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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 806933011:0351
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F OC
ac P, is asche sinc ot che respectire retracted An-, ac cach renth of an Inch distance From the AXis, the
sle. Whence in all Cases oF Parallet RaYS, C F i5) Foci are as FolloWS.
EOP F, in che lame constant Rario ot Retraction.
IF ic Mall be desired ro effect in Numbers wtar
re hare here done by Lines, ic will be most casie
to adapt a Calculus ro the toresoins Ceomerrical.
Construction.
For it in che Frianele PO C, there De given the
Radius C P equal 1o Vniey, CO che Distance ot
the Object From che Centre of the Sphere, and che
Perpendiculat P x, equal ro the Siné oF che Anole
P CO, che Side PO = OR, will be equat EO
VEO FCP F 2COin VCP =PF
Then aS OR OF PO EO P x:: So C R 10 che
Sinc oF the Angle C OR, and the Complemenero
180 Degrees ofthe Sum of the Angles C PO and
COR, is ihc Ansle C R Q equal C F P; and a5
P X 1O PO, (0 is the Sine OF the Anple C RO EO
CQ; and aS C QTO C. P, IOC REOC F, which
is the Distance of the respectire Focus oF ai the
RayS P O from the Centre oF che Sphere C.
Burche Foci oE Rays parallel roThe AXIS, may
De compured more readily follomine rhe Foorexs
ot che Construction, For chereby ic ill appear,
Mharche Radius oE che Cirele H F, viZ. a F, 15 c.
qualeo- C P, and C a = =  CP,
For Fmersins RayS, a5 in Fis. I. but For Tmmer-
sins RaYS, 25 in Fis. 2. C a will be tound to be
==C P: And supposins che Distance oF he
RayS From che AXis = P X, in the CasC OF Parallel
RayS Fmergins, rhe Distance of theFocus will be
Found,
PF =
Thatis, r 2O s Beins a5 3 102,
PF= SV CP = ex L VECP =3P~
And Cor Immersins Rays, the Focal Distance i
Coundby alitre Rule:
PF
er
CP = L + 
er = 55 CP = er - 55  x  C P.
Thac is, r and s bcins 25 3 102, 25 betore.
PF = 3 V CF = Pv F V5CP -2P~
CF
These Canons are (0 casly deduced From che
Constructions, thacchere is no necd corrouble che
Reader wich cheir Demonstrarions, onty vou have
here added ero Fables compured trom them, wwirhr
lirele more Work than a continual Addirion; wtrick
may by ar of Example, serre ro instruet and ex
ercileche rouns Scudene in chis parr ot che Mache-
Cussiciene Satisfaction.
FODTNTA, is the Labyrinch in che BMC OE the
RaES.
FAECOTA, Signities a Poder erhich subsidesto
maricks.
Suppole CP ihe Ractius ot ihe Sphere or Ctass) Porder whichis ro be aryed lixhely
2 Ineties, and che Rario ot Retraction 25 3 202;
ILKK 2
si A C
Por Fmersine Rays.
2. 92.76+ V 5. 7276
V 12. 8304 + V 5.6304. 2
V 12.6634. + V 5. 4684: L
V 12. 4.4. 16 +- V 5. 2.4.16.2
12. 1500 = V 4. 9500 2
VTT. 7936+ V 4. 5936.2
IT. 3724 + V 4. 1724
V 10. 3864. + V 3,6864. 
V 10. 3356 + Y31356-2
V 9. 7200.+ V 2.. 5200-
For Immergins Rays.
4.  V5. 7344 +
V2.5024 + V5. 7024+
V 2. 4576 + v5.6576+
4000 + V5.6000.+
2.3296  V5. 5296.+
V2. 2.464 + V5
V 2. 1504
V
V2.04.16 + V5.
10 lV 1. 9200 + V5. 1200+2
Butic is co be Nored, Thac these Foci For Im.
mergins Rars must nor be caken For the Foci OF a
Llano Correa, en n cnreau ls comards
the Object, For che Plane- Side by irs Retractian
does conrraet the Focal Lengch, by about a semi-
diamerer dt elle oplele, cele lupose bous
et Clals concinued.
The Came Ingenious Author, as an Inltance 
the Lxcellence oF che Modern Algebrae, gires al(o
in Philos. Fransact. N. 205, a Way ro And the Foci
Ot all prick Colasses univertally; and ews oF
Wrhar sieat usc his and tuch Theorems are: BUE
lavins cMlarsed (o muest altcaus, L Cast only reter
ee Alsebraieat leacer c, where he will ind
the Borrom in cerrain Hraimings of Vegetables;
For ic is prepared ot lome ercen, wathed, alu pa-
red Roors Deac rogether ich a licrle WVarer, then
Strained, that chere may sublide a evtrire Tort ob
EOEKVS,