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-s7877" xml:space="preserve">
              <pb o="120" file="0138" n="138" rhead=""/>
            hoc eſt AX x CB = 2 AC x CZ; </s>
            <s xml:id="echoid-s7878" xml:space="preserve">vel 2 AX x CE = 2 AC
              <lb/>
            x CZ; </s>
            <s xml:id="echoid-s7879" xml:space="preserve">unde AX. </s>
            <s xml:id="echoid-s7880" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s7881" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s7882" xml:space="preserve">CE; </s>
            <s xml:id="echoid-s7883" xml:space="preserve">hoc eſt XH. </s>
            <s xml:id="echoid-s7884" xml:space="preserve">CE :</s>
            <s xml:id="echoid-s7885" xml:space="preserve">: CZ.
              <lb/>
            </s>
            <s xml:id="echoid-s7886" xml:space="preserve">CE. </s>
            <s xml:id="echoid-s7887" xml:space="preserve">quapropter eſt XH = CZ : </s>
            <s xml:id="echoid-s7888" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s7889" xml:space="preserve">D.</s>
            <s xml:id="echoid-s7890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7891" xml:space="preserve">Quoad radiationem ad partes concavas, planè ſimilis eſt diſcurſus.
              <lb/>
            </s>
            <s xml:id="echoid-s7892" xml:space="preserve">examinetis ipſi, peto.</s>
            <s xml:id="echoid-s7893" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7894" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s7895" xml:space="preserve">Exhinc evidenter liquet, ſi fuerit CA &</s>
            <s xml:id="echoid-s7896" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7897" xml:space="preserve">CE; </s>
            <s xml:id="echoid-s7898" xml:space="preserve">quòd om-
              <lb/>
              <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">Fig. 193,
                <lb/>
              194, 195.</note>
            nes punctorum F limites, ſeu foci (quales Z) ad ellipſin exiſtunt;
              <lb/>
            </s>
            <s xml:id="echoid-s7899" xml:space="preserve">cujus _focus_ C, & </s>
            <s xml:id="echoid-s7900" xml:space="preserve">cujus _axis_ TV è præmiſſis, non uno modo, deter-
              <lb/>
            minatur. </s>
            <s xml:id="echoid-s7901" xml:space="preserve">item ſi CA = CE, limites Z ad parabolam conſiſtent
              <lb/>
            cujus _focus_ C, _axis_ CT = {1/2} CE, _vertex_ T. </s>
            <s xml:id="echoid-s7902" xml:space="preserve">denuò, ſi CA &</s>
            <s xml:id="echoid-s7903" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7904" xml:space="preserve">CB,
              <lb/>
            puncta Z ad _h@perbolas eſſe conſtat_, quarum itidem _focus_ C; </s>
            <s xml:id="echoid-s7905" xml:space="preserve">& </s>
            <s xml:id="echoid-s7906" xml:space="preserve">_axis_
              <lb/>
            TV facilè de modò (vel alibi) dictis reperitur; </s>
            <s xml:id="echoid-s7907" xml:space="preserve">cunctarum verò ſecti-
              <lb/>
            onum _Parameter_ ipſi CB æquatur.</s>
            <s xml:id="echoid-s7908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7909" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s7910" xml:space="preserve">Hinc in ſingulis reſpectivè caſibus, ejuſmodi _ſectiones co-_
              <lb/>
            _nicæ_ ſunt rectarum F α G abſolutæ imagines; </s>
            <s xml:id="echoid-s7911" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s7912" xml:space="preserve">eædem veræ
              <lb/>
            ſunt imagines ad oculum relatæ in ſpeculi centro conſtitutum; </s>
            <s xml:id="echoid-s7913" xml:space="preserve">ex re-
              <lb/>
            flectione ſcilicet ad concavas ſpeculi partes effectæ quæ ſolæ oculo
              <lb/>
            ſic poſito conſpicuæ ſunt.</s>
            <s xml:id="echoid-s7914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7915" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s7916" xml:space="preserve">Patet autem ſirecta F α G infinitè diſtet, quòd _ellipſis_ in _cir-_
              <lb/>
            _culum_ abit. </s>
            <s xml:id="echoid-s7917" xml:space="preserve">utì quoque ſi F α G per centrum tranſeat, quòd _hyperbolæ_
              <lb/>
            iſtæ in rectam lineam degenerant.</s>
            <s xml:id="echoid-s7918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7919" xml:space="preserve">X. </s>
            <s xml:id="echoid-s7920" xml:space="preserve">Subnotetur etiam in caſu quum _imago fit hyperbolica_, quod
              <lb/>
            _hyperbolæ_ YTY pars YEEY, neque non tota ζ V ζ ad circuli partes
              <lb/>
            MBN pertinent; </s>
            <s xml:id="echoid-s7921" xml:space="preserve">(nempe ſi centro C per E deſcriptus circulus ipſam
              <lb/>
            FG interſecet punctis K, tota hyperbola ζ V ζ rectam interceptam KK
              <lb/>
            referet; </s>
            <s xml:id="echoid-s7922" xml:space="preserve">& </s>
            <s xml:id="echoid-s7923" xml:space="preserve">hyperbolicæ lineæ alterius pars ſuperior YEEY quod
              <lb/>
            reliquum eſt repræ ſentabit hinc indè protenſæ rectæ FG) pars autem
              <lb/>
            ETE ad partem concavam MDN ſpectat. </s>
            <s xml:id="echoid-s7924" xml:space="preserve">id quod ſuffecerit ad-
              <lb/>
            monitum.</s>
            <s xml:id="echoid-s7925" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7926" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s7927" xml:space="preserve">Et hæc quidem de rectæ FAG imaginibus abſolutis; </s>
            <s xml:id="echoid-s7928" xml:space="preserve">è qui-
              <lb/>
              <note position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">Fig. 196.</note>
            bus commodius de relatis judicum fiet. </s>
            <s xml:id="echoid-s7929" xml:space="preserve">ſit, inſtantiæ loco, oculus O,
              <lb/>
            ad quem (convexis è partibus) ab F, & </s>
            <s xml:id="echoid-s7930" xml:space="preserve">G reflectantur OMK,
              <lb/>
            ON L; </s>
            <s xml:id="echoid-s7931" xml:space="preserve">& </s>
            <s xml:id="echoid-s7932" xml:space="preserve">ſit ellipſis ZVYT abſoluta (qualem modò definivimus)
              <lb/>
            rectæ FAG imago; </s>
            <s xml:id="echoid-s7933" xml:space="preserve">quam ductæ FC, GC punctis Z, Y ſecent.
              <lb/>
            </s>
            <s xml:id="echoid-s7934" xml:space="preserve">itaque punctorum F, G imagines ad O relatæ (puta φ, &</s>
            <s xml:id="echoid-s7935" xml:space="preserve">γ) </s>
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