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-s11877" xml:space="preserve">
              <pb o="76" file="0254" n="269" rhead=""/>
            ſit ſemper HK = HT; </s>
            <s xml:id="echoid-s11878" xml:space="preserve">tum curvam TKF tangat recta FS in F;</s>
            <s xml:id="echoid-s11879" xml:space="preserve">
              <note symbol="(_a_)" position="left" xlink:label="note-0254-01" xlink:href="note-0254-01a" xml:space="preserve">17. Lect.
                <lb/>
              VIII.</note>
            hæc curvam AIF quoque continget.</s>
            <s xml:id="echoid-s11880" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11881" xml:space="preserve">Eſt enim GK = GH + HK = GH + HT GA = GI.</s>
            <s xml:id="echoid-s11882" xml:space="preserve">
              <note symbol="(_a_)" position="left" xlink:label="note-0254-02" xlink:href="note-0254-02a" xml:space="preserve">22. Lect.
                <lb/>
              VII.</note>
            quare punctum K extra curvam AIF jacet; </s>
            <s xml:id="echoid-s11883" xml:space="preserve">adeóque recta FS cur-
              <lb/>
            vam AIF continget.</s>
            <s xml:id="echoid-s11884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11885" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s11886" xml:space="preserve">Quòd ſi recta EF ad arcum AE eandem aliquamcunque ſtatu-
              <lb/>
            atur habere proportionem, tangens ejus facilè determinatur ex hac, & </s>
            <s xml:id="echoid-s11887" xml:space="preserve">
              <lb/>
            octava octavæ Lectionis.</s>
            <s xml:id="echoid-s11888" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11889" xml:space="preserve">V. </s>
            <s xml:id="echoid-s11890" xml:space="preserve">Sint recta AP, duæque _curvæ_ AEG, AFI, ità ad ſe relatæ
              <lb/>
              <note position="left" xlink:label="note-0254-03" xlink:href="note-0254-03a" xml:space="preserve">Fig. 106.</note>
            ut ductâ utcunque rectâ DEF (quæ rectam AP, curvas AEG,
              <lb/>
            AFI punctis D, E, F, ſecet) ſit ſemper recta DT æqualis arcui AE;
              <lb/>
            </s>
            <s xml:id="echoid-s11891" xml:space="preserve">tangat autem recta ET curvam AEG ad E; </s>
            <s xml:id="echoid-s11892" xml:space="preserve">ſumatúrque ET par
              <lb/>
            arcui EA; </s>
            <s xml:id="echoid-s11893" xml:space="preserve">& </s>
            <s xml:id="echoid-s11894" xml:space="preserve">ſit TR ad BA parallela; </s>
            <s xml:id="echoid-s11895" xml:space="preserve">connectatur denuò recta RF; </s>
            <s xml:id="echoid-s11896" xml:space="preserve">
              <lb/>
            hæc curvam AFI tanget.</s>
            <s xml:id="echoid-s11897" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11898" xml:space="preserve">Concipiatur enim curva LFL talis; </s>
            <s xml:id="echoid-s11899" xml:space="preserve">ut ductâ quâcunque rectâ PL
              <lb/>
              <note symbol="(_a_)" position="left" xlink:label="note-0254-04" xlink:href="note-0254-04a" xml:space="preserve">22. Lect.
                <lb/>
              VII.</note>
            ad AB parallelâ (quæ curvam AEG in G, rectam TE in H, cur-
              <lb/>
              <note symbol="(_b_)" position="left" xlink:label="note-0254-05" xlink:href="note-0254-05a" xml:space="preserve">26. Lect.
                <lb/>
              VI.</note>
            vam LFL in L ſecet) ſit perpetuò recta PL æqualis ipſis TH, HG
              <lb/>
            ſimul; </s>
            <s xml:id="echoid-s11900" xml:space="preserve">eſt itaque PL &</s>
            <s xml:id="echoid-s11901" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11902" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s11903" xml:space="preserve">AEG * = PI. </s>
            <s xml:id="echoid-s11904" xml:space="preserve">Unde curva
              <note symbol="* it" position="left" xlink:label="note-0254-06" xlink:href="note-0254-06a" xml:space="preserve">Hyp.</note>
            curvam AFI
              <unsure/>
            tangit. </s>
            <s xml:id="echoid-s11905" xml:space="preserve">Item recta IK æquatur rectæ TH; </s>
            <s xml:id="echoid-s11906" xml:space="preserve">
              <note symbol="(_c_)" position="left" xlink:label="note-0254-07" xlink:href="note-0254-07a" xml:space="preserve">3 Lect.
                <lb/>
              VIII.</note>
            adeóque curva LFL rectam RFK tangit; </s>
            <s xml:id="echoid-s11907" xml:space="preserve"> quare curvam
              <note symbol="(_d_)" position="left" xlink:label="note-0254-08" xlink:href="note-0254-08a" xml:space="preserve">2. Lect.
                <lb/>
              VIII.</note>
            tanget recta.</s>
            <s xml:id="echoid-s11908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11909" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s11910" xml:space="preserve">Etiam ſi rectæ DE ad arcus AE quamlibet ſemper eandem ra-
              <lb/>
            tionem habeant, recta RF nihilominus curvam AFI tanget, ut
              <lb/>
            ex hac, & </s>
            <s xml:id="echoid-s11911" xml:space="preserve">ſexta octavæ Lectionis facilè patet.</s>
            <s xml:id="echoid-s11912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11913" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s11914" xml:space="preserve">Sit punctum D; </s>
            <s xml:id="echoid-s11915" xml:space="preserve">duæque curvæ AGE, DIF itâ verſus ſe
              <lb/>
              <note position="left" xlink:label="note-0254-09" xlink:href="note-0254-09a" xml:space="preserve">Fig. 107.</note>
            relatæ ſint, ut à puncto D projectâ quâvis rectâ DFE, ſit perpetuò
              <lb/>
            recta DF æqualis arcui AE; </s>
            <s xml:id="echoid-s11916" xml:space="preserve">tangat autem recta ET curvam AGE
              <lb/>
            ad E; </s>
            <s xml:id="echoid-s11917" xml:space="preserve">deſignanda jam eſt recta, quæ curvam DIF tangat (ad F).</s>
            <s xml:id="echoid-s11918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11919" xml:space="preserve">Sumatur ET par _arcui_ FS; </s>
            <s xml:id="echoid-s11920" xml:space="preserve">concipiatúrque _carva_ DKK talis, ut
              <lb/>
            à D projectâ utcunque rectâ DH (quæ curvam DKK in K, rectam
              <lb/>
              <note symbol="(_a_)" position="left" xlink:label="note-0254-10" xlink:href="note-0254-10a" xml:space="preserve">16. Lect.
                <lb/>
              VIII.</note>
            TE in H ſecet) ſit perpetuò DK = TH; </s>
            <s xml:id="echoid-s11921" xml:space="preserve">tum curvam DKK tangat recta FS ad F; </s>
            <s xml:id="echoid-s11922" xml:space="preserve">hæc curvam DIF quoque tanget.</s>
            <s xml:id="echoid-s11923" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11924" xml:space="preserve">Intelligatur enim _curva_ LFL talis, ut à D projectâ quapiam rectâ
              <lb/>
              <note symbol="(_b_)" position="left" xlink:label="note-0254-11" xlink:href="note-0254-11a" xml:space="preserve">22. Lect.
                <lb/>
              VII.</note>
            DH (quæ rectam TE ſecet in H, curvam LFL in L) ſit ſemper
              <lb/>
              <note symbol="(_c_) it" position="left" xlink:label="note-0254-12" xlink:href="note-0254-12a" xml:space="preserve">Hyp.</note>
            DL = TH + HG; </s>
            <s xml:id="echoid-s11925" xml:space="preserve">eſt itaque DL &</s>
            <s xml:id="echoid-s11926" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11927" xml:space="preserve">are. </s>
            <s xml:id="echoid-s11928" xml:space="preserve">AG =
              <note symbol="(_d_)" position="left" xlink:label="note-0254-13" xlink:href="note-0254-13a" xml:space="preserve">4. Lect.
                <lb/>
              VIII.</note>
            itaque curvæ DIF, LFL ſeſe contingent, item curvæ </s>
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