23

Row; and, if their Sum be less than ten, set it down underneath its own Place; but if it exceeds ten, the Excess is only to be set down, carrying one for every ten to the next Row, and so on, continuing to the last Row, at which set down the total Amount.

PROOF.

Vary the-adding, by beginning at the Top of the Sum, and reckon the Figures downwards, in the same Manner as you added them upwards; and if the Sum comes the same as before, it is supposed to be right.

TABLE of ADDITION,

which is to be got by Heart by those who are Beginners in

01

2 3 4 5

6

7 8

12 3

4 5 6

8

9

2

4 5

6

7

8

9

10

8

9 | 10 |

11

|

11

9 The Manner of using 10the Table is thus: Take the greater of the two Digits, whose 12 Sum is sought, in the 13 upper Line, and the

1314lesser on the Left-hand 14 | 15Column, in the same

14 | 15 | 16

Line with this; and

8

9

16 | 17

| 18

underneath the other stands the Sum.

As suppose

I wanted the Sum of 9 and 7; then I look for 9

on the Head of the Table, and in the same Line with 7, on the Left-hand Side, stands 16-the Sum.

TEACHETH to take a lesser Number from a greater, and thereby shows the Difference or Remainder.

RULE.

1 Place your Numbers according to the Direction given in Addition.

2 Begin at the Right-hand, and subtract each under Figure from that which stands over it, writing each Remainder under the Figure it proceeds from; so shall all the Remainder together express the Difference required.

3 But when the under Figure exceeds that which stands over it, you must borrow ten (the same which you stopped at in Addition), from which take the lower Figure, and to that Difference add the upper Figure and set down the Sum, always remembering to carry or add one to the next Figure on the Left-hand before you subtract.

PROOF.

To the lesser Number add the Remainder; if the Sum be like the greater, the work is right.

TABLE of SUBTRACTION.

0 1 2 3 4 5 6 7 8 9

10 12

3

41

5

6

7

8

314 5 6178

-|01|2|3

4 567

0 | 1 | 2 | 3 | 4 | 5 | 6

The Manner of using this Table is the same with that

012 345 of Addition; only,

0 1 2

01

34 instead of adding the

23

1011 2

Digits together sub

tract them.

TEACHETH how to increase any one Number by another so often as there are Units in that Number by which the one is increased, and serves instead of many Additions.,

To this Rule belong three principal Members, viz. 1 The Multiplicand, or Number to be increased or multiplied.

2 The Multiplier, or Number by which the Multiplicand is increased or multiplied.

3 The Product, or Number produced in multiplying.

Note. Before any Operation can be performed in this Rule, it is absolutely necessary that the following Table be got by heart; as the ready Performance of this and all the following Rules entirely depends upon having a perfect Knowledge of it.

TABLE.

112 3 4 5 6 7 8 9 10 11

24 | 6 | 8 | 10 | 12|14|16|18| 20 22

12

24

Seek the greater of the two Digits in the upper Line, and underneath it, against the lesser, taken in the left-hand Column, is the Product sought. Thus, to multiply 9 by 6, seek 9 in the upper Line, and under it against 6 on the left, is 54 the Product: and so of any other.

Note. For the Conveniency of dividing by 11 or 12, I have continued the Table to 12 Times, or else in Multiplication it is only required to 9 Times.

Case 1. To multiply by a single Figure.

RULE.

1 Place the Multiplier underneath the Unit's Place of the Multiplicand.

2 Multiply the Unit Figure of the Multiplicand by the Multiplier; if their Product be less than ten, set it down un

der its own Place of Units; but if their Product exceeds ten (or tens), then set down the Excess only (as in Addition), and bear (or carry) the said ten (or tens) in Mind, until you have multiplied the next Figure of the Multiplicand by the same Figure of the Multiplier, and to their product add one for each ten borne in Mind, setting down the Excess of their Sum above ten (or tens) as before; and so proceed in the same Manner until all the Figures of the Multiplicand are multiplied by the Multiplier.

PROOF.

The most sure and unerring Way is by Division. But as the Learner is supposed not yet to know that Rule, he cannot prove by it; let him therefore make the Multiplicand the Multiplier, and if the Product comes out the same as before, the Work is right.

Some Masters that teach (and several Authors that write of) Arithmetic, prove Multiplication by the Cross. But this Method is not to be depended upon, as it will prove a Sum to be right, when at the same Time the Work is utterly false. But it will not prove a Sum false that is right.

Case 2. When the Multiplier consists of several Figures.

RULE.

1 Place each Figure in the Multiplier respectively under its own Kind in the Multiplicand.

2 Multiply the Multiplicand by each Figure of the Multiplier (as before), observing to place the first Figure of each