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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            unde Problematis conſtructio, ſeu puncti Z dererminatio habetur.</s>
            <s xml:id="echoid-s6291" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6292" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s6293" xml:space="preserve">Subnectam & </s>
            <s xml:id="echoid-s6294" xml:space="preserve">ab amico communicatam (aliâ methodo
              <lb/>
              <note position="left" xlink:label="note-0112-01" xlink:href="note-0112-01a" xml:space="preserve">Fig. 147.</note>
            repertam ab ipſo, concinneque demonſtratam) conſtructionem:
              <lb/>
            </s>
            <s xml:id="echoid-s6295" xml:space="preserve">Duc NR incidenti AN perpendicularem, & </s>
            <s xml:id="echoid-s6296" xml:space="preserve">ſecantem axin in R. </s>
            <s xml:id="echoid-s6297" xml:space="preserve">
              <lb/>
            Fac NP. </s>
            <s xml:id="echoid-s6298" xml:space="preserve">N π :</s>
            <s xml:id="echoid-s6299" xml:space="preserve">: NR. </s>
            <s xml:id="echoid-s6300" xml:space="preserve">T. </s>
            <s xml:id="echoid-s6301" xml:space="preserve">duc N Qrefracto NK perpendicularem,
              <lb/>
            & </s>
            <s xml:id="echoid-s6302" xml:space="preserve">æqualem ipſi T; </s>
            <s xml:id="echoid-s6303" xml:space="preserve">denique jungatur QC; </s>
            <s xml:id="echoid-s6304" xml:space="preserve">hæc producta ſecabit
              <lb/>
            NK in foco quæſito Z.</s>
            <s xml:id="echoid-s6305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6306" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s6307" xml:space="preserve">Hujuſmodi verò punctum Z eſſe locum ipſiſſimum ima-
              <lb/>
            ginis puncti A, oculo apparentis in ipſa N π conſtituto, ſæpiùs expo-
              <lb/>
            ſitæ rationes manifeſtant.</s>
            <s xml:id="echoid-s6308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6309" xml:space="preserve">XXVIII. </s>
            <s xml:id="echoid-s6310" xml:space="preserve">Attendenti porrò conſtabit, ſiquidem fuerit NG ad
              <note symbol="*" position="left" xlink:label="note-0112-02" xlink:href="note-0112-02a" xml:space="preserve">_In Num. 25._</note>
            ratio æqualitatis, quòd punctum Z infinito à puncto G, vel N inter-
              <lb/>
            vallo diſtabit; </s>
            <s xml:id="echoid-s6311" xml:space="preserve">ſeu proximi radio N π refracti ipſi N π paralleli erunt;
              <lb/>
            </s>
            <s xml:id="echoid-s6312" xml:space="preserve">ſin ratio NG ad M ſit majoris inæqualitatis, quòd punctum Z exiſtet
              <lb/>
            infra G, vel in NG antrorſum protracta; </s>
            <s xml:id="echoid-s6313" xml:space="preserve">verùm denuò ſi NG &</s>
            <s xml:id="echoid-s6314" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6315" xml:space="preserve">M,
              <lb/>
            quod punctum Z ſupra N, vel in NG retrò tractâ verſatur. </s>
            <s xml:id="echoid-s6316" xml:space="preserve">Hæc
              <lb/>
            ſuffecerit innuiſſe. </s>
            <s xml:id="echoid-s6317" xml:space="preserve">Hinc etiam poſticæ circuli partis illuminatæ quan-
              <lb/>
            titas utcunque poſſit determinari. </s>
            <s xml:id="echoid-s6318" xml:space="preserve">ſed ad locum Solidum res ſpectat,
              <lb/>
            ipsámque proinde miſſam facio.</s>
            <s xml:id="echoid-s6319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6320" xml:space="preserve">XXIX. </s>
            <s xml:id="echoid-s6321" xml:space="preserve">Inſeremus autem hîc _Phænomeni_ cujuſdam ſatìs obvii, quód-
              <lb/>
              <note position="left" xlink:label="note-0112-03" xlink:href="note-0112-03a" xml:space="preserve">Fig. 148.</note>
            que nonnullis forſan (_utpote communibus Opticæ decretis apparenter_
              <lb/>
            _adverſum)_ mirabile videatur, explicationem. </s>
            <s xml:id="echoid-s6322" xml:space="preserve">Sit lucidi puncti A
              <lb/>
            (modicè diſtantis, & </s>
            <s xml:id="echoid-s6323" xml:space="preserve">vividè radios ejaculantis) ad arcum circularem
              <lb/>
            MBN (ab axe A B biſectum) imago, ſeufocus Z; </s>
            <s xml:id="echoid-s6324" xml:space="preserve">& </s>
            <s xml:id="echoid-s6325" xml:space="preserve">per Z, ad ipſam
              <lb/>
            AZ perpendicularis traducta concipiatur linea XY. </s>
            <s xml:id="echoid-s6326" xml:space="preserve">porrò, deſu-
              <lb/>
            matur aliud punctum remotius E; </s>
            <s xml:id="echoid-s6327" xml:space="preserve">liquet ejus imaginem citra punctum
              <lb/>
            Z (centrum verſus) jacere; </s>
            <s xml:id="echoid-s6328" xml:space="preserve">ductis itaque rectis EM, EN, harum
              <lb/>
            refracti adhuc altiùs ſe interſecant, puta ad K; </s>
            <s xml:id="echoid-s6329" xml:space="preserve">productæque MK,
              <lb/>
            NK lineam XY ſecent punctis O, P. </s>
            <s xml:id="echoid-s6330" xml:space="preserve">quinetiam ulterius accipiatur
              <lb/>
            punctum F; </s>
            <s xml:id="echoid-s6331" xml:space="preserve">ductarúmque rectarum FM, FN refracti ſint ML, NL;
              <lb/>
            </s>
            <s xml:id="echoid-s6332" xml:space="preserve">lineæ XY occurrentes ad puncta R, S; </s>
            <s xml:id="echoid-s6333" xml:space="preserve">quibus peractis manifeſtum eſt
              <lb/>
            intervallum RS ipſo OP majus eſſe. </s>
            <s xml:id="echoid-s6334" xml:space="preserve">Hinc facilis habetur ratio, cur
              <lb/>
            punctum lucidum (velut _ardens lucerna,_ vel _Imago Solis_ ad _Speculum_
              <lb/>
            aut _lentem diaphanam_ effecta, (quin & </s>
            <s xml:id="echoid-s6335" xml:space="preserve">ſtellæ fixæ) quæ propter exi-
              <lb/>
            guitatem ſuam apparentem punctorum ad inſtar haberi poſſunt) quò
              <lb/>
            a diſtinctæ viſionis loco longiùs amovetur, eò (contra quàm in </s>
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