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CONTENTS.

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28

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31

SECTION III.

SUBTRACTION, Mental Exercises,

Subtraction Table,

Exercises for the Slate, .

Illustration of the principle of borrowing,

Proof of Subtraction,

General Rule,

Examples for practice,

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42

45

45

46

SECTION IV.

MULTIPLICATION, Mental Exercises,

Exercises for the Slate,

Illustration of carrying in Multiplication,

General Rule,

Examples for practice,

Contractions in Multiplication,

50

56

58

62

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Position,

Ex. 107–120, 285

SECTION XII.

Ratio,

PROPORTION,

Simple Proportion or Rule of Three,

Compound Proportion, or Double Rule of Three,

286

290

293

299

SECTION XIII.

Duodecimals,

Multiplication of Duodecimals,

302

303

SECTION XIV.

Involution,

Evolution,

Square Root,

Applications of Square Root,

Demonstration of Cube Root by Cubical Blocks,

Cube Root,

306

309

313

318

321

320

SECTION XV.

Equation of Payments,

Partnership or Fellowship,

Exchange of Currencies,

Promiscuous Examples,

324

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330

334

ARITHMETIC.

SECTION I.

NOTATION AND NUMERATION.

Art. 1. Any single thing, as a peach, a rose, a book, &c., is called a unit, or one ; if another single thing is put with it, the collection is called two; if another still, it is called three ; if another, four; if another, five, &c.

The terms, one, two, three, four, five, &c., by which we designate how many single things or units are under consideration, are the names or expressions of numbers. Hence,

2. Number signifies a unit, or a collection of units.

OBs. Numbers have various properties and relations, and are applied to various computations and practical concerns of life. These properties and applications are formed into a system, called Arithmetic. Hence,

3. ARITHMETIC is the science of numbers.

Numbers are usually denoted by certain letters of the alphabet ; or by arbitrary characters called figures.

QUEST.-1. What is a single thing called ? If another is put with it, what is the collection called? If another, what? What are the terms one, two, three, &c. ? 2. What does number signify? Obs. To what are numbers applied ? 3. What is Arithmetic ? How are numbers usually denoted ?

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