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-div222" type="section" level="1" n="31">
          <pb o="56" file="0234" n="249"/>
        </div>
        <div xml:id="echoid-div283" type="section" level="1" n="32">
          <head xml:id="echoid-head35" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . VII.</head>
          <p>
            <s xml:id="echoid-s10544" xml:space="preserve">ADhuc in _Veſtibulo_ hæremus; </s>
            <s xml:id="echoid-s10545" xml:space="preserve">nec aliud quàm velitamus.</s>
            <s xml:id="echoid-s10546" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10547" xml:space="preserve">I. </s>
            <s xml:id="echoid-s10548" xml:space="preserve">Sint duo quanta A, B; </s>
            <s xml:id="echoid-s10549" xml:space="preserve">quorum majus A; </s>
            <s xml:id="echoid-s10550" xml:space="preserve">adſumpto tertio quo-
              <lb/>
            piam X, erit A + X. </s>
            <s xml:id="echoid-s10551" xml:space="preserve">B + X &</s>
            <s xml:id="echoid-s10552" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10553" xml:space="preserve">A. </s>
            <s xml:id="echoid-s10554" xml:space="preserve">B.</s>
            <s xml:id="echoid-s10555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10556" xml:space="preserve">Nam ob X. </s>
            <s xml:id="echoid-s10557" xml:space="preserve">A &</s>
            <s xml:id="echoid-s10558" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10559" xml:space="preserve">X. </s>
            <s xml:id="echoid-s10560" xml:space="preserve">B; </s>
            <s xml:id="echoid-s10561" xml:space="preserve">erit componendo X + A. </s>
            <s xml:id="echoid-s10562" xml:space="preserve">A. </s>
            <s xml:id="echoid-s10563" xml:space="preserve">&</s>
            <s xml:id="echoid-s10564" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10565" xml:space="preserve">X +
              <lb/>
            B. </s>
            <s xml:id="echoid-s10566" xml:space="preserve">B. </s>
            <s xml:id="echoid-s10567" xml:space="preserve">vel permutando X + A. </s>
            <s xml:id="echoid-s10568" xml:space="preserve">X + B &</s>
            <s xml:id="echoid-s10569" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s10570" xml:space="preserve">A. </s>
            <s xml:id="echoid-s10571" xml:space="preserve">B.</s>
            <s xml:id="echoid-s10572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10573" xml:space="preserve">II. </s>
            <s xml:id="echoid-s10574" xml:space="preserve">In linea YZ ſignentur tria puncta, L, M, N; </s>
            <s xml:id="echoid-s10575" xml:space="preserve">& </s>
            <s xml:id="echoid-s10576" xml:space="preserve">inter puncta
              <lb/>
            L, N ſumpto puncto quopiam E, alteróque G extra LN (verſus Z);
              <lb/>
            </s>
            <s xml:id="echoid-s10577" xml:space="preserve">ſecetur EG in F, ut ſit GE. </s>
            <s xml:id="echoid-s10578" xml:space="preserve">EF :</s>
            <s xml:id="echoid-s10579" xml:space="preserve">: NL. </s>
            <s xml:id="echoid-s10580" xml:space="preserve">LM; </s>
            <s xml:id="echoid-s10581" xml:space="preserve">cadet punctum F ad
              <lb/>
              <note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">Fig. 61.</note>
            partes MZ:</s>
            <s xml:id="echoid-s10582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10583" xml:space="preserve">Nam eſt N E. </s>
            <s xml:id="echoid-s10584" xml:space="preserve">ME &</s>
            <s xml:id="echoid-s10585" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s10586" xml:space="preserve">NL. </s>
            <s xml:id="echoid-s10587" xml:space="preserve">ML :</s>
            <s xml:id="echoid-s10588" xml:space="preserve">: GE. </s>
            <s xml:id="echoid-s10589" xml:space="preserve">FE &</s>
            <s xml:id="echoid-s10590" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s10591" xml:space="preserve">NE. </s>
            <s xml:id="echoid-s10592" xml:space="preserve">PE.</s>
            <s xml:id="echoid-s10593" xml:space="preserve">
              <note position="left" xlink:label="note-0234-02" xlink:href="note-0234-02a" xml:space="preserve">* I _hujus_.</note>
            ergo FE &</s>
            <s xml:id="echoid-s10594" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s10595" xml:space="preserve">ME.</s>
            <s xml:id="echoid-s10596" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10597" xml:space="preserve">III. </s>
            <s xml:id="echoid-s10598" xml:space="preserve">Sint rectæ BA, DC parallelæ item rectæ BD, GP parallelæ;
              <lb/>
            </s>
            <s xml:id="echoid-s10599" xml:space="preserve">pérque punctum B ducantur utcunque duæ rectæ BT, BS ipſam GP
              <lb/>
              <note position="left" xlink:label="note-0234-03" xlink:href="note-0234-03a" xml:space="preserve">Fig. 62.</note>
            ſecantes punctis L, K, dico fore D S. </s>
            <s xml:id="echoid-s10600" xml:space="preserve">DT :</s>
            <s xml:id="echoid-s10601" xml:space="preserve">: KG. </s>
            <s xml:id="echoid-s10602" xml:space="preserve">LG.</s>
            <s xml:id="echoid-s10603" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10604" xml:space="preserve">Nam eſt KG. </s>
            <s xml:id="echoid-s10605" xml:space="preserve">LG = KG. </s>
            <s xml:id="echoid-s10606" xml:space="preserve">GB + GB. </s>
            <s xml:id="echoid-s10607" xml:space="preserve">LG = PK. </s>
            <s xml:id="echoid-s10608" xml:space="preserve">PS +
              <lb/>
            PT. </s>
            <s xml:id="echoid-s10609" xml:space="preserve">PL = DB. </s>
            <s xml:id="echoid-s10610" xml:space="preserve">DS + DT. </s>
            <s xml:id="echoid-s10611" xml:space="preserve">DB = DT. </s>
            <s xml:id="echoid-s10612" xml:space="preserve">DS.</s>
            <s xml:id="echoid-s10613" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10614" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s10615" xml:space="preserve">Eſto triangulum BDT, basíque DB parallelam quamvis PG
              <lb/>
            interſecent per B ductæ quæpiam duæ rectæ BS, BR punctis L, K;
              <lb/>
            </s>
            <s xml:id="echoid-s10616" xml:space="preserve">dico fore LG x TD + KL x RD. </s>
            <s xml:id="echoid-s10617" xml:space="preserve">KG x TD :</s>
            <s xml:id="echoid-s10618" xml:space="preserve">: RD. </s>
            <s xml:id="echoid-s10619" xml:space="preserve">SD.</s>
            <s xml:id="echoid-s10620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10621" xml:space="preserve">Sumantur enim BM = GP, & </s>
            <s xml:id="echoid-s10622" xml:space="preserve">BN = LP; </s>
            <s xml:id="echoid-s10623" xml:space="preserve">& </s>
            <s xml:id="echoid-s10624" xml:space="preserve">BO = KP;
              <lb/>
            </s>
            <s xml:id="echoid-s10625" xml:space="preserve">
              <note position="left" xlink:label="note-0234-04" xlink:href="note-0234-04a" xml:space="preserve">Fig. 63</note>
            unde conſtat junctas PM, PN, PO ipſis TB, SB, RB (reſpectivè)
              <lb/>
            parallelas eſſe. </s>
            <s xml:id="echoid-s10626" xml:space="preserve">Et quoniam eſt DM. </s>
            <s xml:id="echoid-s10627" xml:space="preserve">PD :</s>
            <s xml:id="echoid-s10628" xml:space="preserve">: DB. </s>
            <s xml:id="echoid-s10629" xml:space="preserve">TD. </s>
            <s xml:id="echoid-s10630" xml:space="preserve">erit DM x
              <lb/>
            TD = PD x
              <emph style="sc">Db</emph>
            . </s>
            <s xml:id="echoid-s10631" xml:space="preserve">Similiter eſt DN x SD = PD x DB. </s>
            <s xml:id="echoid-s10632" xml:space="preserve">quare
              <lb/>
            DM x TD = DN x SD = DM x SD + MN x SD, tranſpo-
              <lb/>
            nendóque DM x TD - DM x SD = MN x SD. </s>
            <s xml:id="echoid-s10633" xml:space="preserve">Simili </s>
          </p>
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