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

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11092

XXI. Imò univerſim ſi radii quivis AF, _a_ φ ad circulum refrin-
11Fig. 144. gentem æqualiter inclinentur, híſque conveniant refracti FL, φ λ,
erit C λ & gt; CL. id quod hoc modo non inelegantèr oſtenditur. Du-
catur recta BX cum BC angulum efficiens parem angulo refracto
ad poſitam inclinationem pertinenti; perque puncta F, φ; & cen-
trum C tranſeuntes rectæ ipſi BX occurant punctis P, π. tum quo-
niam triangula FC L, BCPæquiangula ſunt (angulus enim CB P
angulo CFLex conſtructione par eſt, & ang. BCPverticali ſuo
FCLæquatur) nec non latus CB lateri CF æquatur, erit CP =
C L. Simili planè diſcurſu eſt C π = C λ. Porrò quia C φ ad
C _a_ (hoc eſt Sinus anguli C _a_ φ ad Sinum anguli C φ _a_) majorem
rationem habet, quàm CF ad CA (hoc eſt quàm Sinus anguli CA F
ad Sinum anguli AF C, vel æ qualis anguli C φ α) liquet angulum
C _a_ φ majorem eſſe angulo CA F, adeóque reliquum _a_ C φ minorem
eſſe reliquo AC F; vel angulum PCBangulo π CB. unde liquet
eſſe C π majorem quàm CP; hoc eſt C λ majorem eſſe quàm CL:
Quod E. D.

_Coroll._ Vides arcum BF majorem eſſe arcu B φ.

Notes etiam omnes ejuſdem inclinationis refractos ope ductæ rectæ
BX promptiſſimè deſignari. ſed hæc an πρργδ fuerint neſcio.

XXII. _Subjiciam & hoc Theorema:_ Convexo denſiori inciden-
22Fig. 145. tiùm radiorum AM, AN (quorum AN ſit obliquior) refracti
MK, NL axem ad eaſdem partes, directè pergentes, ſecent, iſte ad K,
hic ad L; dico fore CK majorem quàm CL.

Nam connexis CN, KN; & ductâ LH ad KN parallelâ quo-
niam, è præmiſſis, eſt CK. CR : : MK. MA. & CR. CL : :
NA. NL. erit CK. CK + CR. CL = MK. MA + NA. NL.
eſt autem NK. NA& lt; MK. MA (quia NK& lt; MK, & NA
& gt; MA)ergo CK. CR + CR. CL& gt; NK. NA + NA.
NL. hoc eſt CK. CL & gt; NK. NL. hoc eſt NK. HL. & gt;
NK. NL. quapropter eſt LH& lt; NL. eſt autem angulus LCN
obtufus; ergò recta LH angulum CLNſecat; ac angulus LHC
interno LNCmajor eſt; hoc eſt angulus KNCangulo LNC
major eſt. unde liquidò patet fore CK& gt; CL.

_Coroll._ CK. CL = MK. MA + NA. NL.

XXIII. Hinc, ejuſmodi omnes refracti ſeipſos priùs quàm axem
interſecant, velut ad X. ‖ Hoc ſpeciminis loco pro caſu, qui

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