(i6)


Alligation, of Falfe Pofition, Extradion ofSquare and Cub
Roots, Progreffion, &tc.- But thefe are only Applica
tions of the firft four Rules. See RULE; fee alfo PRoPoR
TION, ALLIGATION, POSITION, EXTRACTION, &C.
We have very little Intelligence about the Origin an
Invention of Arithmetic; Hiflory neither fixes the Authoi
nor the Time.-In all Probability, however, it mull hav
taken its Rife from the Introduffion of Commerce; ani
confequently, be of Sylrian Invention. See COMMERCE.
Prom 4qia it paffed into Agypt, (Jofephus fays by mean
of Abraham.) Here it was greatly cultivated and improved
infomuch, that a great part of their Philofophy-and Theo
logy, feem to have turned altogether upon Numbers. Hence
thofe Wonders related by them about .Unity, 2'rinity; the
Numbers Seven, fen, Four, &c. See UNITY, TRINITY
TETRACrTYS, SC.
In effecd, Kircher, in his Oedip. Jfgypt. Tom  II. P. a.
lhews, that the Egyptians explained every thing by Num
bets; Pythagoras himfeif afirming, that the Nature o
Numbers goes through the whole Univerfe; and that the
Knowledge of Numbers is the Knowledge of the Deity
See PYT}IAGORIAN.
From Egypt Arithmetic was transmitted to the Greeks
who handed it forward, with great Improvements, which ii
had received by the Computations of their Afironomers, tc
the Romans; from whom it came to us.
The antient Arithmetic, however, fell far Jhort of that ol
the Moderns: All they did was to confider the various Divi-
fions of Numbers; as appears from the Treatifes of Nico-
machus, wrote in the third Century of Rome, and that of
Boethins, fill extant. A Compendium of the antient Arith-
mnetic, wrote in Greek, by Pftllus, in'the ninth Century
fromn our Saviour, was given us in Latin by Xylander, in
I 5 56.-A more ample Work of the farne Kind, was wrote
by 7ordanus, in the Year 12 0o; publifh'd with a Comment
by Faber Stapulenlis in 1480.
Arithmetic, under its prefentState, is variouflydivided,
into various Kinds; Theoretical, Praifical, Infjrumental,
Logarithmical, Numerous, Specious, 2Decadal, Dynamical,
Z'etraliycal, Duodecimal, Sexagef/mal, Vulgar, Decimal,
Finite, Infinite, &c.
T72eoreticalARITTIMETIC, is theScienceof the Properties,
Relations, bc. of Numbers confider'd abffra~tedly; -with the
Reafons and Demonfilrations of the feveral Rules. See
NUMBER.
Euclid furnifhes a 7Teoretical Arithmetic, in the feventh,
eighth, and ninth Books of his Elements.-Bazlaamus Mona-
chis has alfo given a Theory for demonflrating the com-
mon Operations, both in Integers and broken Numbers, in
his LogftJica, publilh'd in Latin by Chambers, in r6oo.-
To which may be added Lucas de Burgo, who, in an Italian
Treatife publifh'd in I 523, gives the feveral Divifions of
Numbers from Nicomachus, and their Properties from Eu-
clid; with the Algorithm, both in Integers, Fradions, Ex-
tradcions of Roots, &c.
Praaical AR I TiIMETI C, is the Art of Computing; that is,
from certain Numbers given, of finding certain others whofe
Relation to the fortner is known-As, if a Number be re-
quired equal to two given Numbers 6 and 8.
The firfi entire Body of Trafical Arithmetic, was given
by Nicb. T'artaglia a Venetian, in I 556, confifding of two
Books, the former, the Application of Arithmetic to civil
Ufes; the latter, the Grounds of Algebra. Something had
been done before by Stifeliuts, in i 544; where we have feve-
ral Particulars concerning the Application ofIrrationals, Cof-
ficks, &c. no where elfe to be met withall.-
We omit other merely pradical Authors which have come
fince, the Number whereof is almoff infinite; as Gemma
Friftns, Metius, Wingate, &c.
The Theory of Arithmetic is joined with the Pradice, and
even improved in feveral Parts, by Maurolycuis in his Opufcula
Mathematica, X 57 5; .Henechius in his Arithmetica Perfel a,
x639, where the Dernonflrations are all reduced into the
Form of Syllogifms; and 2acquet in his 1717eoria Fe Praxis
Arithrmetices, 1704.-
IJnfru1tental ARITHnMETIC, is that where the common
Rules are performed by means of Infiruments contrived
for Eafe and Difpatch; fuch are Nepair's 'Bones, described
under their proper Article; Sir Sam. Morland's Infirument,
the Defcription whereof was published by himfelf in x6665
that of M. Leibnitz, described in the Mifcellan. Berolin.
and that of Polenus, publifl'd in the Venetian Mifcellany,
17o9.-To thefe maybe added,
Logarithmical ARITHMETIC, perform'd by Tables of Lo-
garithm5. See IOGARIT11M.
The bef{ Piece on this Subjed, isjlenu. 7riggs's Arithme-
tica Lrgarithmica, I644.
. Tp this Head may alfo be added, the univerfal Arithme-
tical hf bles of 'ProJlapherefes, publiffed in 16i0, by Her-
'wart ao lTohenburg; whereby Multiplication is eafily and
accurately perform'd by Addition, and Divifion by Subflrac-
tion,--


e    The Chinefe have little Regard to
Calculations; inflead of which, they
made of a little Plate, a Foot and half
are fitted ten or twelve Iron Wires, 0o
d little round Balls. By drawing thefe tol
r, fing them again one after another, the
e after the Manner in which we do by Coi
i much Eafe and Readinefs, that they wii
Man reading a Book of Accounts, let h
s pedition he can. And at the End the
; compleatly done; and they have their
See COMTE.
Numerous ARITHMRTIC, CS that whici
of Numbers or indeterminate Quantities
{, by the common Numeral, or Arabic Ch
BIC and CHARACTER.


Specious AR ITHMETIC, is that which gives the C
- Quantities; ufing Letters of the Alphabet inflea,
F gures, to denote the Quantities. See S-Ecious j
e tic.


Specious Arithmetic coincides with what we ufl
Algebra. See ALGEBRA.


P Dr. Walits has joined the Numeral with the lii
t culus; and by means hereof, demonfirated the
I                      VI    Rfn;. P-A r - n  _ . e


I JL4r.llos, I ro porlions, ixrractions o0 0oots, 05C. A
pendium of which is given by Dr. Wells, under thc
f of P        Aenet f  rihnt  An  xnQ


I
I
0
A
i
A
9
II
M
I


1o
I


J
t


. L .VlhtflS.s VJ fl flht{fl&gfl 111. 1 IyU.;
- DecadalARITrIMETIc, is that performed by a Seril
ten Characters, Co that the Progreffion is from  to to xo-S
is the common Arithmetic among us, which makes Uri
the ten Arabic Figures, o, r, 2, 3, 4, 5, 6, 7, 8, 9; a
which we begin 10, 11, l , Ee Tc.
This Method of Computation is not very antient, IN
utterly unknown to the Greeks and Romans.-It was
troduced into Europe by Gerbert, afterwards Pope, ut
the Name of Sylvefler II. who borrowed it from the Me
of Spain.- No doubt it took its Origin from the ten X
gers of the Hands, which were made ufe of in Comm
tions before Arithmetic was brought into an Art.  -i
The Eaflern Miflionaries affure us, that to this Day
Indians are very expert at computing on their FP
without any Ufe of Pen and Ink, Lat. Edif & Cur.
that the Natives of Peru, who do all by the diflerent
rangement of Grains of Maife, out-do any European, b
for Surenefs and Difpatch, with all his Rules; Savaryfl
de Corm.
* Binary, or Dyadic ARITHIMETIC, is that wherein C
two Figures, Unity, or I, and o, are ufed. See Blii
Arithmetic.
M. Danticourt, in the Berlin Mifcell. gives us a Sp
men of the Ufe hereof in Arithmetical Progrefibi
where he fhews, that the Laws of Progreffion may
eafier discovered hereby, than in any other Method wh
more Characters are ufed.
Yletratlyc ARITHMETIC, is that wherein only theFigu
I, 2, 3, and (s, are ufed.
We have a Treatife of this Arithmetic, by Erhard N
gel: But both Binary and this are little better than Cui
fities, efpecially with regard to Praffice; inafmuch, as I
Numbers ma be much more compendiously expreffed
Decadal Arithnmetic, than by either of them.
Vtulgar ARITHMETIC, is that converfant about ItI
and Vulgar Fracions. See INTEGER and FRACTIOWN.
Sexagefimal ARITHMETIC is that which proceeds byS
ties; or, the Dodrine of Sexahefimal Fradions. See SE*
GESIMAL.
Sam. Reyher has invented a Kind of Sexagenal Ro
in Imitation of Nepair's Bones; by means whereof the St


agenary A'l2thretic; is eaniiy performed.
Decimal ARITHMETIC, is the Doctrine of De
tions. See DECIMAL FRACTION.
Political AR I THMETI C, is the Application of At
Political Subjedis; as, the Strength and Revenues
Number of Inhabitants, Births, Burials, Wc. See I
Arithmetic.
ARITHMETIC of Infinites, is the Method of fX
a Series of Numbers confiding of infiniteTerms;
ing the Ratio's thereof. See INPINITE, SERIES,
This Method was firfi invented by Dr. Wallis;
from his Opera Mathematica, where he 1hews
Geometry, in finding the Areas of Superficies, an
tents of Solids, and their Proportions.-But the
Fluxions, which is an univerfal Arithmetic of Inf
forms all this much eafier; and Multitude of ot'
which the former will not reach. See Ftux!
CULUS, Uc.
ARITHMETIC of Rationals and Irrationals.
ON AL, CC.
ARITHMETICAL Complement, of a Loga
what the Logarithm wants of io.oooooco. See
MENT.


C
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AR~~IL


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