Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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            <s xml:id="echoid-s11837" xml:space="preserve">
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            ſit rectus, erit curva SEE _Ciſſois vulgaris_, ſeu _Dioslea_; </s>
            <s xml:id="echoid-s11838" xml:space="preserve">alioquin
              <lb/>
            alterius generis _Ciſſoidalis_. </s>
            <s xml:id="echoid-s11839" xml:space="preserve">Hoc autem ἐγ παςόδφ perſtringo. </s>
            <s xml:id="echoid-s11840" xml:space="preserve">Neq;
              <lb/>
            </s>
            <s xml:id="echoid-s11841" xml:space="preserve">jam ampliùs vos detinebo.</s>
            <s xml:id="echoid-s11842" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div350" type="section" level="1" n="35">
          <head xml:id="echoid-head38" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . X.</head>
          <p>
            <s xml:id="echoid-s11843" xml:space="preserve">IN ſtitutum circa tangentes negotium adhuc urgeo.</s>
            <s xml:id="echoid-s11844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11845" xml:space="preserve">I. </s>
            <s xml:id="echoid-s11846" xml:space="preserve">Sit curva quæpiam AEG, nec non alia AFI ſic ad illam rela-
              <lb/>
              <note position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve">Fig. 104.</note>
            ta, ut ductâ quâcunque EF ad poſitione datam AB parallelâ (quæ
              <lb/>
            curvam AFG ſecet in E, curvámque AFI in F (ſit perpetim EF
              <lb/>
            æqualis curvæ AEG ab A intercepto arcui AE; </s>
            <s xml:id="echoid-s11847" xml:space="preserve">tangat autem recta
              <lb/>
            ET curvam AEG in E, ſitque ET æqualis arcui AE, & </s>
            <s xml:id="echoid-s11848" xml:space="preserve">connecta-
              <lb/>
            tur recta TF; </s>
            <s xml:id="echoid-s11849" xml:space="preserve">hæc curvam AFI tanget.</s>
            <s xml:id="echoid-s11850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11851" xml:space="preserve">Nam ducatur ntcunque recta GK ad AB parallela, lineas propo-
              <lb/>
            ſitas ſecans, ut cernis; </s>
            <s xml:id="echoid-s11852" xml:space="preserve">éſtque GK = GH + HK = GH + HT
              <lb/>
            &</s>
            <s xml:id="echoid-s11853" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11854" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s11855" xml:space="preserve">AG = GI; </s>
            <s xml:id="echoid-s11856" xml:space="preserve">unde punctum K extra curvam AFI
              <note symbol="(_a_)" position="right" xlink:label="note-0253-02" xlink:href="note-0253-02a" xml:space="preserve">22 Lect.
                <lb/>
              VII.</note>
            tum eſt; </s>
            <s xml:id="echoid-s11857" xml:space="preserve">adeóque recta TK ipſam tangit.</s>
            <s xml:id="echoid-s11858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11859" xml:space="preserve">II. </s>
            <s xml:id="echoid-s11860" xml:space="preserve">Quòd ſi recta EF quamlibet ad arcum AE rationem ſemper
              <lb/>
            eandem habeat, nihilo ſeciùs recta FT curvam AFI tanget; </s>
            <s xml:id="echoid-s11861" xml:space="preserve">ut ex
              <lb/>
            hac, & </s>
            <s xml:id="echoid-s11862" xml:space="preserve">octavæ Lectionis ſexta manifeſtæ conſectatur.</s>
            <s xml:id="echoid-s11863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11864" xml:space="preserve">Hæc antea pridem aliter oſtendimus; </s>
            <s xml:id="echoid-s11865" xml:space="preserve">aſt hæc demonſtratio ſimpli-
              <lb/>
            cior aliquanto videtur, & </s>
            <s xml:id="echoid-s11866" xml:space="preserve">clarior; </s>
            <s xml:id="echoid-s11867" xml:space="preserve">methodóque quam inſinuamus ac-
              <lb/>
            commodatior.</s>
            <s xml:id="echoid-s11868" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11869" xml:space="preserve">III. </s>
            <s xml:id="echoid-s11870" xml:space="preserve">Sit _curva_ quæpiam AGE, punctúmque deſignatum D; </s>
            <s xml:id="echoid-s11871" xml:space="preserve">ſit
              <lb/>
            item alia curva AIF talis, ut à D projectâ rectâ quâ cunque DEF,
              <lb/>
              <note position="right" xlink:label="note-0253-03" xlink:href="note-0253-03a" xml:space="preserve">Fig. 105.</note>
            ſit ſemper intercepta EF par arcui AE; </s>
            <s xml:id="echoid-s11872" xml:space="preserve">tangátque recta ET curvam
              <lb/>
            AGE; </s>
            <s xml:id="echoid-s11873" xml:space="preserve">oportet curvæ AIF _Tangentem_ (ad F) deſignare.</s>
            <s xml:id="echoid-s11874" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11875" xml:space="preserve">Fiat TE = arc. </s>
            <s xml:id="echoid-s11876" xml:space="preserve">AE; </s>
            <s xml:id="echoid-s11877" xml:space="preserve">ſitque curva TKF talis, ut ductâ utcunque
              <lb/>
            (è D) rectâ DK (quæ curvam TKF ſecet in K, rectámque TE in </s>
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