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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 806933011:0151
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von nre c0 suppole il 10 be che summ ot hole
tvo Ouancicies à and b.
Is rhe Noce oE Necation, Nfalive Fxistence
OF Non Fintiry in Algebra. L Whenever il
stands Cingly: betore any Ouancus. lMens
ehac Ouanciti 1o be sio real onc, DuL selS Thas
nochins; and. chieretore such Mlanciries are
calsed Nerative. Thus = 3 I a IVBaBC 5, b
3 less chan Noching. And rus TuCH. Onan
ries as chèle arc orily lmaginals, Hey have ye
very ereac ule in Algebra. si aus bile mlay
Hare a distinct. Idea ot such 2 Lesative OHan.
ciry; le ne consider a Man co dDe in CaM, 0
to be vorili bur 1000 Pounds, aites sel l ove
500; For chen etiac Man 1 Celtainy 5001
worle chan Noching; Whies Mantiey ot 5001
in respect co him, will provents be expresseo
by puicins chis Nesatire Sion belore it; fo
rIS eruly EO thaE Man -5001: or 5001. lel
chan, or vorle than nochins.
This Character i5 allo the NOre oF Substraction
and wten vou sec ab, vou must read , a
substractins oe abatine. Or a5 etic Wlval Way
now, a less b; implyins, chat chat CHatcleris Ine
Difference berween a and b, c c uut.
otien b che lesser is substracted FroM a IAC
Sllarer. Theresore chis Nore (as aHe _MM iHC
eregoins) alvass betolss lo anuset
lowine ic.
 Is che Character expresins che Difference be.
civeen any cro Ouanciries when ris not yet
discorered which is che prearer: And cheretore
che sion- cannor be uled, becaule il alvass
suppoles the Ouanciry Follomi l de lels than
Whac precedes ic.
IS che Character. OE Mulciplicarion: Implyine
che Granciries on cach side che sion are to be
mulciplyed one inco anocher. Thus axb is 10
be read, a mulriplyed by b; or che Rectansie
becmeen, or Produet ot a and b: Buc chis Sien
in Algebra is ulually omicred, and che Guanci
ries are pur donn like Lecrers in a Word. Thus
ab tienities che Produet ot a mulciplied by b.
In compound Ouancicies che sust ls Mole times
uled, 25 a F bXc F d c
= I5 che Mark oF Division: ThuS ab Ggnities
chat che Ouanciey a is ro be dirided D V. 
Mb Ches in Alsebra the Guorienr is expressed
4. 6:: 8, 12; and Mes, chac A hach ehC
lame Rario 106 Thac B hath e0 12.
:Is che MarK OF Geomerrical Proportion conti-
nued, and implies che. Rario ro be Aill carried
on wichour any Incerruprion, 25 2, 4, 8, 16
32, 64, 128:.. Some French Writers use chis
Mark Tor Arithmetical Proportion.
J: Is. the Sien ot Radicaliry; atid. MCCS, (ACCOE-
Ding co che Index of rhe Porver that iS SeE OVeF
Or aster i1) chat chie Square. Cube or octier
Roor is extracted, or is ro bc (0, our ot any
Oranciry; 25 V: 25, O1 7: 25, Or Y (2) 25, (18.
nities ehe Square ROOr OF 25; and is 25, Or
V: (3) 25, Signities the Cube R00r ot Tvency
sive. Someriries ehis Radical Sien belones 10
as many ot the following uanciries a5 have 2
Line drann over chem; 25, V: b L d Sionities
the Square ROOF oF the Summ ot b and d ad
ded ropether: And Y (3) f+C- 3. 3 sionities
the Cube Rooc ot che Summ of fand 0, atrer z
is substracted troiri. ihiac Suirim; and rhac after
chis, 3 is c0 be cakem trom ihe laid Cube ROOT.
Or = Is che Character oE Greater, aud.
7 Or C The Sign oE che Lesser OF any rVO
Ouanticies.
I5 Che Mark FoF Parallet, and implies, chat 2
Tiries Ox Planes are equidistane one trom ano.
ther.
a Trianele.
S Square.
De Rectanele.
OCircle, or Sot che Sun.
Equi angular or Similar.
Egailareral.
Anole
=Riehe. Anele.
E Perpendicular:
:: I5 che Mark Cor Arichmerical Proporcion.
X, Z. Any Lerters Wvich POinES (0 over their
Fleads, denore che Fluxions ot Variable Ouan-
cities: and it chey hare 2, 3, Or a Points, cher
denore Second. Third, or Fourch Fluxions:
Sec Fluxions
23
3. =4 Oc. are ihe Faponenes ot 2
Series oE Fractions in Geomerricat Propret
SOB.
5,  areche Exponents oFV: X. Y. X. V: x. Wwtich
cheresore in che new Norarion are riuren chus.
X2, X2, X 4 (90. AIIC
F Aands For i. Xr. and in Fractions,
- - X  2. X . Aand fOr  = 3, (90. AIIO
∞3 +  expresses che Produet oE x = inco xz. and
3 5 (Or x 5) is che Produet of x : into
its selt, or rhe Square of x ,
c: (Or Xt iS chC LXpOneBE OF che Gaorient
OF xt by x2.
+ b (= c Exprestes an Vnice divised by a + b.
atb(=3 is an Vaice dinlect by che Cube
oE a. + b.
Fraction. WayS; a5 Z Cienities  MOlienEO.
a divided by b. Some Wrirers express ic chus
a) bl, a5 in Common Divilion.
∞. Is che Charactor oE Involurion, 25 chey call il
char is of producins che Square olany Ouancirs
Os ot mulciplyins any Ouancier inco ic lelt. In
Branter and PellS Alsebra, and since rhac, in
Wards and orhers, ris placed in ehe Margin
and Biews, chac chac Scep of che Equarion a.
Bainst which ic stands is eo be mulciplied by il
TelE, or squared, or il ic be a Square already
chen ro berailed up eo rhiac Pover which chc
Index ler atter che Character expresses, s
110 3)4) aaa + 3a ab + 3b6 a + bbb) MC
chac che Airst Scep oF char Rquarion, wtich (was
a. +b,) as, in che ach Scep, mulriplied Cubical.
ly, or raised ux ro the 3d POver.
uv Is the Charaeter oF Evolution: chac is, OE FX
straction of RootS out of the several Povers; anc
is che Rererle ot che forexoins Sien .
3: Isthe Mark OF Geometrical Proporrion disjunet.
poctionato, ad in ihe eotdem eca, a
oE 8. +. 6.
analio uluallu paced vecacen Eio Paico ot Esa) ats l2 is ihe. Biguadcarict Rooe ot she Crbe
Cd.