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-s11106" xml:space="preserve">
              <pb o="64" file="0242" n="257" rhead=""/>
            FG, FH interceptæ pares interceptis ab EB, EC; </s>
            <s xml:id="echoid-s11107" xml:space="preserve">hoc eſt minores
              <lb/>
            interceptis à curvis EY, EZ; </s>
            <s xml:id="echoid-s11108" xml:space="preserve">hoc eſt minores interceptis à curva
              <lb/>
            FX, & </s>
            <s xml:id="echoid-s11109" xml:space="preserve">recta FA; </s>
            <s xml:id="echoid-s11110" xml:space="preserve">quapropter angulus XFA rectilineo HFG ma-
              <lb/>
            jor eſt; </s>
            <s xml:id="echoid-s11111" xml:space="preserve">unde recta FA curvam FX non tangit, contra _Hy-_
              <lb/>
            _potheſin_.</s>
            <s xml:id="echoid-s11112" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11113" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s11114" xml:space="preserve">Itidem, Tangat recta FA curvam FX, & </s>
            <s xml:id="echoid-s11115" xml:space="preserve">ſint duæ curvæ
              <lb/>
            EY, EZ tales, ut ab aſſignato puncto D utcunque ductâ rectâ IL
              <lb/>
              <note position="left" xlink:label="note-0242-01" xlink:href="note-0242-01a" xml:space="preserve">Fig. 79.</note>
            ( quæ lineas expoſitas ſecet ut vides ) ſit ſemper KL = IG; </s>
            <s xml:id="echoid-s11116" xml:space="preserve">curvæ
              <lb/>
            EY, EZ ſeſe tangent.</s>
            <s xml:id="echoid-s11117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11118" xml:space="preserve">Nam, ſineges, his interſeratur _angulus rectiline
              <unsure/>
            us_ BEC; </s>
            <s xml:id="echoid-s11119" xml:space="preserve">quem
              <lb/>
            utcunque a D projecta ſecet recta DL; </s>
            <s xml:id="echoid-s11120" xml:space="preserve"> poteſt jam ab F recta
              <note position="left" xlink:label="note-0242-02" xlink:href="note-0242-02a" xml:space="preserve">(_a_) 20 Lect.
                <lb/>
              VII.</note>
            ci _(_puta FH_)_ talis, ut ſint è projectis à D a rectis FG, FH inter-
              <lb/>
            ceptæ minores interceptis abipſis EB, EC, hoc eſt multo minores in-
              <lb/>
            terceptis à recta E A, curváque FX. </s>
            <s xml:id="echoid-s11121" xml:space="preserve">Unde ſequetur angulum AFX
              <lb/>
            rectilineo GF H majorem eſſe; </s>
            <s xml:id="echoid-s11122" xml:space="preserve">ac idcircò rectam AF non conting ere
              <lb/>
            curvam FX, adverſus _Hypotheſin_.</s>
            <s xml:id="echoid-s11123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11124" xml:space="preserve">Hæ præcedentes duæ Concluſiones veræ ſunt, & </s>
            <s xml:id="echoid-s11125" xml:space="preserve">ſimili ratione de-
              <lb/>
            monſtrantur, poſito interceptas IG, KL quamvis ad ſe perpetim ha-
              <lb/>
            bere proportionem eandem. </s>
            <s xml:id="echoid-s11126" xml:space="preserve">Parco verbis.</s>
            <s xml:id="echoid-s11127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11128" xml:space="preserve">Propoſuimus hæc, ut ſequentium nonnulla à ſcrupulis munian-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s11129" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11130" xml:space="preserve">V. </s>
            <s xml:id="echoid-s11131" xml:space="preserve">Sit recta VEI, duæque curvæ YFN, ZGO ſic ad ſe relatæ,
              <lb/>
            ut ductâ utcunque rectâ EFG ad poſitione datam AB parallelâ, ha-
              <lb/>
            beant interceptæ E G, EF ſemper eandem rationem inter ſe; </s>
            <s xml:id="echoid-s11132" xml:space="preserve">tangat
              <lb/>
            autem recta TG curvarum unam ZGO in G _(_cum recta VE con-
              <lb/>
            veniens in T _)_ ducta TF alteram YFN quoque continget.</s>
            <s xml:id="echoid-s11133" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11134" xml:space="preserve">Nam utcun que ducatur recta IL (lineas expoſitas ut vides interſe-
              <lb/>
            cans ) Eſtigitur IL. </s>
            <s xml:id="echoid-s11135" xml:space="preserve">IN &</s>
            <s xml:id="echoid-s11136" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11137" xml:space="preserve">IO. </s>
            <s xml:id="echoid-s11138" xml:space="preserve">IN :</s>
            <s xml:id="echoid-s11139" xml:space="preserve">: EG. </s>
            <s xml:id="echoid-s11140" xml:space="preserve">EF :</s>
            <s xml:id="echoid-s11141" xml:space="preserve">: IL. </s>
            <s xml:id="echoid-s11142" xml:space="preserve">IK.</s>
            <s xml:id="echoid-s11143" xml:space="preserve">
              <note position="left" xlink:label="note-0242-03" xlink:href="note-0242-03a" xml:space="preserve">(_a_) _Hyp_</note>
            Igitur IN &</s>
            <s xml:id="echoid-s11144" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11145" xml:space="preserve">IK. </s>
            <s xml:id="echoid-s11146" xml:space="preserve">ergò punctum K extra curvam YFN jacet; </s>
            <s xml:id="echoid-s11147" xml:space="preserve">totáq;
              <lb/>
            </s>
            <s xml:id="echoid-s11148" xml:space="preserve">recta TF.</s>
            <s xml:id="echoid-s11149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11150" xml:space="preserve">Aliter. </s>
            <s xml:id="echoid-s11151" xml:space="preserve">Eſt IL. </s>
            <s xml:id="echoid-s11152" xml:space="preserve">IK :</s>
            <s xml:id="echoid-s11153" xml:space="preserve">: (IO. </s>
            <s xml:id="echoid-s11154" xml:space="preserve">IN :</s>
            <s xml:id="echoid-s11155" xml:space="preserve">: IK-IO. </s>
            <s xml:id="echoid-s11156" xml:space="preserve">IK-IN :</s>
            <s xml:id="echoid-s11157" xml:space="preserve">:)
              <lb/>
            OL. </s>
            <s xml:id="echoid-s11158" xml:space="preserve">NK, ergò cùm lineæ GL, GO ſe tangant, etiam
              <note position="left" xlink:label="note-0242-04" xlink:href="note-0242-04a" xml:space="preserve">(_b_)_Hyp_.</note>
            neæ F N, FK ſeſe tangent.</s>
            <s xml:id="echoid-s11159" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">_(c)Schol. 4. bu-_
            <lb/>
          _jus._</note>
          <p>
            <s xml:id="echoid-s11160" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s11161" xml:space="preserve">Etiam ſi tres curvæ XEM, YFN, ZGO itâ referantur ad ſe,
              <lb/>
              <note position="left" xlink:label="note-0242-06" xlink:href="note-0242-06a" xml:space="preserve">Fig. 80.</note>
            ut ductâ utcunque rectâ EFG ad poſitione datam parallelâ, ſint ſem-
              <lb/>
            per EG, EF in eadem ra ione, concurrant autem duarum XEM,
              <lb/>
            ZGO tangentes ET, GT in T; </s>
            <s xml:id="echoid-s11162" xml:space="preserve">adjuncta TF curvam YFN tan-
              <lb/>
            get.</s>
            <s xml:id="echoid-s11163" xml:space="preserve"/>
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