Page:Cyclopaedia, Chambers - Volume 1.djvu/181

 ARI

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ARI

The Chinefe have little Regard to any Rules i n ,i. Calculations ; instead of which, they ufe an Inftrssali!? made of a little Plate, a Foot and half long, a-crofs vl'

Alligation, of Falfe Pofition, Extraction of Square and Cube Roots, Progreffion , igc. But thefe are only Applica- tions of the "first four Rules. See Rule ; fee alio Propor- tion, Alligation, Position, Extraction,^. are fitted ten or twelve Iron Wires, on which are tl

We have very little Intelligence about the Origin and little round Balls. By drawing thefe together, and air"""

Invention .of Arithmetic ; History neither fixes the Author, ring them again one afrer another, they count, fcn le ^\*~

nor the Time. — In all Probability, however, it mud have after the Manner in which we do by Counters; but withf'

taken its Rife from the Introduction of Commerce ; and much Safe and Readinefs, that they will keep pace with

confequently, be otTyrian Invention. See Commerce. Man reading a Book of Accounts, let him make what F *

From AJia it paffed into JEgyft, (Jofipbtls fays by means pedition he can : And at the End the Operation is {j\

of Abraham.) Here it was greatly cultivated and improved ; compleatly done ; and they have their Way of provino:

infomuch, that a great part of their Philofophy. and Theo- See Comte. ° !t '

logy, feem to have turned altogether upon Numbers. Hence Numerous Arithmetic^ that which gives the Calcul

thole Wonders related by them about Unity, Trinity ; the of Numbers or indeterminate Quantities ; and is perform J

Numbers Seven, Ten, Four, &c. See Unity, Trinity, by the common Numeral, or Arabic Characters. See A,,

Tetractys, %$c.

In effect, Kircher, in his Oedip. A'.gypt. Tom. II. p. 2. ITiews, that the Egyptians explained every thing by Num- bers; 'Pythagoras himfelf affirming, that the Nature of Numbers goes through the whole Univerfc 5 and that the Knowledge of Numbers is the Knowledge of the Deity. See Pythagorian.

From Egypt Arithmetic was ttanlmitted to the Greeks, who handed it forward, with great Improvements, which it had received by the Computations of their Astronomers, to Fractions, Proportions, Extractions of Roots, S?c. A"Com

---Ar 4. bic and Character.

Specious Arithmetic, is that which gives the Calculusof Quantities; ufing Letters of the Alphabet instead off, gures, to denote the Quantities. See Specious Arithtxc tic.

Specious Arithmetic coincides with what we ufually c ,n Algebra. See Algebra.

Dr. JVallis has joined the Numeral with the literal Cal- culus ; and by means hereof, demonstrated the Rules

the Romans ; from whom it came to us.

The aiuient Arithmetic, however, fell far fhort of that of the Moderns : AH they did was to confider the various Divi- sions of Numbers ; as appears from the Treatifes of Nico- machus, wrote in the third Century of Rome, and that of Boethius, ftill extant. A Compendium of the antient Arith- metic, wrote in Greek, by 'Pfellus, in the ninth " from our Saviour, was given us in Latin by Xylander, 1556. — A more ample Work of the fame Kind, was wrote by Jordanus, in the Year 12:0 ; publifh'd with a Comment by Faber Stapulenfis in 14S0.

Arithmetic, under its prefent State, is varioufly divided, into various Kinds; Theoretical, TraUical, Infirumental, I.ogarithmical, Numerous, Specious, Decadal, Dynamical, TetraBycal, Duodecimal, Sexagefimal, Vulgar, Decimal,

pendium of which is given by Dr. Wells, under the Title of Elements of Arithmetic, An. i<So8.

Decadal Arithmetic, is that performed by a Series of

ten Characters, fo that the Progreffion is from 10 to 10— Such

is the common Arithmetic among us, which makes TJIe of

the ten Arabic Figures, o, 1, 2, 3, 4, 5, 6, 7, 8, 9 ; after

Century which we begin 10, 11, 12, He.

This Method of Computation is not very antient, being utterly unknown to the Greeks and Romans. — It was io. troduced inro Europe by Gerbert, afterwards Pope, under the Name of Sylvejter II. who borrowed it from the Moors of Spain. — No doubt it took its Origin from the ten Fin- gers of the Hands, which were made ufe of in Computa- tions before Arithmetic was brought into an Art.

The Eaflern Miffionaries allure us, that to this Day the Indians are very expert at computing on their Fingers,

Finite, Infinite, &c.

Theoretical Arithmetic, is the Science of the Properties, without any Ufe of Pen andink, fat.Edif.&Cur.—AAi,

Relations, &c. of Numbers confider'd abstractedly ; with the that the Natives of 'Peru, who do all by the different Ar-

Reafons and Demonstrations of the feveral Rules. See rangement of Grains of Maife, out-do any European, both

Number. f or Surenefs and Dispatch, with all his Rules ; Savary TAB.

Euclid furnifhes a Theoretical Arithmetic, in the feventh, de Com.

eighth.and ninth Books of hhElements.—BazlaamusMona- Binary, or Dyadic Arithmetic, is that wherein only

ckus has alfo given a Theory for demonstrating the com- two Figures, Unity, or i, and o, are ufed. See Binary

mon Operations, both in Integers and broken Numbers, in Arithmetic.

his Logiftica, publifh'd in Latin by Chambers, in rtfoo.— M. 'Dangicourt, in the Berlin Mifcell. gives us a Speci-

To which may be added Lucas de Burgo, who, in an Italian men of the Ufe hereof in Arithmetical Progreffions;

Treatife pubhfhd in 1523, gives the feveral Divifions of where he fhews, that the Laws of Progreffion may be Numbers from Nicomachus, and their Properties from Eu-

clid; with the Algorithm, both in Integers, Fractions, Ex- tractions of Roots, SSfr.

'Practical Arithmetic, is the Art of Computing; that is, from certain Numbers given, of finding certain others whofe Relation to the former is known — As, if a Number be re- quired equal to two given Numbers 6 and 8.

eafier difcovered hereby, than in any other Method where more Characters are ufed.

Tetratjyc Arithmetic, is that wherein only the Figures 1, 2, 3, and o, are ufed.

We have a Treatife of this Arithmetic, by Erhard Wei- gel : But both Binary and this are little better than Curio- fities, elpecially with regard to Practice ; inafmuch, as the

The firfl .entire Body of 'PraBical Arithmetic, was given Numbers may be much more compendioully expre'iTed by by Nich.Tartaglta a Venetian, in 1 556", confuting of two Decadal Arithmetic, than by either of them.

Books ; the former, the Application of Arithmetic to civil Ufes; the latter, the Grounds of Algebra. Something had been done before by Slifelius, in 1544.; where we have feve- ral Particulars concerning the Application oflrrationals, Cot ficks, &c. no where elfe to be met withall. —

We omit other merely practical Authors which have come iince, the Number whereof is almoit infinite ; as Gemma Frifitu, Metius, Wingate, &c.

The Theory of Arithmetic is joined with the Practice, and even improved in feveral Parts, by Maurolycus in his Opufcula Mathematica, 1575; Henefcbllts in his Arithmetica TerfeBa, itfc-o, where the Demonltrations are all reduced into the Form of Syllogifms ; and Tacquet in his Theoria t$ <Praxis Arithmctiees, 1704. —

Infirumental Arithmetic, is that where the common Rules are performed by means of Instruments contrived for Eafe and Difpatch ; fuch arc Nepair's Bones, defcribed under their proper Article ; Sir Sam. Morland's Inftrumcnt, the Description whereof was publifhed by himfelf in 1666 ; that of M. Leibnitz, defcribed in the Mifccllan. Berolin. and that of 'Polenus, publifh'd in the Venetian Mifcellany 1 700. — To thefe may be added,

Logarithmical Arithmetic, perform'd by Tables ofLo- garit'nms. See Iogarithm.

The best Piece on this. Subject, is ^feu.Briggs's Arithme- tica I.'garithmica, i6z$.

. To this Head may alfo be added, the univerfal Arithme- tical Tables of ' Profiapkdlrefes, publifhed in 11S10, by Her- •xart ab llohenburg; whereby Multiplication is easily and accurately perform'd by Addition, and Division by Subtrac- tion.-^

Vulgar Arithmetic, is that converfant about Integers and Vulgar Fractions. See Integer and Fraction.

Sexagefimal Arithmetic, is that which proceeds by Six- ties; or, the Doctrine of Sexagefimal Fractions. See Sexa- gesimal.

Sam. Reyhcr has invented a Kind of Sexagenal Rods, in Imitation of Nepair's Bones ; by means whereof the Sex- agenary Arithmetic is easily performed. _ Decimal Arithmetic, is the Doctrine of Decimal Frac- tions. See Decimal Fraction.

'Political Arithmetic, is the Application of Arithmetics Political Subjects; as, the Strength and Revenues of Princes, Number of Inhabitants, Births, Burials, Effc. See Political Arithmetic.

Arithmetic of Infinites, is the Method of fumming up a Series of Numbers confuting of infiniteTerms ; or of fine!' ing the Ratio's thereof. See Inbinite, Series, &c.

This Method was first invented by Dr. JVallis ; as appea" from his Opera Mathcmatiea, where he Ihews its life in Geometry, in finding the Areas of Superficies, and the Con- tents of Solids, and their Proportions. — But the Method of Fluxions, which is an univerfal Arithmetic of Infinites, per- forms all this much eafier; and Multitude of other Thing 5 which the former will not reach. See Fluxions, Cal- culus, t$c.

Arithmetic of Rational s and Irrationals. See Rati- onal,^.

ARITHMETICAL Complement, of a Logarithm, ' s what the Logarithm wants of io.ocooooo. See CoMft 5 '

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