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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          <p>
            <s xml:id="echoid-s493" xml:space="preserve">
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            ſpecularis; </s>
            <s xml:id="echoid-s494" xml:space="preserve">hæc utique circulum continget; </s>
            <s xml:id="echoid-s495" xml:space="preserve">(quia ſpeculi planum, ex
              <lb/>
            hypotheſi, non alibi præterquam ad B circulo occurrit, adeóque nec
              <lb/>
            rec
              <unsure/>
            ta G H) quare rectæ G H, O P ſunt parallelæ. </s>
            <s xml:id="echoid-s496" xml:space="preserve">Ergo P O eſt ad
              <lb/>
            ſpeculi planum parallela. </s>
            <s xml:id="echoid-s497" xml:space="preserve">Huic verò perpendicularia ſunt plana præ-
              <lb/>
            dicta cylindrum contingentia per M O, N P ducta; </s>
            <s xml:id="echoid-s498" xml:space="preserve">axi parallela.
              <lb/>
            </s>
            <s xml:id="echoid-s499" xml:space="preserve">Quapropter eadem ſpeculi plano recta erunt. </s>
            <s xml:id="echoid-s500" xml:space="preserve">Hinc, ut anteà ſi totus
              <lb/>
            radius habeatur inſtar rectæ lineæ, continget ejus reflectio velut in ſu-
              <lb/>
            perficie ad ſpeculum planum recta; </s>
            <s xml:id="echoid-s501" xml:space="preserve">quippe cùm ejus latitudo tota com-
              <lb/>
            prehendatur inter ejuſniodi duo plana; </s>
            <s xml:id="echoid-s502" xml:space="preserve">quæ proinde ſi nulla ſuppona-
              <lb/>
            tur, in unum illa coaleſcent. </s>
            <s xml:id="echoid-s503" xml:space="preserve">Accommodari poſſent hæc cuicunque
              <lb/>
            radii figuræ tali, qualem ſupra deſcripſimus, utcunque nonnulla de-
              <lb/>
            mutando; </s>
            <s xml:id="echoid-s504" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s505" xml:space="preserve">eadem pari ratione radiorum refractionibus adapten-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s506" xml:space="preserve">Atpluribus parco.</s>
            <s xml:id="echoid-s507" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div13" type="section" level="1" n="10">
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            <emph style="sc">Lect.</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s508" xml:space="preserve">1. </s>
            <s xml:id="echoid-s509" xml:space="preserve">V Iæ, quam nuper aperuimus, & </s>
            <s xml:id="echoid-s510" xml:space="preserve">aliquatenus ingreſſi ſumus,
              <lb/>
            inhærentes eò jam devenimus, ut nobis incumbat proximè
              <lb/>
            celebres illas hypotheſes (an Theoremata malitis appellare) radiorum
              <lb/>
            inflexorum itineri penitus determinando (imaginúmque proinde locis,
              <lb/>
            figuris, quantitatibus inveſtigandis, nec non apparentiarum quarum-
              <lb/>
            cunque cauſis explicandis) neceſſarias, experientiæ quidem bene con-
              <lb/>
            ſonas illas, etiam aliquo rationis ſuffragio communire; </s>
            <s xml:id="echoid-s511" xml:space="preserve">præſtratis
              <lb/>
            utique ſundamentis, ac ſuppoſitionibus inſiſtendo. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Cùm itaque lucis
              <lb/>
            radio corpus adſignatum ſit figurâ priſmaticum, aut cylindricum; </s>
            <s xml:id="echoid-s513" xml:space="preserve">Et
              <lb/>
            hoc quidem rectum (utpote præ reliquis ſimplex, & </s>
            <s xml:id="echoid-s514" xml:space="preserve">naturæ totas ſuas
              <lb/>
            in agendo vires exerenti præſertim conveniens;) </s>
            <s xml:id="echoid-s515" xml:space="preserve">cùm & </s>
            <s xml:id="echoid-s516" xml:space="preserve">exinde pro-
              <lb/>
            greſſus ejus eatenus fuerit definitus, ut intra ſuperficies duas planas in-
              <lb/>
            Hectenti medio perpendiculares includatur; </s>
            <s xml:id="echoid-s517" xml:space="preserve">quas quidem abhinc (quan-
              <lb/>
            do nullus tranſverſæ dimenſionis illius, vel intervalli ſuperficies iſtas
              <lb/>
            dirimentis ad rem noſtram, illam ſaltem quam nunc attingimus ſpe-
              <lb/>
            ctans effectus, aut uſus ſit) brevitatis & </s>
            <s xml:id="echoid-s518" xml:space="preserve">perſpicuitatis cauſâ, velut u-
              <lb/>
            nam habere poſſumus; </s>
            <s xml:id="echoid-s519" xml:space="preserve">adeóque jam radium ut duabus ſolummodò di-
              <lb/>
            menſionibus præditum, & </s>
            <s xml:id="echoid-s520" xml:space="preserve">ad inſtar Parallelogrammi cujuſdam rect-
              <lb/>
            anguli, in plano ad medii inflectentis ſuperficiem recto jacentis, con-
              <lb/>
            fiderantes, reliquam itineris quod perſequitur determinationem, </s>
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