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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[Item 1.]
[2.] Imprimatur,
[3.] LECTIONES _OPTICÆ & GEOMETRICÆ:_ In quibus PHÆNOMENωN OPTICORUM Genuinæ _Rationes_ inveſtigantur, ac exponuntur: ET _Generalia_ Curvarum Linearum _Symptomata declarantur_. Auctore Isaaco Barrow, Collegii _S S. Trinitatis_ in Academia _Cantab._ Præfecto, Et _SOCIETATIS REGIÆ_ Sodale.
[4.] LONDINI, Typis _Guilielmi Godbid_, & proſtant venales apud _Robertum Scott_, in vico Little-Britain. 1674.
[5.] SPECTATISSIMIS VIRIS Roberto Raworth & Thomæ Buck ARMIGERIS;
[6.] Iſaac Barrow
[7.] Epistola ad LECTOREM.
[8.] Epiſtola; in qua Operis hujus Argumen-tum, & ſcopus brevitèr exponuntur.
[9.] Lect. I.
[10.] Lect. II.
[11.] Lect. III.
[12.] _Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP. 2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.
[13.] Lect. IV.
[14.] Lect.V.
[15.] Lect. VI.
[16.] Lect. VI I.
[17.] Lect. VIII.
[18.] Lect. IX.
[19.] Lect. X.
[20.] Lect. XIV.
[21.] Lect. XV.
[22.] APPENDICVLA.
[23.] Lect. XVI.
[24.] Lect. XVII.
[25.] Lect. XVIII.
[26.] ERRATA.
[27.] Benevolo Lectori.
[28.] Lectio I.
[29.] Lect. II.
[30.] Lect. III.
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          <head xml:id="echoid-head18" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . VI.</head>
          <p>
            <s xml:id="echoid-s2599" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2600" xml:space="preserve">ABſolutis iis, quæ radiis accidunt ad planam ſuperficiem in-
              <lb/>
            flexis (obſervatu quæ videbantur non indigna, cúmque: </s>
            <s xml:id="echoid-s2601" xml:space="preserve">prin-
              <lb/>
            cipiis noſtris cohærentia; </s>
            <s xml:id="echoid-s2602" xml:space="preserve">quæ denuò viam ſternebant, aut metho-
              <lb/>
            dum aperiebant ſequentibus) ad curvas jam gradum promovemus;
              <lb/>
            </s>
            <s xml:id="echoid-s2603" xml:space="preserve">circa quas equidem cogitâram communia quædam delibare; </s>
            <s xml:id="echoid-s2604" xml:space="preserve">verùm
              <lb/>
            excuſſà re, tam exilem illam & </s>
            <s xml:id="echoid-s2605" xml:space="preserve">abſtractam deprehendo, ſatius ut
              <lb/>
            exiſtimem actutùm ad particularia deſcendere. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">curvarum utique prin-
              <lb/>
            cipem, & </s>
            <s xml:id="echoid-s2607" xml:space="preserve">ad praxes Opticas longè paratiſſimam, Superficiem Sphæ-
              <lb/>
            ricam aggrediar è veſtigio. </s>
            <s xml:id="echoid-s2608" xml:space="preserve">pro qua tamen, ob cauſas pridem aſſigna-
              <lb/>
            tas, circulos ſubrogabo per oculi Sphæræque centra, pérque ſingula
              <lb/>
            radiantia puncta trajectos. </s>
            <s xml:id="echoid-s2609" xml:space="preserve">& </s>
            <s xml:id="echoid-s2610" xml:space="preserve">quoad hos _Catoptrica_ primo, _D@op-_
              <lb/>
            _trica_ poſtmodum exequemur. </s>
            <s xml:id="echoid-s2611" xml:space="preserve">Ad illa.</s>
            <s xml:id="echoid-s2612" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2613" xml:space="preserve">II. </s>
            <s xml:id="echoid-s2614" xml:space="preserve">Præſternemus autem _λημμdηον_ unum vel alterum; </s>
            <s xml:id="echoid-s2615" xml:space="preserve">hoc impri-
              <lb/>
            mìs: </s>
            <s xml:id="echoid-s2616" xml:space="preserve">Incidenti@m circulo radiorum obliquior eſt, qui magis à centro
              <lb/>
              <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">Fig. 62.</note>
            diſtat; </s>
            <s xml:id="echoid-s2617" xml:space="preserve">vel qui minorem arcum (ſubſemicircularem) ſubtendit. </s>
            <s xml:id="echoid-s2618" xml:space="preserve">ſci-
              <lb/>
            licet obliquiùs incidit recta QRS, quàm recta MNP. </s>
            <s xml:id="echoid-s2619" xml:space="preserve">Nam à
              <lb/>
            centro C ducantur CN, CP; </s>
            <s xml:id="echoid-s2620" xml:space="preserve">& </s>
            <s xml:id="echoid-s2621" xml:space="preserve">CR; </s>
            <s xml:id="echoid-s2622" xml:space="preserve">CS. </s>
            <s xml:id="echoid-s2623" xml:space="preserve">& </s>
            <s xml:id="echoid-s2624" xml:space="preserve">quoniam angulus
              <lb/>
            RCS angulo NCP (hypotheſi nimirum inſiſtendo) minor eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s2625" xml:space="preserve">pater reliquos CRS, CSR reliquos CN, P, CPN (cùm junctim,
              <lb/>
            tum ſingulum ſingulo) majores eſſe. </s>
            <s xml:id="echoid-s2626" xml:space="preserve">Cùm itaque Semidiametxi
              <lb/>
            CR, CN, circumferentiæ perpendiculares ſint; </s>
            <s xml:id="echoid-s2627" xml:space="preserve">omninò liquet pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s2628" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2629" xml:space="preserve">III. </s>
            <s xml:id="echoid-s2630" xml:space="preserve">Dato radio MN ad circulum incidenti congruum reflexum
              <lb/>
            reſignare.</s>
            <s xml:id="echoid-s2631" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 63.</note>
          <p>
            <s xml:id="echoid-s2632" xml:space="preserve">Variis modis huc facilè peragitur; </s>
            <s xml:id="echoid-s2633" xml:space="preserve">quorum nunc unum adhibere,
              <lb/>
            tunc alium ex uſu ſit. </s>
            <s xml:id="echoid-s2634" xml:space="preserve">nos unum aut alterum ex expeditoribus attinge-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s2635" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">Incidens MN protrahatur ut circulum denuò ſecet in P. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">;
              <lb/>
            </s>
            <s xml:id="echoid-s2638" xml:space="preserve">& </s>
            <s xml:id="echoid-s2639" xml:space="preserve">ſumatur arcus N Π = NP; </s>
            <s xml:id="echoid-s2640" xml:space="preserve">erit connexa Π NH ipſius MNP
              <lb/>
            reflexus. </s>
            <s xml:id="echoid-s2641" xml:space="preserve">nam à centro C connexâ CN, manifeſtum eſt </s>
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