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-s10752" xml:space="preserve">
              <pb o="59" file="0237" n="252" rhead=""/>
            DK eodem ordine media inter DL, DI, quo fuerat DF inter DG,
              <lb/>
            DE; </s>
            <s xml:id="echoid-s10753" xml:space="preserve">erunt curvæ FBF, KBK analogæ, ſeu perpetuò DR. </s>
            <s xml:id="echoid-s10754" xml:space="preserve">DK :</s>
            <s xml:id="echoid-s10755" xml:space="preserve">:
              <lb/>
            DF. </s>
            <s xml:id="echoid-s10756" xml:space="preserve">DE.</s>
            <s xml:id="echoid-s10757" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10758" xml:space="preserve">Nam rurſus DS.</s>
            <s xml:id="echoid-s10759" xml:space="preserve">* DR.</s>
            <s xml:id="echoid-s10760" xml:space="preserve">* DI. </s>
            <s xml:id="echoid-s10761" xml:space="preserve">\\ DL.</s>
            <s xml:id="echoid-s10762" xml:space="preserve">* DK.</s>
            <s xml:id="echoid-s10763" xml:space="preserve">* DI. </s>
            <s xml:id="echoid-s10764" xml:space="preserve">\\ DG.</s>
            <s xml:id="echoid-s10765" xml:space="preserve">*DF.</s>
            <s xml:id="echoid-s10766" xml:space="preserve">* DE \\ DE.</s>
            <s xml:id="echoid-s10767" xml:space="preserve">* DE.</s>
            <s xml:id="echoid-s10768" xml:space="preserve">* DE.</s>
            <s xml:id="echoid-s10769" xml:space="preserve">} ſunt {.</s>
            <s xml:id="echoid-s10770" xml:space="preserve">./.</s>
            <s xml:id="echoid-s10771" xml:space="preserve">.}.</s>
            <s xml:id="echoid-s10772" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10773" xml:space="preserve">unde DR. </s>
            <s xml:id="echoid-s10774" xml:space="preserve">DK :</s>
            <s xml:id="echoid-s10775" xml:space="preserve">:
              <lb/>
            DF. </s>
            <s xml:id="echoid-s10776" xml:space="preserve">DE.</s>
            <s xml:id="echoid-s10777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10778" xml:space="preserve">Rurſus, pro circulis aliæ lineæ parallelæ, vel analogæ ſubſtitui
              <lb/>
            poſſent.</s>
            <s xml:id="echoid-s10779" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10780" xml:space="preserve">X. </s>
            <s xml:id="echoid-s10781" xml:space="preserve">Sint denuò duæ lineæ quævis A GBG, EBE; </s>
            <s xml:id="echoid-s10782" xml:space="preserve">& </s>
            <s xml:id="echoid-s10783" xml:space="preserve">altera
              <lb/>
            FBF ſic ad iſtas relata, ut ductâ utcunque à deſignaro puncto D recta
              <lb/>
            DG, ſit perpetuò DF eodem ordine media proportionalis inter DG,
              <lb/>
            DE; </s>
            <s xml:id="echoid-s10784" xml:space="preserve">tum adſumatur linea HEL lineæ AGB analoga (ſeu talis, ut
              <lb/>
            per D utcunque ductâ DLS, ſint perpetuò DS, DL in eadem ratio-
              <lb/>
            ne) ſit denuò linea KEK talis, ut ductâ utcunque DL, ſit perpetuò
              <lb/>
            DK eodem ordine media inter DL, DI, quo priùs DF inter DG,
              <lb/>
            DE; </s>
            <s xml:id="echoid-s10785" xml:space="preserve">erit itidem linea FBF lineæ K EK analoga.</s>
            <s xml:id="echoid-s10786" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10787" xml:space="preserve">Rurſus enim DS.</s>
            <s xml:id="echoid-s10788" xml:space="preserve">* DR* DI. </s>
            <s xml:id="echoid-s10789" xml:space="preserve">\\ DL.</s>
            <s xml:id="echoid-s10790" xml:space="preserve">* DK* DI. </s>
            <s xml:id="echoid-s10791" xml:space="preserve">\\ DG.</s>
            <s xml:id="echoid-s10792" xml:space="preserve">* DF* DE \\ DE.</s>
            <s xml:id="echoid-s10793" xml:space="preserve">* DE* DE} ſunt {.</s>
            <s xml:id="echoid-s10794" xml:space="preserve">./.</s>
            <s xml:id="echoid-s10795" xml:space="preserve">.};</s>
            <s xml:id="echoid-s10796" xml:space="preserve">}Et tam primi quàm ulti-
              <lb/>
            mi quatuor termini
              <lb/>
            ſunt proportionales.
              <lb/>
            </s>
            <s xml:id="echoid-s10797" xml:space="preserve">Unde liquet Propoſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s10798" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10799" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s10800" xml:space="preserve">Sit Arithmeticè proportionalium Series A. </s>
            <s xml:id="echoid-s10801" xml:space="preserve">B. </s>
            <s xml:id="echoid-s10802" xml:space="preserve">C. </s>
            <s xml:id="echoid-s10803" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10804" xml:space="preserve">E. </s>
            <s xml:id="echoid-s10805" xml:space="preserve">F; </s>
            <s xml:id="echoid-s10806" xml:space="preserve">in
              <lb/>
            qua ſumptis quibuſcunque duobus terminis D, F; </s>
            <s xml:id="echoid-s10807" xml:space="preserve">ſit terminorum à
              <lb/>
            primo A (excluſivè) ad ipſum D numerus, N; </s>
            <s xml:id="echoid-s10808" xml:space="preserve">& </s>
            <s xml:id="echoid-s10809" xml:space="preserve">terminorum ab A
              <lb/>
            (itidem excluſivè) ad F, ſit numerus M; </s>
            <s xml:id="echoid-s10810" xml:space="preserve">erit A -: </s>
            <s xml:id="echoid-s10811" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10812" xml:space="preserve">A -: </s>
            <s xml:id="echoid-s10813" xml:space="preserve">F :</s>
            <s xml:id="echoid-s10814" xml:space="preserve">:
              <lb/>
            N. </s>
            <s xml:id="echoid-s10815" xml:space="preserve">M.</s>
            <s xml:id="echoid-s10816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10817" xml:space="preserve">Nam eſto differentia communis, X. </s>
            <s xml:id="echoid-s10818" xml:space="preserve">eſt ergò D = A ± NX. </s>
            <s xml:id="echoid-s10819" xml:space="preserve">& </s>
            <s xml:id="echoid-s10820" xml:space="preserve">
              <lb/>
            F = A ± MX. </s>
            <s xml:id="echoid-s10821" xml:space="preserve">quare A -: </s>
            <s xml:id="echoid-s10822" xml:space="preserve">D = NX. </s>
            <s xml:id="echoid-s10823" xml:space="preserve">& </s>
            <s xml:id="echoid-s10824" xml:space="preserve">A -: </s>
            <s xml:id="echoid-s10825" xml:space="preserve">F = MX.
              <lb/>
            </s>
            <s xml:id="echoid-s10826" xml:space="preserve">unde A -: </s>
            <s xml:id="echoid-s10827" xml:space="preserve">D. </s>
            <s xml:id="echoid-s10828" xml:space="preserve">A -: </s>
            <s xml:id="echoid-s10829" xml:space="preserve">F :</s>
            <s xml:id="echoid-s10830" xml:space="preserve">: ( NX. </s>
            <s xml:id="echoid-s10831" xml:space="preserve">MX:</s>
            <s xml:id="echoid-s10832" xml:space="preserve">:) N. </s>
            <s xml:id="echoid-s10833" xml:space="preserve">M.</s>
            <s xml:id="echoid-s10834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10835" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s10836" xml:space="preserve">Hinc, ſi duæ fuerint ejuſmodi ſeries; </s>
            <s xml:id="echoid-s10837" xml:space="preserve">& </s>
            <s xml:id="echoid-s10838" xml:space="preserve">in utraque </s>
          </p>
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