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

Table of contents

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[51.] Prop. 3.
Page: 313 (120)
[52.] Prop. 4.
Page: 313 (120)
[53.] APPENDICULA 3.
Page: 314 (121)
[54.] Problema I.
Page: 314 (121)
[55.] Exemp. I.
Page: 314 (121)
[56.] Exemp. II.
Page: 315 (122)
[57.] Probl. II.
Page: 315 (122)
[58.] Exemp. I.
Page: 315 (122)
[59.] _Exemp_. II.
Page: 316 (123)
[60.] _Probl_. III.
Page: 316 (123)
[61.] _Probl_. IV.
Page: 317 (124)
[62.] _Probl_. V.
Page: 317 (124)
[63.] _Probl_. VI.
Page: 318 (125)
[64.] _Probl_. VII
Page: 318 (125)
[65.] _Probl_. VIII.
Page: 319 (126)
[66.] _Probl_. IX.
Page: 319 (126)
[67.] _Probl_. X.
Page: 320 (127)
[68.] _Corol. Theor_. I.
Page: 321 (128)
[69.] _Theor_. II.
Page: 321 (128)
[70.] _Theor_. III.
Page: 321 (128)
[71.] _Theor_. IV.
Page: 321 (128)
[72.] _Theor_. V.
Page: 322 (129)
[73.] _Theor_. VI.
Page: 323 (130)
[74.] _Theor_. VII.
Page: 323 (130)
[75.] Lect. XIII.
Page: 324 (131)
[76.] Æquationum Series prima.
Page: 324 (131)
[77.] _Notetur autem_,
Page: 325 (132)
[78.] Series ſecunda.
Page: 325 (132)
[79.] Not.
Page: 326 (133)
[80.] Series tertia.
Page: 326 (133)
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            <s xml:id="echoid-s2002" xml:space="preserve">
              <pb o="38" file="0056" n="56" rhead=""/>
            provcniant infinitè diſſito) circa radios parallelos obſervatiunculam,
              <lb/>
            compendio ſervientem, etiam hîc tempeſtivum fuerit adjungere; </s>
            <s xml:id="echoid-s2003" xml:space="preserve">pa-
              <lb/>
            rallelorum nempe Convexis incidentium partibus radiorum inflexi,
              <lb/>
            quoad poſitionis directionem, iidem erunt cum inflexis ipſorum con-
              <lb/>
            cavis partibus incidentium; </s>
            <s xml:id="echoid-s2004" xml:space="preserve">modò tranſpoſita concipiantur media.
              <lb/>
            </s>
            <s xml:id="echoid-s2005" xml:space="preserve">Quare parallelorum radiationes examinando nihil erit opus convexas
              <lb/>
            partes à concavis diſtinguere; </s>
            <s xml:id="echoid-s2006" xml:space="preserve">ſeu exinde caſus multiplicare. </s>
            <s xml:id="echoid-s2007" xml:space="preserve">Res è
              <lb/>
            poſthac dicendis clarior evadet. </s>
            <s xml:id="echoid-s2008" xml:space="preserve">His admonitis, de tabula jam manum ; </s>
            <s xml:id="echoid-s2009" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s2010" xml:space="preserve">quam propoſuimus inſtituendam proximè diſquiſitionem ſequenti
              <lb/>
            reſervamus.</s>
            <s xml:id="echoid-s2011" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div58" type="section" level="1" n="14">
          <head xml:id="echoid-head17" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          V.</head>
          <p>
            <s xml:id="echoid-s2012" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">EO jam provecti ſumus, ut radiantis (à ſenſibiliter finita diſtan-
              <lb/>
            tia) puncti locum apparentem inveſtigemus, illum nempe qui
              <lb/>
            reſultat, è peracta ad planam ſuperficiem refractione; </s>
            <s xml:id="echoid-s2014" xml:space="preserve">nec non reſpe-
              <lb/>
            ctu viſus extra radiationis axem conſtituti. </s>
            <s xml:id="echoid-s2015" xml:space="preserve">Quorſum imprimis ſpectat,
              <lb/>
            ut rectam determinemus lineam, in qua locus ille verſatur; </s>
            <s xml:id="echoid-s2016" xml:space="preserve">tum ut
              <lb/>
            ſingulare deſignemus in illa recta punctum, circa quod exquiſitè con-
              <lb/>
            ſiſtit. </s>
            <s xml:id="echoid-s2017" xml:space="preserve">Utriuſque quæſiti gratiâ conficiendum, (imo penitius excutien-
              <lb/>
            endum) venit hujuſmodi _Problema_:</s>
            <s xml:id="echoid-s2018" xml:space="preserve"/>
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            <s xml:id="echoid-s2019" xml:space="preserve">_II_. </s>
            <s xml:id="echoid-s2020" xml:space="preserve">Dato puncto A, in poſitione datam rectam EF radiante, deſig-
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            nandus eſt incidens, qui per alterum tranſeat datum punctum.</s>
            <s xml:id="echoid-s2021" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2022" xml:space="preserve">III. </s>
            <s xml:id="echoid-s2023" xml:space="preserve">Si datum punctum alterum (puta jam K) in recta AB exiſtat,
              <lb/>
              <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">Fig. 48, 49.</note>
            ad refringentem EF perpendiculari Problema planum erit, ac ità faci-
              <lb/>
            lè conficietur. </s>
            <s xml:id="echoid-s2024" xml:space="preserve">In primo caſu (quando ſcilicet I &</s>
            <s xml:id="echoid-s2025" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2026" xml:space="preserve">R) fiat AB. </s>
            <s xml:id="echoid-s2027" xml:space="preserve">YB
              <lb/>
            :</s>
            <s xml:id="echoid-s2028" xml:space="preserve">: √ Iq - Rq. </s>
            <s xml:id="echoid-s2029" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2030" xml:space="preserve">itemque fiat KB. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">T :</s>
            <s xml:id="echoid-s2032" xml:space="preserve">: √ Iq - Rq. </s>
            <s xml:id="echoid-s2033" xml:space="preserve">R; </s>
            <s xml:id="echoid-s2034" xml:space="preserve">tum cen-
              <lb/>
            tro Y intervallo T deſcriptus circulus ipſam EF ſecet in N ; </s>
            <s xml:id="echoid-s2035" xml:space="preserve">conne-
              <lb/>
            ctantunrque AN, KN; </s>
            <s xml:id="echoid-s2036" xml:space="preserve">erit KN _a_ ipſius AN refractus.</s>
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            <s xml:id="echoid-s2038" xml:space="preserve">Itidem in ſecundo caſu (cùm I &</s>
            <s xml:id="echoid-s2039" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s2040" xml:space="preserve">R) fiat KB. </s>
            <s xml:id="echoid-s2041" xml:space="preserve">YB :</s>
            <s xml:id="echoid-s2042" xml:space="preserve">: √ Rq. </s>
            <s xml:id="echoid-s2043" xml:space="preserve">-
              <lb/>
            Iq. </s>
            <s xml:id="echoid-s2044" xml:space="preserve">R. </s>
            <s xml:id="echoid-s2045" xml:space="preserve">AB. </s>
            <s xml:id="echoid-s2046" xml:space="preserve">T :</s>
            <s xml:id="echoid-s2047" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2049" xml:space="preserve">centroque Y intervallo T deſcri-
              <lb/>
            batur circulus ipſi EF occurrens in N ; </s>
            <s xml:id="echoid-s2050" xml:space="preserve">critque rurſus KN _a_ </s>
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