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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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Compare chese tvo Series, wrich the rive
Tet ehere be anocher Nuiiber i I - y: There
OE che Theorem, and YoWH And a = 1, b = 0, Fore us Losarictim ill bC a Y F b y 2 -- cy 2
641 d = 0, = 4042s=0, 5 = n, b=0
6421 k = 0, 1:
Hence Z = ny. 
4041, m = 0, ec.
64: 32, ec. OF n y 
2X34= ) A, Bc. Supposins A co denore the whol
proccedine Term, wtiich vill De chie same Series
2o MI. Nermcon has tiest Eound:
On che larme Mectiod chis Beneral Pioblem mas
besolved.
The Abscissa correspondins 10 a certain Area in
any Curre beins giren, co sind etie Abseisa, wtiole
Noi il 1 F 2 = r-  - y, it Sollons,
That a Z. F b2 = c2, etc. : ay 1 bgr f
C73, ec. :. n: r.
Thac 15, a Z-  b32  cZ, eC. = n ay-
n b92 = n cy. ec.
Thetehote ve may ind ehie Value ot Z. exprese
by che Povers oEy.
apain: Since 1. + Z = 2 - y; cherelore
= + - g - 1.
Thacis, 2 = ny  = x  - 9. +  X
n - +
n.
correspondins Area Mallbe co rtie tust in a siren = X
Ratio.
Theresore q is doubly exprest by che Pomets ox
The Locarirtimick Series mistir also be Pound y: Compare chese Wvo Values rogertier, and rhe
vichout borromine any ortier Idea, rtianthac LO8a= Coesficients, a, b, c, _cc. Will be determined, ex
richns are che Indices ot Povers:
cept che Arst (a) Which may be cakten ac pleasure
Let ihc Number wtose Loearichi inc imagine, and sires accordinoly all ehie disserene Species of
ver Y Z; suppose is L ogarictimi 10 be a Z  b2 Losacietims:
623 dic.
redmeto Publish:
The follomine Convergins Series for the L. s at ne o) The LOOES O) au quatiOnS, nhe-
cher Simple or Adfected; the late Mr. Wastellof ihe Navy. OHice, senc me; and desi-
A = Wdars Ablolure Number.
n = to ehe Exponent ot ans Porrer.
hP, q rySy e. che several Coesicienes in ans Equation.
Then in ans Equarion it will be
LX 4  = pX Xn - 1 = 9X . d - 2  p X r n - 3 = 5, 8c. = 4.
And we have Unirertally,
 2 fY n = + F gXn:  31In = 2F p X n  4Y n = 3+ BC
FKnN  = 1 = p Xn - LH n - 2 = gXn - 2R 1 - 3 = rXn- 3N 1 - 4 =, 3C.
In irticti Series oblerre,
L. Thac ehie lalie SIBA IH che eiven Lquarion, mult Ve in he Theorem OE Series respectirely.
II. Any Term urhichis vanvine in che Equarion, must be omitted in che Series.
III. The Oucrient at everr Operation, mustbe made a Ne N.
IV. Thac ie terminares in che ROOr, Or Calls inco a Series, is it be a Surd.
V. Suchi Series will be praclucee (in Nubes os Places) By a Ceometrical Proeretion Scom Unitr;
Cirtiole Ratio is tw0) each Operarion.
VL The nearer N is eaken eo etie rue Roor, ihe Pooner il Will Converse ro il.
Ane in his Pdicion oE Passoni s Arichmerick, Docke 2. Cbap. 21. Vou may see a Cariher Accounc or etis ses
sies, and che lame exemplitied in Numibersi
Let id dus tumber allumed.
n
EA LAANONDANE