10. An army consists of 52714 infantry, or foot, 5110 horse, 6250 dragoons, 3927 light horse, 928 artillery, or gunners, 1410 pioneers, 250 sappers, and 406 miners: what is the whole number of men? Ans. 70995.

OF SUBTRACTION.

SUBTRACTION is the finding how much one number exceeds another, by taking the less from the greater.

7. Sir Isaac Newton was born in the year 1642, and he died in 1727: how old was he at the time of his decease?

Ans. 85 years.

Christ 1847 the birth of Ans. 733 years.

8. Homer was born 2580 years ago, and years ago: then how long before Christ was Homer?

9. Noah's flood happened about the year of the world

1656, and the birth of Christ about the

how long was the flood before Christ?

year 4000: then Ans. 2344 years.

10. The Arabian or Indian method of notation was first known in England about the year 1250: then how long is it since to this present year 1847? Ans. 597 years.

11. Gunpowder was invented in the year 1330: how long was that before the invention of printing, which was in 1441? Ans. 111 years.

12. The mariner's compass was invented in Europe in the year 1302: how long was that before the discovery of America by Columbus, which happened in 1492? Ans. 190 years.

OF MULTIPLICATION.

MULTIPLICATION is a compendious method of Addition, teaching how to find the amount of any given number when repeated a certain number of times; as, 4 times 6, which is 24.

The number to be multiplied, or repeated, is called the Multiplicand. The number you multiply by, or the number of repetitions, is the Multiplier. And the number found, being the total amount, is called the Product. Also, both the multiplier and multiplicand are, in general, named the Terms or Factors.

9 18 27 36 45 54 63 72 81 90 9 99 108

225

33 44 55 66 77 88 99

12 24 36 48 60 72 84 96 108 120 132 144

99 110 121 132

OF DIVISION.

DIVISION is a kind of compendious method of Subtraction, teaching to find how often one number is contained in another, or may be taken from it, which is the same thing.

The number to be divided, is called the Dividend.-The number to divide by, is the Divisor.-And the number of times the dividend contains the divisor, is called the Quotient. Sometimes there is a Remainder left, after the division is finished.

In the operation of Division a change might advantageously be made, for if any number, 787695, be to be divided by 5, the operation ought to stand thus : —

Ex. 3. Let 648314 be divided by 7.

648314 92616+ 926162.

7

In this process the only difference from the common method is, that a logical equality is preserved, which may be useful in leading the pupil gradually to higher acquirements. Before a pupil is much troubled with long division, it is desirable to let him learn fractions and decimals; and at the same time also pay great attention to the solution of simple equations in algebra. By oral instruction he should also be made to thoroughly understand the meanings of square numbers and square roots, &c., with the signification of areas and solids. But every thing must be quietly and slowly explained in the simplest way, and the chief part of the instruction be given in classes, and no rules used but only principles.

Ans. 8049611787.

11. Divide 4637064283 by 57606.

12. Suppose 471 men are formed into ranks of 3 deep, what is the number in each rank? Ans. 157.

13. A party, at the distance of 378 miles from the headquarters, receive orders to join their corps in 18 days: what number of miles must they march each day to obey their orders? Ans. 21.

14. The annual revenue of a nobleman being £37960; how much per day is that equivalent to, there being 365 days in the year? Ans. £104.

OF REDUCTION.

REDUCTION is the changing of numbers from one name or denomination to another, without altering their value. This is chiefly concerned in reducing money, weights, and mea

sures.

When the numbers are to be reduced from a higher name to a lower, it is called Reduction descending; but when contrarywise, from a lower name to a higher, it is called ·Reduction ascending.

Before we proceed to the rules and questions of Reduction, it will be proper to set down the usual tables of money, weights, and measures, which are as follow: