ARITHMETIC:

FOR

THE USE OF SCHOOL S.

WITH NUMEROUS EXAMPLES.

BY THE REV. T. G. HALL, M.A.
PROFESSOR OF MATHEMATICS IN KING'S COLLEGE, LONDON.

PUBLISHED UNDER THE DIRECTION OF

THE COMMITTEE OF GENERAL LITERATURE AND EDUCATION,
APPOINTED BY THE SOCIETY FOR PROMOTING

CHRISTIAN KNOWLEDGE.

LONDON:

PRINTED FOR THE

SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE;
SOLD AT THE DEPOSITORY,

GREAT QUEEN STREET, LINCOLN'S INN FIELDS;

4, ROYAL EXCHANGE; 16, HANOVER STREET, HANOVER SQUARE;

AND BY ALL BOOKSELLERS.

ARITHMETIC.

INTRODUCTION.

I. ARITHMETIC, derived from a Greek word, signifying a number, teaches the knowledge and use of numbers. Numbers are of two kinds-whole numbers, and fractions. Whole numbers are such as, one, five, ten, a hundred, a thousand. Fractions (or broken numbers) are such as, a half, a third, a fourth, or three fourths. Of these fractions we shall have something to say by and by, but now we will attend only to whole numbers.

II. A little consideration will show that we always count by tens, and the reason of this is, that there are ten fingers on the two hands; the two thumbs being called fingers; from this circumstance, the first ten numbers are called digits, digit being taken from a Latin word signifying finger. The names of the first ten numbers are One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten. The names of the next two are Eleven and Twelve, which mean, leave one, and two leave; for if you had to count eleven pebbles, you would first count ten, and leave one; if there were twelve pebbles, you would, after counting ten, leave two. It is from the Latin word for pebble that we have our word calculate, for calculus is the Latin for a pebble.

Next to twelve comes thirteen, then fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty. Thirteen means three and ten; fourteen, four and ten; fifteen, five and ten, and so on; twenty means twice ten; after twenty, we say twenty-one, twenty-two, or twenty and one, twenty and two, and thus to twenty-nine, and the next number is thirty, or thrice ten. After thirty we count as we did from twenty, till we come to forty, or four tens; then to fifty, or five tens; and so on to a

B