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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[31.] Lect. IV.
Page: 222 (29)
[32.] Lect. VII.
Page: 249 (56)
[33.] Lect. VIII.
Page: 256 (63)
[34.] Lect. IX.
Page: 263 (70)
[35.] Lect. X.
Page: 268 (75)
[36.] Exemp. I.
Page: 274 (81)
[37.] _Exemp_. II.
Page: 275 (82)
[38.] _Exemp_. III
Page: 275 (82)
[39.] Exemp. IV.
Page: 276 (83)
[40.] Eæemp. V.
Page: 277 (84)
[41.] Lect. XI.
Page: 278 (85)
[42.] APPENDICUL A.
Page: 287 (94)
[43.] Lect. XII.
Page: 298 (105)
[44.] APPENDICULA 1.
Page: 303 (110)
[45.] Præparatio Communis.
Page: 303 (110)
[46.] APPENDICULA 2.
Page: 308 (115)
[47.] Conicorum Superſicies dimetiendi Metbodus.
Page: 310 (117)
[48.] Exemplum.
Page: 311 (118)
[49.] Prop. 1.
Page: 312 (119)
[50.] Prop. 2.
Page: 312 (119)
[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)
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            <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"/>
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          <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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            <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"/>
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          <p>
            <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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            <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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