Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

[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.

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[4.] LONDINI, Typis _Guilielmi Godbid_, & proſtant venales apud _Robertum Scott_, in vico Little-Britain. 1674.

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[5.] SPECTATISSIMIS VIRIS Roberto Raworth & Thomæ Buck ARMIGERIS;

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[6.] Iſaac Barrow

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[7.] Epistola ad LECTOREM.

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[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.

6143 jam aliquoties inſinuatâ; ſcilicet ut ſit AB. YB : : √ Iq -Rq. I;
& deſignetur quilibet refractus KN; tum continuetur ratio YB ad
BN; ut ſit ad has proportione quarta BP; & per punctum P du-
11Fig. 57, 58. catur recta PZ ad AB parallela; refracto KN occurrens in Z; dico
nullum alium refractum per Z traſire. Nam ſi ſieri poteſt tranſeat
alius ZR; & per Y traducantur rectæ NYG, RYS ; è præmon-
ſtratis apparet quòd ſit RS = NG. item è prædictis manifeſtum 2212. Lect. 4. quò RS & gt; N G. quæ repugnant.

339 hujus Lect.

XVI. Non diſpari ratione, quoad caſum ſecundum, deſignetur quilibet
refractus KN; & fiat KB . GB : : √ Rq - Iq. R; tum adnexâ
GN, ad ipſas NG, GB ſumatur tertia proportionalis V; & ſiat
NG. V : : BN. NP; & per punctum P ducatur PY ad BA pa-
rallela refractum NK decuſſans in Z; dico nullum alium refractum
per ipſum Z meare. Nam, ſi neges, tranſeat alius ZR; & per
Y trajiciatur RY S; & quoniam ZP . YP : : KB. GB : : √ Rq
- Iq. R. ex * antedictis apparet fore RS = NG. quinetiam ob
44* 14. Lect.4. NGq . GBq : : NG. V : : BN . NP . erit dividendo NBq.
GBq : : BP . NP . hoc eſt NPq. PYq : : BP . NP; inde facile
deducitur eſſe BP quartam proportionalem in ratione YP ad PN ;
conſequentérque fore RS minimâ NG majorem . quod adver-
ſatur oſtenſis . itaque potiùs per Z nullus alius tranſit reſractus:
Q. E. D.

XV I. Prætereà, ſi refractum NKZ interſecet alius quilibet M I,
ad rectiorem pertinens incidentem (hoc eſt ut incidentiæ punctum M
inter B, & N jaceat) interſectio X ſolitario puncto Z citerior erit
(ſeu perpendiculari KB propinquior) . Nam ab X demittatur per-
55Fig. 59, 60. pendicularis XQ. ipſam NG ſecans in γ ; & (in primo caſu) per
M, Y traducatur recta MY H. ergò MH = Nγ. quare minima earum
quæ per Y angulo XQF interſeri poſſuntinter puncta M, N cadet
(utì nuper admonitum, & adſtructum). puta ad φ. ergò quum ſit
BP quarta proportionalis in ratione YB ad BN ; & BQ quarta
proportionalis in ratione YB ad B φ, erit PB & gt; QB; adeóque
recta XQ rectis ZP, KB interjacet : Q. E . D.

In ſecundo caſu, per γ trajiciatur recta M γ H. ergò cùm ſit
Q X. Q γ : : PZ. PY : : √ Rq - Iq. R. erit HM = GN. ergò
minima per γ ducibilium angulo AB F intercipienda punctis M, N
intercider; puta ad φ. quare QB quarta proportionalis erit in ratione
γ Qad Q φ; & eſt γ Q. Qφ & gt; (γ Q. QN.) : : YP. PN . &

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