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

Table of Notes

< >
[Note]
Page: 135
[Note]
Page: 136
[Note]
Page: 137
[Note]
Page: 137
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 139
[Note]
Page: 140
[Note]
Page: 141
[Note]
Page: 141
[Note]
Page: 142
[Note]
Page: 143
[Note]
Page: 194
[Note]
Page: 197
[Note]
Page: 197
[Note]
Page: 199
[Note]
Page: 203
[Note]
Page: 204
[Note]
Page: 205
[Note]
Page: 207
[Note]
Page: 207
[Note]
Page: 207
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 209
[Note]
Page: 210
[Note]
Page: 211
[Note]
Page: 211
[Note]
Page: 212
< >
page |< < (122) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div206" type="section" level="1" n="25">
          <p>
            <s xml:id="echoid-s7989" xml:space="preserve">
              <pb o="122" file="0140" n="140" rhead=""/>
            CZ. </s>
            <s xml:id="echoid-s7990" xml:space="preserve">FC :</s>
            <s xml:id="echoid-s7991" xml:space="preserve">: CX. </s>
            <s xml:id="echoid-s7992" xml:space="preserve">CA; </s>
            <s xml:id="echoid-s7993" xml:space="preserve">adeóque CZ x CA = FC x CX). </s>
            <s xml:id="echoid-s7994" xml:space="preserve">qua-
              <lb/>
            propter (elidendo FC) eſt CM x CR + CZ x CR = CZ x
              <lb/>
            CA - CM x CX; </s>
            <s xml:id="echoid-s7995" xml:space="preserve">tranſponendóque CM x CR + CM x
              <lb/>
            CX = CZ x CA - CZ x CR. </s>
            <s xml:id="echoid-s7996" xml:space="preserve">hoc eſt CM x RX = CZ x
              <lb/>
            AR, quare (ad analogiſmum redigendo) eſt AR. </s>
            <s xml:id="echoid-s7997" xml:space="preserve">CM :</s>
            <s xml:id="echoid-s7998" xml:space="preserve">: RX.
              <lb/>
            </s>
            <s xml:id="echoid-s7999" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s8000" xml:space="preserve">hoc eſt CR. </s>
            <s xml:id="echoid-s8001" xml:space="preserve">CE :</s>
            <s xml:id="echoid-s8002" xml:space="preserve">: RX. </s>
            <s xml:id="echoid-s8003" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s8004" xml:space="preserve">hoc eſt RX. </s>
            <s xml:id="echoid-s8005" xml:space="preserve">XH :</s>
            <s xml:id="echoid-s8006" xml:space="preserve">: RX. </s>
            <s xml:id="echoid-s8007" xml:space="preserve">
              <lb/>
            CZ; </s>
            <s xml:id="echoid-s8008" xml:space="preserve">unde XH = CZ : </s>
            <s xml:id="echoid-s8009" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s8010" xml:space="preserve">D.</s>
            <s xml:id="echoid-s8011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8012" xml:space="preserve">II. </s>
            <s xml:id="echoid-s8013" xml:space="preserve">Exhinc (& </s>
            <s xml:id="echoid-s8014" xml:space="preserve">ex iis quæ circa _ſectiones conicas_ nuperrimè ſunt
              <lb/>
            oſtenſa) liquido conſectatur, ſi CR major fuerit quàm CE (vel
              <lb/>
            quod eódem recidit, AR major quam CB) quòd punctorum om-
              <lb/>
            nium F in recta FA G imagines abſolutæ (quales Z) ad _ellipſin_ con-
              <lb/>
            ſiftent, cujus _Focus_ C, cujúſque penitus determinandæ modum ſatìs
              <lb/>
            facilem tunc oſtendimus. </s>
            <s xml:id="echoid-s8015" xml:space="preserve">item ſi CR = CE, quòd imagines iſtæ ad
              <lb/>
            parabolam erunt; </s>
            <s xml:id="echoid-s8016" xml:space="preserve">& </s>
            <s xml:id="echoid-s8017" xml:space="preserve">denique, ſi CR &</s>
            <s xml:id="echoid-s8018" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s8019" xml:space="preserve">CE, quòd eædem in hy-
              <lb/>
            perbolis oppoſitis reperientur; </s>
            <s xml:id="echoid-s8020" xml:space="preserve">quarum etiam ſectionum focus com-
              <lb/>
            munis eſt punctum C, & </s>
            <s xml:id="echoid-s8021" xml:space="preserve">quarum axes deſignandi modum reliquáque
              <lb/>
            circa ipſas præſertim advertenda declaravimus. </s>
            <s xml:id="echoid-s8022" xml:space="preserve">(Nempe, ſi rectæ
              <lb/>
            CP cum ipſa CA ſemirectos conſtituant angulos; </s>
            <s xml:id="echoid-s8023" xml:space="preserve">& </s>
            <s xml:id="echoid-s8024" xml:space="preserve">hæ rectam RE
              <lb/>
            interſecent ad puncta S, indéque demittantur ad A@ perpendiculares
              <lb/>
            ST, SV, erunt T, V axis termini, rectáque CE ſemi-parameter erit)
              <lb/>
            unde patet totius rectæ FAG ad infinitum protenſæ abſolutam ima-
              <lb/>
            ginem (quin & </s>
            <s xml:id="echoid-s8025" xml:space="preserve">illam, quæ ad oculum in centro O poſitum refertur)
              <lb/>
            aliquam eſſe dictarum conicarum, pro ſuo peculiari ſitu hanc vel illam
              <lb/>
            reſpectivè.</s>
            <s xml:id="echoid-s8026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8027" xml:space="preserve">III. </s>
            <s xml:id="echoid-s8028" xml:space="preserve">Adnotari porrò debet in iſto caſu, _ſectionis ellipticæ_ (quinetiam
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">Fig. 198.</note>
            & </s>
            <s xml:id="echoid-s8029" xml:space="preserve">_parabolicæ_) TE Z partem anticam TE ad concavas circuli partes
              <lb/>
            LDL ſpectare; </s>
            <s xml:id="echoid-s8030" xml:space="preserve">ſicuti poſtica EY ad convexas MB N pertinet. </s>
            <s xml:id="echoid-s8031" xml:space="preserve">in
              <lb/>
            hoc autem altero tota _byperbola_ ZVZ, nec non _hyperbotæ_ ETE pars
              <lb/>
            (infra ECE) YEEY ad partem circuli convexam referri debent
              <lb/>
            (nempe ſi centro C, intervallo CE deſcriptus circulus rectam FG
              <lb/>
            ſecet punctis K, K; </s>
            <s xml:id="echoid-s8032" xml:space="preserve">hyperbola ZVZ rectam interceptam KK repræ-
              <lb/>
            ſentabit, ipſiúſque FG quod reliquum eſt hinc indè protenſum pars
              <lb/>
            YEEY referet) pars autem ſuperior ETE ad cavam circuli partem
              <lb/>
            LDL ſpectat.</s>
            <s xml:id="echoid-s8033" xml:space="preserve">‖ Semper autem (cúm hîc, tum ubique) intelligatur
              <lb/>
            ad utraſque propoſiti circuli partes ejuſdem generis refractionem effici,
              <lb/>
            ſeu ejuſdem ſpeciei medio radios incidere.</s>
            <s xml:id="echoid-s8034" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8035" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s8036" xml:space="preserve">Ex his obiter naturæ, quam in oculi figura conſtruenda </s>
          </p>
        </div>
      </text>
    </echo>
Impressum