The description and use of two arithmetick instruments together with a short treatise, explaining and demonstrating the ordinary operations of arithmetick, as likewise a perpetual almanack and several useful tables : presented to His most excellent Majesty Charles II ... / by S. Morland.

CHAP: IV. The Precept for DIVISION in Plain Numbers.

DIVISION, is in effect nothing else, but the de∣ducting of a less number as oft as may be out of a Greater, and so finding at last the number, by whose U∣nites that less number being repeated, makes a number equal to the Greater.

Now the greater of these numbers is Vulgarly called the Dividend, the less the Divisor, and the last the Quo∣tus or Quotient.

The method of this Operation is thus;

1. Set the Figures of the Divisor under an equal num∣ber of Figures of the Dividend on the left hand, if those Figures of the Dividend be of greater, or at least of equal value with those of the Divisor: Otherwise you must place the first Figure of the Divisor under the second Fi∣gure of the Dividend. And having set the Divisor right, put pricks over the Figures of the Dividend, from the Unite place of the Divisor, inclusivè. And the number of pricks denote the number of places in the Quotient.

2. You must evermore prepare such a Tariffa (or Ta∣ble of Multiplication) for the Divisor, as is here set down on one side of the Operation, and is of excellent use, making the work ten times more easie and certain.

3. You must find by the Tariffa how many times the Divisor is found in those Figures of the Dividend under which they are placed, and the answer to that, is the first Figure of the Quotient; by which you have multiplied the Divisor in the Tariffa, then deduct the product out of those upper Figures of the Dividend, and what remains must be considered in the next operation, if there be more pla∣ces then one in the Divisor.

4. The next Figure of the Dividend must be taken down and set next to the Remainder, if there be any. And the Divisor must be again set under it, if the value

of the upper Figures be sufficient; if not, there must a Null or (0) be set in the Quotient, and then the next Figure of the Dividend taken down, and the very same Operation repeated, till the work be at an end. But one Example in things of this nature clearly and distinctly set down, is better then a thousand verbal directions.

Let the Dividend be that Number, which was last found by Multiplying (426) by (327)

That is to say, Let the Dividend be And the Divisor be 〈 math 〉〈 math 〉

Having pointed the Dividend, and pla∣ced the Divisor un∣der (1393;) look for 1393 (or the nearest number to it) in the Tariffa, which is 1308. wherefore I set that down; and sub∣tracting it from 1393, there remains 85; then (having set down 4 for the first Figure of the Quotient) I take down the next Figure, or Cypher of the Dividend, viz. (0) which makes it (850) In this (327) the Divisor by the aforesaid method is found twice; wherefore I set (2) in the Quotient, and then deduct the Product, viz. (654) out of it, and there remains (196) to which in the last place, I take down (2) the last Figure of the Dividend, and make it (1962) in which (327) is found 6 times, and so the work is at end.

The reason of this Operation is plain in the subsequent Table.

	C M	X M	M	C	X	U
	1	3	9	3	0	2	Dividend.
		3	2	7			Divisor, which is advanced 3 places, and is not now 327. but 32700.
Quot. 400.	1	3	0	8			This Product is not 1308, but 130800, which is 4 times 32700, that is 420 times 327, which is the Quotient in the Margent.
			8	5			That is 32700 being deducted out of 130800, the remainder is 8500, and so is ended the first Operation.
			8	5	0		Here begins a second Operati∣on. And this is not 850, but 8500.
			3	2	7		This is not 327 but 3270, which being doubled makes 6540, which in effect is 20 times 327, as is exprest by the Quotient in the Margent.
Quot. 20.			6	5	4
			1	9	6		That is, 6540, being deducted out of 8500, there remains 1960, and so ends the second Operation.
			1	9	6	2
				3	2	7	Here 327 is brought down to its own value again.
Quot. 6.			1	9	6	2	That is 6 times 327 is just e∣qual to 1962, and so the work is at end.
			0	0	0	0

But now if this Dividend had been greater by 20 Unites, that is, if it had been (139322) the work had been the same, and the Quotient had been the same num∣ber of Integers, but there had been found remaining a broken part of Fraction of 20. which must have been be set thus 20/327