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-s6766" xml:space="preserve">Si A cadat extra BC, fiat AB - {R/I} AC. </s>
            <s xml:id="echoid-s6767" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6768" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6769" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s6770" xml:space="preserve">ſin A
              <lb/>
              <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">Fig. 159.</note>
            cadat inter B, C; </s>
            <s xml:id="echoid-s6771" xml:space="preserve">fiat AB + {R/I} AC. </s>
            <s xml:id="echoid-s6772" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6773" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6774" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s6775" xml:space="preserve">deinde fac
              <lb/>
            {I/R} KZ - DZ. </s>
            <s xml:id="echoid-s6776" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6777" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">DY.</s>
            <s xml:id="echoid-s6779" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6780" xml:space="preserve">Coroll- Adintegram Sphæram converg.</s>
            <s xml:id="echoid-s6781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6782" xml:space="preserve">Si punctum A extra BC ponatur, fiat AB + {I-2R/I} AC :</s>
            <s xml:id="echoid-s6783" xml:space="preserve">: BC.
              <lb/>
            </s>
            <s xml:id="echoid-s6784" xml:space="preserve">CY. </s>
            <s xml:id="echoid-s6785" xml:space="preserve">ſin A cadat inter B, & </s>
            <s xml:id="echoid-s6786" xml:space="preserve">C; </s>
            <s xml:id="echoid-s6787" xml:space="preserve">fiat AB+{2R-I/I} AC. </s>
            <s xml:id="echoid-s6788" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s6789" xml:space="preserve">:
              <lb/>
            BC. </s>
            <s xml:id="echoid-s6790" xml:space="preserve">CY; </s>
            <s xml:id="echoid-s6791" xml:space="preserve">& </s>
            <s xml:id="echoid-s6792" xml:space="preserve">cape CY ad partes centri verſus A.</s>
            <s xml:id="echoid-s6793" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6794" xml:space="preserve">_XV._ </s>
            <s xml:id="echoid-s6795" xml:space="preserve">Ad lentera convexo-concavam diverg.</s>
            <s xml:id="echoid-s6796" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 160,
            <lb/>
          161.</note>
          <p style="it">
            <s xml:id="echoid-s6797" xml:space="preserve">_XVI._ </s>
            <s xml:id="echoid-s6798" xml:space="preserve">Ad lentem concavo convexam converg.</s>
            <s xml:id="echoid-s6799" xml:space="preserve"/>
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            <s xml:id="echoid-s6800" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6801" xml:space="preserve">Si AB &</s>
            <s xml:id="echoid-s6802" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6803" xml:space="preserve">{R/I} AC; </s>
            <s xml:id="echoid-s6804" xml:space="preserve">puncta Z, & </s>
            <s xml:id="echoid-s6805" xml:space="preserve">Y verſus A cadunt, facto
              <lb/>
            {R/I} AC - AB. </s>
            <s xml:id="echoid-s6806" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6807" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6808" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s6809" xml:space="preserve">& </s>
            <s xml:id="echoid-s6810" xml:space="preserve">{I/R} KZ - DZ. </s>
            <s xml:id="echoid-s6811" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6812" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6813" xml:space="preserve">DY.</s>
            <s xml:id="echoid-s6814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6815" xml:space="preserve">2.</s>
            <s xml:id="echoid-s6816" xml:space="preserve">Si AB = {R/I} AC; </s>
            <s xml:id="echoid-s6817" xml:space="preserve">fac I - R. </s>
            <s xml:id="echoid-s6818" xml:space="preserve">R :</s>
            <s xml:id="echoid-s6819" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6820" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6821" xml:space="preserve">& </s>
            <s xml:id="echoid-s6822" xml:space="preserve">cape DY
              <lb/>
            verſus A.</s>
            <s xml:id="echoid-s6823" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6824" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6825" xml:space="preserve">Si AB &</s>
            <s xml:id="echoid-s6826" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6827" xml:space="preserve">{R/I} AC; </s>
            <s xml:id="echoid-s6828" xml:space="preserve">fac AB - {R/I} AC. </s>
            <s xml:id="echoid-s6829" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s6830" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6831" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s6832" xml:space="preserve">& </s>
            <s xml:id="echoid-s6833" xml:space="preserve">
              <lb/>
            cape BZ adverſus A. </s>
            <s xml:id="echoid-s6834" xml:space="preserve">Jam quum Z cadit extra DK, tum primò ſi
              <lb/>
            {I/R} KZ &</s>
            <s xml:id="echoid-s6835" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6836" xml:space="preserve">DZ, fac {I/R} KZ - DZ. </s>
            <s xml:id="echoid-s6837" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6838" xml:space="preserve">: DK. </s>
            <s xml:id="echoid-s6839" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6840" xml:space="preserve">& </s>
            <s xml:id="echoid-s6841" xml:space="preserve">cape DY
              <lb/>
            verſus A.</s>
            <s xml:id="echoid-s6842" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s6843" xml:space="preserve">4.</s>
            <s xml:id="echoid-s6844" xml:space="preserve">Secundò, ſi {I/R} KZ = DZ, imago infinitè diſtabit.</s>
            <s xml:id="echoid-s6845" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6846" xml:space="preserve">5. </s>
            <s xml:id="echoid-s6847" xml:space="preserve">Tertiò, ſi {I/R} KZ &</s>
            <s xml:id="echoid-s6848" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6849" xml:space="preserve">DZ, fac DZ - {I/R} KZ. </s>
            <s xml:id="echoid-s6850" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6851" xml:space="preserve">: DK.
              <lb/>
            </s>
            <s xml:id="echoid-s6852" xml:space="preserve">DY, & </s>
            <s xml:id="echoid-s6853" xml:space="preserve">ſume DY adverſus A.</s>
            <s xml:id="echoid-s6854" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6855" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6856" xml:space="preserve">Sed quando Z inter D, & </s>
            <s xml:id="echoid-s6857" xml:space="preserve">K cadit; </s>
            <s xml:id="echoid-s6858" xml:space="preserve">fiat DZ + {I/R} KZ. </s>
            <s xml:id="echoid-s6859" xml:space="preserve">DZ :</s>
            <s xml:id="echoid-s6860" xml:space="preserve">:
              <lb/>
            DK. </s>
            <s xml:id="echoid-s6861" xml:space="preserve">DY; </s>
            <s xml:id="echoid-s6862" xml:space="preserve">& </s>
            <s xml:id="echoid-s6863" xml:space="preserve">ſumatur DY adverſus A.</s>
            <s xml:id="echoid-s6864" xml:space="preserve"/>
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