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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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Curre, and hachics Velocier in a Subduplicare Racio
O ihe Alcirude: And it a Parricle ot Lighe comine
trem a siren Point, and pals chrousB a Medium
ertose Rarier increases in a Subduplicare Rario of
the Alricude or Dexch, ehen Wwill che Velocier ot
che Parricle, or Ray oE Liphr be in a Subduplicare
Racio oF such Fleighch or Dexth; and consequent.
ly, lnce che Velociey becomes che lame, Wherher
produced by che unitorm Action et Cravity, or
By ene Raricy oF che Medium, ehe Line oF DC.
SCenE Or Morion, Or the Curve deseribed will be in
boch cases che same. There hare been publistred
marts Mechods oE Investisarine che Nacure oF chis
Curre; and che follorins one (wtich is MOrE.
plain, and easie) recommends ic self e0 us wirh
ehis Adrancase, char ruo noble Problems in rvo
distinet Sciences, are solred ac one and che Came
time; the one an Oprical one, cheorher a MC.
chatricat.
NToW lec the Lawr of che Rarity or Densey ol
the Medium be wrhac ie wwill, e may thus in ge
neral proceed, eo decermine che Curre. Lec ib.
Medium FC D R be cerminated by che LTorixon.
tal Line FC, r0 ertich A D is perpendiculer, ane
is che AXoFthe Curre AH L wtose Ordinate i
FTC; and ler rhe Ordinares TC Aill reprelene rhe
Roxicies of the Medium in che Deprts AC, 0
iotrich is all one, the Velociries of ehe Clobule ot
Lighe in che Poines of the Curve M. The ineur.
ved Ray, oe ehe semita ot che Globule is che
Curve AM B, the nacure of irhich is eo be inqui-
Ee
red into. The Lines FC M and cn m aro paraI
sel EO F C, and MLn paralel 1O AD. L et AC,
a, C0 =M n = Y, C M =,, nm-y, A M- it
NImq TIC D; and a a Rable quentity ca-
ken at liberry. IE e Duc Mm For Radius, ris
plain charnm is che sine ot che retracted Angle
Cor ot elie Curres inclinarion ro rhe Verrical Line
Nn aC the Poine M) cherefore since the Sires ot
oF chose ansles are. (a5 Was laid betore) alvays a5
che Celericies, ehem
is, 2 is a constane Racio, (0 chat 7 = 2. (sor che
Ruxions a beins raten equal, as chey may chen
 is also a ccable Rario) and a; =oz, and aa y7
=00Z 2i but 2 2=y y + i ir, cherelore aa yy
General Equation in Fluxions For che Curre AMB.
No ris all ore Whecher re consider ehie Incre
riries os che Mediums in chose sereral Points, chac menes of che Velocies as dependins upon rhe BC
i5, asthe Velociciesot the Globule oF Lighe in hore) dium more or less rehstins che Globule, or ihe
places; and since also chose retracted Ansles are scher abstractins trom all considerarion ot a Me.
he Anples ofche Inclinarion olche Lines b e, eh, dium vre suppose chem 20 be che etects os ano
2C. 20 ihe Perpendiculars b0, ef, _cc. ris elear cher Cause, buc acting accordine ro che lame LaW
hacthe Curre must have chis ProperFy, Thac ehe chac ras observ d in rhe former, since on borhe
Lines of the Inclinations to a Perpendicular must sides the Curve is Suppoled to be run in the CitOrE
be erery where in che Ratio ot ihe Celericies.
est rime. Nou il ve imagine che Globule c0 be
a heary Body, ana Graviry 1o be the Couse ob
che Accelerarion, rhen che Curve A e si will Be
che common Paca bola. sinec H C oc v reprelento
Lec us imaxine che Medium AB C D 1O
inace up ot Fluids ot several differene deprelsc
DenREY, buE rhe Densiries (proccedins M 
rhe several Incervals oF rhe ParaIlelS AC, C e, 
Et Bo) eo encrease or diminim in a cerrairt L aB
In chis lixample we II suppole che degrees ot la
ciry in che Fluidsto encrease a5 Wve 80 tront  10
vards B; (0 char che Ray a b is turned by l
Retraction into b e, and b e into ch, and et
into hI ecco. trom ehe P’erpendicular b 0, 0), 
ecc. at Ihe Points ot Incidence b, e, h. _. ec
prick d Lines beins che leveral Incident Rays pro
duced. The retracted Ray incercepted belleer
ehe Poines b and o, viz. b ch l0 is a P0l)br
made up oF alt che Retracted Rays, b e, 8B, ec
erhich defect trom onc anocher by che Angles 0
Retraction made ac the several Poines b, e, dc
Voir it che Distances of che Parallels are lellertc
intinicesy, che Polzson b c h lo becomes a Curve
Lirie; bur al(o che Curve Ray in its paltase chro
ehc serctal Mediums is suppoled ro cake luch 
courle, chac it comes trom the Radiacins Point c0
che Point co be enlighined in che Morrestrime, ris
evident (since eis lo every where chroughour the
PolygoH b ch10) char che Curre inco wrhich char
Dolyson degenerares (beins ihe Curve Wvhich che
Ray by rhe continued Retractions is bene into) id
ehe Lishr palles trom che Poine b ro che Poineo in
rhe Morcest Time. And since che Sines  ine le.
sracted Ansteo ob e, feb, ecc. are Aill as the L a-
Ebe Curre oF tvisteA MOriOn, Or thac By wotich 0 0yy +0DX X, and r-- 2, ehich is che