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EXPLANATION of the CHARACTERS made use

of in this BOOK.

Signs. Names.

Significations. + Plus, or more, The sign of Addition, as 6+2 is 8.

Minus, or less, The sign of Subtraction, as 6 — 2 is 4. S Multiplied? The sign of Multiplication, as 6x2 is X { into or by S 12.

Divided by, The sign of Division, as 6-2 is 3.

Equal to, The sign of Equality, as 6+2=8.
: S Is to,

The Signs of Proportionals, as 2 : 4 :: 6:12.
Sois,
Extraction ? The Square Root of 9=3 is /9=3, and

of the Roots, the Cube Root of 8=2 is V3=2. 6-4X9=18; signifies, that 6, less 4, multiplied by 9=18. N. B. 82 vienotes that s is to be squared.

93 denotes that 9 is to be cubed.
34, or 4), denotes the Cube Root of the Num-

ber 4.

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The Twelve SIGNS of the ZODIAC. go Aries, the Ram.

14 Libra, the Balance. 8 Taurus, the Bull. m Scorpio, the Scorpion. II Gemini, the Twins. f Sagittarius, the Archer. o Cancer, ihe Crab.

Le Capricornus, the Goat. r Leo, the Lion,

Aquarius, the Water-bearer. in Virgo, the Virgin. * Pisces, the Fishes.

TUTOR'S GUIDE;

BEING

A COMPLETE SYSTEM OF ARITHMETIC.

BOOK I.

Arithmetic in Whole and Compound Numbers.

INTRODUCTION. ARITHMETIC is the science or knowledge of Numbers, which is either Unit, or a multitude of Units.

Upit is any thing considered as one, or 1.

Digits, or Figures, are the marks by which Numbers are denoted or expressed, and are the nine following, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9: with these there is used the mark 0, called a Cipher, which of itself stands for nothing; but being annexed to the right-hand of a Digit, alters its value; thus, 40 signifies forty, and 400 stands for four hundred, &c. (See the following Table.)

Integers, or whole Numbers, are such as express a Number or multitude of things, whereof each is considered as an Unit. Thus, 6 Pounds, 12 Yards, 140 Miles, &c. each of which is called an Integer, or whoie Number.

Compound Numbers are such as consist of different denominations, as Pounds, Shillings, Pence, and Farthings; or Hundreds, Quarters, Pounds, Ounces, &c.

Thus 471. 12s. 64d. or 4C. 2grs. 14lb. &c.

A Fraction, or broken Number, is always less than Unit, as represents three quarters of any thing or Unit, and is six eighths of Unit, or 1, &c.

Arithmetic, with regard to art and science, consists both in Theory and Practice.

Theory considers the nature and quality of Numbers, and demonstrates the reason of practical operations.

The Practice is that which shows the method of working by Numbers, so as to be the most useful and expeditious for

B

TRACTION.

business, and has five principal or fundamental Rules for the operation; viz. 1. NUMERATION, or NOTATION. 2. Addition., 3. SUB

4. MULTIPLICATION. 5. Division.

Sect. I. NUMERATION TEACHETH to read or express the true value of any Number when written down; and consequently to write down any proposed Number, according to its true value; and this consisteth of two parts:

1. The due order of placing down Figures.

2. The true value of each Figure in its place; both of which are plainly exhibited in the following

TABLE.

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EXAMPLES. Write down the Value of the following Numbers in Words at length, viz. (1) 94

(6) 6040390 (2) 762

(7) 47639121 (3) 3024

(8) 790401950 (4) 37460

(9) 79041955 (5) 142613

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In Figures, express (1) Seventy-seven. (2) Four hundred and ninety.

(3) Six thousand and fifty-five. (4) Seventeen thousand seven hundred and nine. (5) Eight hundred thousand and two. (6) Seven millions forty-four thousand and seventy-four. (7) Six hundred and ninety-four millions four hundred thousand and sixty.

NOTATION

by Roman Numerical Letters. One, five, ten, fifty, hundred, five hundred, thousand. I, V, X, L, C,

M. When a lesser numerical letter stands before a greater, it must be taken from it; as, I before V or X; and X before L, or C, &c. Thus,

four, nine, forty, ninety, &c.

IV, IX, XL, XC. When a lesser numerical letter stands after a greater, it is to be added to it. Thus,

six, eleven, sixty, one hundred and ten.
VI, XI, LX,

CX. A Line drawn over any number less than a thousand signifies so many thousands; as LX, is sixty thousand; C, is one hundred thousand; M, is one Million, &c.

Write down in common Figures the following Numbers, expressed in numerical letters, viz. XIX, CC, DC, DEX. MI, MDCCL, LXX, CX, MD, and MDC.

Write down in numerical letters the following Numbers, expressed in common Figures, viz.

29, 104, 419, 1741, 2007, 17678, 10004, and 674084.

II. ADDITION of INTEGERS TEACHETH to add sundry Numbers together into one Sum, called the Total.

RULE. 1. Place all the Numbers of a like name under another; that is, units under units, tens under tens, hundreds under hundreds, &c. 2. Begin with the Units, and singly collect the Sum of each

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