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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0350
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COLLhRX VI.
cither Dirergins or Convergins: le no reman
20 add somethins concernins Rays Parallet 0 E
Axis.
In chis Case che Point D must be considered as
infinicelr distane; and consequenty O P, OC, and
C R, are all Intinire; and OP, O C, are in this
Casc ro be accounced alvars equal, (since they
differ bue by a pare ot che Radius oF che Sphel
Rays, and a5 r tos For chosechat Limerse. And by
20 And all ihe Lrrareles C. L F, Wwherein C ti 1
E0 P F in the Rario siren b ie Desiceo lC.
Fraction.
the celebraced Or. WVallis, in his Freatise of Alxe
bra, Pa5. 258. bur che Construction chereot munt
be repearede.
Flicherro we have considered oniy Oblique Rays
GPV L, which is no part ot cither ot chem;
Wheretore che Ratio ot CR, 100 P, Wilt bc 2l.
ays che Caire, viz. A5s eo r For Immergins
ehis Proposirion C F isto P L in chelame Ratio:
Ir remains cheretore ro Meu on che Bale CP
Ehis Problem has beeh very tully considered by
LEEOP V LBCa Lens, V C or P C Htie RadtiuS
ot IES Sphere; and ler it be required eo sind alche
POInES f, f, Cuch a5 C F, May be to Ps in che gi
ven Racio oE stor TOr Bin S RaYS, OP 25r 1C
Divide C V in K, and continue C V 1O F, char
nued CP eill ir inversect the Circle in F, P F MaII
De alvays equalro Vf che Distance oF che Focus
ot each respectire Parcet OF RaySO P, FrOM thC
Vercex or Poe osche Lens.
Demonstration.
sForthe Prersins.
CR May DC FO V R, and C F 1OV F in che pro-
Posed Rario: Itien divide K F equallr inche Point
; and wichettac Cenere (vcep the Lircle FR F;
ehis Circle beins drawn, sires ceadils all che Foc
OF che Parallel RaySOP, OP. Forhavins conri-
Racio.
equal ro che Angle of Incidence, and che Angle a
Prothe Retracted Ansle; Wheretore P Frhe Side
oppolire co the Anole aE C, is a5 the sine ot rhC
Ansse ot Inciderce, aud C l orpolice 10che dnesc
Draw che Pricke Line V F, ada D) Wobar 15 deli
vered bY Or. WVallis in the atore-Che place, VP
and C F. will be alivays in etie same proposed
Aeain, V fbeins made equal to PF, CF andes
Will bC ARCC CGua do dlC C P and VC; and
equal. Wherelore Pf wrili be equal ro V F, and
the Angles PCF, V CF beins ad verricem, are alic
consequener lf 10 lf in elle same Ratio 25 C F
tOV E; whence, and by whac forgoes, the Points
fifarethe several respectire Foci oF che leveral PaFs
cet ot Ra5SL,I. L L. V.
ThatC F isr0 P F in the Ratio oF che Retracti.
on, in che Cale ol Parallel RayS, Will yer be mere
erident, it ic be considered, chat the Angle ac C is