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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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caliez
Caustick rouch one anocher ac rhe Poine a
Corol. 3. IF che Radius oF Concavity MLC BC
=0, then again a= =o, and 2=0; Trom Wtienc
MF= AFF perperualIY. Thac is the POrrion OFTOlIOWS, thac the Curre AM D and che Caustich
Corol. 4. IFC MI De infinite, rhen a (= = HIF) 15
Corol.. 5.Tis easie t0 apply alI ehis char ha
23
have 2= 2y f 4) and co Mevr vohen ne restectect
Rajs will come convergine or divergins.
Corol. 6. When che Curve A ML D is a Geome
eriek Curre che Caustick will bc (0 100; for it
AMD bC a Geomerrick Curve, the F voluta. Will
be(0roo; that is, all chePoines C may De Geome
ericallr derermined, and from che Evoluta, che
POInES FOF che Caustick may be Ceomerrically de
termined al(o. Buc farcher, ehe Caustick upor
this Supposicion Mall alrvars be rectitiable 100, tor
Rixhe sines may alvays be found equal 10 any
Porrions OF ir.
Corol. 7. Tis plain, char girins any 2 OF thC3
PoinEs, B, C, F, that is, Ihe Radiatine Point, che
Tex ThC POInE C DC AE the Fvolura OE the re- Point os che Evolura, and che Point os ihe Caustick
Aecting Curve AM D, Or wrtrich is al one, ser che 3d Poine may be derermined.
MIC bethe Radius otthe Concariry for the Poine
MI; and suppolins che Arch Mm infinicely (maiI
lec Bm, Cm, Fm be drawn. F’arrher, uxon che
Centers B, F, lec che licele Arches MR, M1O b
delcribed, and trom che Poine C the Perpendicu
TarS CF, C e, CG, C5, c0 che incidene and re
Aected Rays. The Priansles MIRm, MIOn
are similar and equal, as was Meon betore, and
MR = MIO. AIIO ihe Triangles C F M and
COML are similar and equal, and (0 are Cc m
and C∞ m; For the Ansles aE L, e, G, c are risHE
and MLC, me are common, and F NI C-GNIC
and em C=g m C (becaule MVC, m C are Nor
mals ro ehie Curve by suppolicion ot the Evolut
and che Ansles oF Incidence and Reflection arc
egua) Theretore CF==C C, and C’e-C, ane
contequencly C F. C cC 6- C5, Thar I5, F O-
56. LatIy, che TrianBles, B MLR and BF ∞
aee similar, and (O arC F MO, FCS. NToW lec
BMy, MF= MO=a; cheretore BNI + B F
-2y - a; let RM.O M x, and F MI
WHeresore F C==a 2, and ler it be required rO
sind Z which derermines rhe Poine F in che Cau:
sick. Then F  proma and F e + M R=
2ji an, al(0 5C - ai 2i and 56 + M0- u
but by what Wvas Mewn beFOTC RN== O MI, and
S6= PF, theretore F.Q FR M=S6 + MO.
By chis general Theorem and ies Corollaries, che
Causticks ot particulas Curres aie easily derermi-
s
Ned, horvever the RayS 30, Convergins, Diver-
Sins, or Parallel; bur e ill suppose che simplee
Case ot Parallel Rays. Thus in the common Pa-
rabola, il che Incidene Rays are parallel, and cur
Ehe AX ac righE Angles, Thac is, are co. incident wirt
che Ordinaces 10 chat AX; then we have 2- = a:
(0 char cakins in cach reflected Ray che lengin ol
2 a (a being che reflected Ray incercepred Be-
ecen che Point oF Incidence, and che Point where
the Normal From che Fivoluta meers that resected
Ray) by this means che several POinES OF che
Caustick woill be derermined. The lenorh oF the
Causticke Curve allo catien trom iHe Vertex OF itie
Parabola (Wrhere it begins) eo any ocher Poine, is
equat 10 ihic Summ ot che Iucidenr and Rerected
Ray5.
chac is, 21x.-. au ax and 272 Za =ga; and sCaustick, Becinnins AC che Tame POInE; non be-
2 (=- MIF) =, . 2: F: F.
Corol. 1. IE The Incidene R ays are parallet, eher
a. For y in chis case is infinire, and cheretore
evich y.
27, che Ouanciey a ranictins il compared
Coroll. 2. YE ehe treident R av BMI rouctes EHC
Curve AMD in MI, chen a (=- MI F:) i5
and cheretore Z (= MF) =O El(0; trem wotence
FH L atEe RiPBEsIinE HE, rhaE IS FML L NZ =, ic SollomS, ehac rhc pivea CurDC A M D, aud ihC
AEI L HIF F TL, and MIL IA = A +1, 11F-
MF; buc AX L. F A-B MI B A, and cheresore
the Porrion ot eHe Caustick AF B ML  
Ot che Curre A MI, is equal co rhe difterence ot Angle equal co the Angle ot Incidence.
ehe Incident Raso BM, B a, added co rhe disse-
rence of the reffected Rays MF AFT. Or, ca- intnice litewise, and 2 (= MF) = y; and in
Porrion ot che Caustick whieh is evolved while che Arch Nm becomes a riphe line.
Ray B A approdchech co a ca. incidence wirh BNI
how co determime the Lvoluta oF any siven Curve
che Invenrion  e catacaustick trout chence
the Caustick FYF formed trom ehe reslected Rays do cur ono anocher ac che Poine M, and makie ar
kins any 2 incidene RayS, a5 B , B MI, thac ehis case oF che intinire distance of che POinEC, che
5= to che difference ot these Incidents. F the been said, when the Curve ANT D iS COnVeX IC
difference oE rheir reRected RayS. Non knomins che Radiarine Poine B (in Wwhich cale woc Mall
AS suppose A AL D voere rhc Parabola rohole
Verrex  and AX AK, and AFYF Were the
cause cho incident and reffected Rays at ine Ver
cez are equal eo nochine; thaE iS, AB = 0, and
2FF=0, cheretore iHC Curre AF F (= P M
A + M F- AEL by wehac vas Memn BetorC)
M+ MF.