ, ſit ſemper PF eodem ordine media
              <lb/>
            proportionalis inter PG, PE; </s>
            <s xml:id="echoid-s10718" xml:space="preserve">tum connexâ AE, ſit alia cu
              <unsure/>
            rva
              <lb/>
            KEK talis, ut ductâ quâpiam rectâ QLI ad DB parallelâ ſit ſemper
              <lb/>
            QK eodem ordine media inter QL, QI, quo fuit PF inter P G, PE;
              <lb/>
            </s>
            <s xml:id="echoid-s10719" xml:space="preserve">erit rurſus linea FEF ipſi KBK analoga; </s>
            <s xml:id="echoid-s10720" xml:space="preserve">ſeu perpetim QR. </s>
            <s xml:id="echoid-s10721" xml:space="preserve">QK :</s>
            <s xml:id="echoid-s10722" xml:space="preserve">:
              <lb/>
            PF. </s>
            <s xml:id="echoid-s10723" xml:space="preserve">PE.</s>
            <s xml:id="echoid-s10724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10725" xml:space="preserve">Nam QS* QR* QI. </s>
            <s xml:id="echoid-s10726" xml:space="preserve">\\ QL* QK* QI. </s>
            <s xml:id="echoid-s10727" xml:space="preserve">\\ PG* PF* PE. </s>
            <s xml:id="echoid-s10728" xml:space="preserve">\\ PE* PE* PE.</s>
            <s xml:id="echoid-s10729" xml:space="preserve">} ſunt {.</s>
            <s xml:id="echoid-s10730" xml:space="preserve">./.</s>
            <s xml:id="echoid-s10731" xml:space="preserve">.}.</s>
            <s xml:id="echoid-s10732" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10733" xml:space="preserve">item QS. </s>
            <s xml:id="echoid-s10734" xml:space="preserve">QL :</s>
            <s xml:id="echoid-s10735" xml:space="preserve">: \\ PG. </s>
            <s xml:id="echoid-s10736" xml:space="preserve">PE. </s>
            <s xml:id="echoid-s10737" xml:space="preserve">\\ Et QI. </s>
            <s xml:id="echoid-s10738" xml:space="preserve">QI :</s>
            <s xml:id="echoid-s10739" xml:space="preserve">: \\ PE. </s>
            <s xml:id="echoid-s10740" xml:space="preserve">PE.</s>
            <s xml:id="echoid-s10741" xml:space="preserve">}ergò QR.
              <lb/>
            </s>
            <s xml:id="echoid-s10742" xml:space="preserve">QK :</s>
            <s xml:id="echoid-s10743" xml:space="preserve">:
              <lb/>
            PF. </s>
            <s xml:id="echoid-s10744" xml:space="preserve">PE.</s>
            <s xml:id="echoid-s10745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10746" xml:space="preserve">_Not_. </s>
            <s xml:id="echoid-s10747" xml:space="preserve">Pro rectis AB, AH, AD ſubſtitui poſſent tres quævis lineæ
              <lb/>
            analogæ.</s>
            <s xml:id="echoid-s10748" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10749" xml:space="preserve">XI Item, ſit circulus AG B, cujus centrum D; </s>
            <s xml:id="echoid-s10750" xml:space="preserve">aliæque duæ curvæ
              <lb/>
            EBE, FBF tales, utper D ductâ quâcunque rectâ DG, ſit perpe-
              <lb/>
              <note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">Fig. 67.</note>
            tuò DF eodem ordine media propor
              <unsure/>
            ionalis inter DG, DE; </s>
            <s xml:id="echoid-s10751" xml:space="preserve">tum
              <lb/>
            centro D per E deſ@ribatur circulus H E; </s>
            <s xml:id="echoid-s10752" xml:space="preserve">ſitque præterea curva KEK
              <lb/>
            talis, ut ductâ per D quâpiam (ad circulum HE) rectâ DL, ſit </s>
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