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THE

NEW COMPLETE SYSTEM

OF

ARITHMETIC,

COMPOSED FOR THE

USE OF THE CITIZENS OF THE UNITED STATES.

By NICOLAS PIKE, A. M.
Member of the AMERICAN ACADEMY of Arts and SCIENCES.

ABRIDGED

FOR THL

USE OF SCHOOLS.

FOURTH EDITION.

PRINTED AT BOSTON, BY D. CARLISLE,
For THOMAS & ANDREWS.
Sold by them at No. 45, Newbury Street ; by said Thomas at
Worcester ; by O PENNIMAN 6 Co. Troy ; by WHITING,
LEAVENworth and WHITINI, Albany and by the

Booksellers generally.

Dec. 120.2.

EXPLANATION of CHARACTERS used in this TREA

TISE.

"HE sign of Equality: As 17 Pence=I Shil

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Shilling; and, in general, that whatever pre(cedes it is equal to what follows.

The sign of Addition : As, 5+5=10, that is, + 5 added to 5 is equal to 10.-Read 5 plus 5, or 5

more 5 equal to 10.

The sign of Subtraction : As, 12-438, that is, 12 lessened by 4 is equal to 8, or 4 from 12 and 8 remains. Read 12 minus 4, or 12 less 4 equal to 8.

The sign of Multiplication: As, 6X5=30, X that is, 6 multiply by 5 is equal to 30.-Read

C6 into 5 equal to 30.

The sign of Division : As, 30-3=6, that is, * Or 6)301 30 divided by 5 is equal to 6.-Read 30 by 5

equal to 6.

Numbers, placed fractionwife, do likewise denote division, the Numerator or upper number

being the dividend, and the Denominator or low25

er number, the divisor, thus 82% is the same as 875+35=35.

The sign of Proportion, thus, 2 : 4 :: 8 : 16, Ithat is, As 2 is to 4 fo is 8 to 16.

Shews that the difference between

added to 6 is equal to 13.--Read 9 minus 2 plus 19-2 +6=13 6 equal to 13 ; and that the line a top (called a ,

Vinculuni) connects all the numbers over which

it is drawn.
12-3Fs=4 {indicaves or is equal to 4.

Signifies that the sum of 3 and s taken front
Signifies the second Power or Square.
Signifies the third Power or Cube

875

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and 9

CA 35 PBL

4.1

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113

,
UMERATION,
Simple Addition,

12

Subtraction.

15

Multiplication,

16

Division,

Supplement to Contractions in Mutiplication,

30

Tables in Compound Addition,

Compound Addition,

Subtraction,

Probs. resulting from a comparison of the preceding roles, 44

Applications of the preceding rules,

47

Reduction,

51

Vulgar Fractions,

66

Decimal Fractions,

86

Federal Money,

Decimal-Tables of Coin, Weight and Measure, 104

Division,

Rules for reducing the Federal Coin, and the Cur-

rencies of the several United States ; alio, English,

Irish, and French Coins, &c. and Spanish Dollars,

each to the par of all the others,

117

Recapitulation of the preceding Rules of Exchange,

Table of the value of several pieces of Coin in the Fed-

erai Coin, and the several Currencies of the U, States, 138

Cross Multiplication or Duodecimals

139

Single Rule of Three Direct,

The method of making taxes,

150

Rule of Three Direct, in Vulgar Fractions,

154

To find the value of Gold in the Currency of the Nevi-

england States and in Virginia,

Rule of Three Direct in Deciinals,

153

Rule of Three exemplified in several Questiuns relat.

ing to the Federal Coin,

161

Reciprocal Proportion, or Rule of Three Inverse,

Abbreviation of Vulgar Fractions,

166

Compound Proportion, or, Double Rule of Three, 167

Comparison of Weights and Measures,

10

Conjoined Proportion,

171

Arbitration of Exchanges,

173

Single Fellowship,

174

Double Fellowship, or, Fellowship with Time, 178

Fellowship by Decimals,

18

Practice,

182

Form of a Bill of Parcels,

Tare and 'Tret,

ib.

Involution,

Table of Powers,

Evolution, or the extracting of Roots,

Extraction of the Square Root,,

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