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.

4426 GP _a_, HP δ ità diſponantur, ut latera PG, PH ſibi congruant (un-
de major angulus GP _a_ minorem HP δ comprehendet) tum centro P
per δ deſcribatur circulus E δ F ipſas PG, P _a_ ſecans punctis F, E; item
connexâ EH, centro H per δ tranſeat circulus HMN ipſas HP, HE
ſecans punctis N, M; denuò connexa E δ cum PG conveniat in L.
Eſtque jam ang. _a_ P δ. ang. δ PH: : ſector EP δ. ſector δ PF & gt;
triang. EP δ. triang. δ PL: : Eδ. δ L : : triang. EH δ. δ HL & gt;
ſector MH δ. ſector δ HN : : ang. EH δ. ang. δ HP. eſt igi-
tur ang. _a_ P δ. ang. δ PH & gt; ang. EH δ. ang. δ HP. ergóque
compoſitè ang. _a_ PG. ang. δ PH & gt; ang. EHP. ang. δ HP. per-
mutandóque ang. _a_ PG. ang. EHP & gt; ang. δ PH. ang. δ HP. eſt
autem HP. PE : : HP. P δ : : I. R : : GP. P _a_. adeoque EH ad
_a_ G parallela; vel ang. EHP = ang. _a_ GP. ergò erit ang. _a_ PG.
ang. _a_ GP & gt; ang. δ PH. ang. δ HP. hoc eſt ang. _a_ BG, _a_ BP
& gt; ang. δ BH. ang. δ BP. vel componendo ang. GBP. ang. _a_ BP
& gt; ang HBP. ang. δ BP. Quod erat demonſtrandum.

_Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP.
2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.

Opportunum eſt hoc Theorema conciliandis cum experientia pro-
poſitis refractionum legibus. Ut demirari ſubeat nuperrimum Opticæ
ſcriptorem, virum alioqui diffuſè doctum, hujuſmodi ratiocinio leges
iſtas impugnàſſe: “In majoribus tamen angulis inclinationis (Ipſiſ-
"ſima ſunt ejus verba) falſum eſſe conſtat (principium nempe no-
"ſtrum;) in his enim angulus refractionis major eſt ſubtriplo an-
"guli inclinationis; quod mihi aliiſque ex luculentis experimentis
"compertum eſt. Hæc, inquam, ille ταντοεπ@. Quaſi verò dixiſſet;
numeri 6 & 4 ſimul accepti non conficiunt 10, quia numerum effici-
unt majorem quam 8. planè ſimilis eſt diſcurſus; non ovum ovo ſi-
milius. Nam in refractionibus ex. gr. ad vitrum factis ſi ponatur ad
quamvis inclinationem (puta graduum 15.) quòd ſit angulus refra-
ctionis ſubtriplus anguli inclinationis (quem ille vocat, incidentiæ nos
angulum appellare ſolemus) neceſſariò, ſicuti modò demonſtratum
eſt, è principio noſtro conſequetur, quòd ad aliam quamcunque ma-
jorem inclinationem refractionis angulus major erit ſubtriplo anguli
inclinationis; nominatim acceptâ graduum 30 inclinatione juxta di-
ctum principium inſtitutus calculus angulum præbebit reſractum
19. 24'; angulúmque proinde refractionis 10. 36', qui 30 graduum
trientem exuperat. Quare cùm Clariſſimus vir Hypotheſin hanc

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