Socius mercatoris: or The merchant's companion: in three parts. The first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. The second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. The third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. By John Mayne, philo-accomptant.

MULTIPLICATION.

MVltiplication is a kind of Addition, and resolveth Questions to be performed by Addition in a different manner: In order where∣unto, it is necessary the Learner do well ac∣quaint himself with this Table; the having this Table perfectly by heart, will make both this Rule and Division also very facile, other∣wise they will be both troublesome and unplea∣sant.

1	2	3	4	5	6	7	8	9	10	11	12
2	4	6	8	10	12	14	16	18	20	22	24
3	6	9	12	15	18	21	24	27	30	33	36
4	8	12	16	20	24	28	32	36	40	44	48
5	10	15	20	25	30	35	40	45	50	55	60
6	12	18	24	30	36	42	48	54	60	66	72
7	14	21	28	35	42	49	56	63	70	77	84
8	16	24	32	40	48	56	64	72	80	88	96
9	18	27	36	45	54	63	72	81	90	99	108
10	20	30	40	50	60	70	80	90	100	110	120
11	22	33	44	55	66	77	88	99	110	121	132
12	24	36	48	60	72	84	96	108	120	132	144

In the first Rank of this Table, you have an Arithmetical Progression from 1 to 12,

and also in the first Column toward the left hand downwards. This Table doth at first sight exhibit the Sum of any number, so often repeated as you shall require, provided the numbers do neither of them exceed 12.

Multiplication hath three Members, thus called, a Multiplicand, a Multiplicator, and a Product: The Multiplicand, is the number to be repeated; the Multiplicator, is the number of times the first is to be repeated; and the Product, is the Sum of the Multiplicand so often repeated. As for Example.

A Countrey-man sold 6 Bushels of Wheat for 5 s. how many Shillings ought he to receive?

By Addition 6 must be 5 times set down thus: 〈 math 〉〈 math 〉

Or 5 six times repea∣ted thus: 〈 math 〉〈 math 〉

But by Multiplication it is done thus:

6 The Multiplicand.

5 The Multiplicator

Now if you look in the Table precedent, in the first Column find 5, then look in the first Rank for 6, and cast your Eye down to their Angle of meeting, and you will find 30 standing under 6 and against 5, I then con∣clude that 5 times 6 is 30; that is called the Product, and they will stand thus:

6 The Multiplicand.

5 The Multiplicator.

30 The Product.

But when you have a number to multiply, greater than any in the Table, as for Example:

A Gentleman having forborn his Rent of a Farm, at 157 l. per Quarter, for 3 Quarters, what ought he to receive?

The Multiplication will stand thus:

157 The Multiplicand.

3 The Multiplicator.

471 The Product.

I then say, 3 times 7 is 21, I set down 1 and carry 2; then, 3 times 5 is 15 and 2 is 17, I set down 7 next the 1, and carry 1; saying, 3 times 1 is 3 and 1 is 4, as in the Example before-going; and the Product is 471 l.

There is yet more variety, of which take these Examples following.

If 65 Ships do carry 536 Men in every Ship, how many Men will there be in all?

〈 math 〉〈 math 〉

I say 5 times 6 is 30, set down 0 and carry 3; then 5 times 3 is 15 and 3 is 18, set down 8 and carry 1; then 5 times 5 is 25 and 1 is 26, which I set down: Then for the next Fi∣gure, I say, 6 times 6 is 36, I set down 6 one place short of the former rank, and carry 3; then 6 times 3 is 18 and 3 is 21, set down 1 and carry 2; again, 6 times 5 is 30 and 2 is 32, these I set down: Then draw a line, and cast them up as they are placed, and the Sum is the Product and Answer to the Question, viz. 34840 Men.

In Multiplication, always make the lesser Number the Multiplicator, for it is all one whether I multiply 5 by 15, or 15 by 5, the Product is always the same.

If 128 Men of War have each made 746 Shot, how many Shot were made in all?

〈 math 〉〈 math 〉

Begin as before with the Unites place, and say, 8 times 6 is 48, set down 8 and carry 4; 8 times 4 is 32 and 4 is 36, set down 6 and carry 3; then 8 times 7 is 56 and 3 is 59, which set down: Then go forward with the 2, (but remember to place your remainder one Figure short of the former) saying, 2 times 6 is 12, set down 2 under the 6 and carry 1; 3 times 4 is 8 and 1 is 9, which set down; twice 7 is 14, which set down: Also then, once 6 is 6, which place under the 9; once 4 is 4, which set under the 4; and once 7 is 7, which set under the 1: Then cast th•••• up, as in Addition, and the Sum is the Product, and answers the Question, viz. 95488 Shot.

If any number be to be multiplied by 1 with Cyphers, it is but adding so many Cyphers to the Multiplicand as there is in the Multipli∣cator.

As for Example.

If 35678 be to be multiplied by 10, add one Cypher to the Multiplicand, thus, 356780; if by 100, add two Cyphers, thus, 3567800; &c.

And when any number is to be multiplied by any other number, that hath Cyphers an∣nexed, always place the Cyphers immediately under the Line, as in these Examples.

〈 math 〉〈 math 〉