Arithmetick: vulgar, decimal, instrumental, algebraical.: In four parts: conteining I Vulgar arithmetick, both in whole numbers and fractions, in a most plain and easie method. II Decimal arithmetick, with the ground and reason thereof, illustrated by divers examples. III Instrumental arithmetick, exactly performing all questions of what nature soever in a decimal way, by scales, with much more ease and facility then can be effected, either by vulgar or decimal arithmetick, the work of reduction being wholly avoided. Nothing in this kind having been hitherto published by any. IV Algebraical arithmetick, conteining an abridgement of the precepts of that art, and the use thereof, illustrated by examples and questions of divers kinds. Whereunto is added the construction and use of several tables of interest and annuities, weights and measures, both of our own and other countries. / By William Leybourn.

Addition.

WHat Addition is, and the manner of working of it hath been already taught, both in the first and second Parts, we will now come to an Exam∣ple, which let be in Addition of English Coin, and let the sums to be added be 36 l. 8 s. 8 d. 29 l. 0 s. 2 d. 31 l. 16 s. 9 d. and 6 l. 2 s. 5 d.

First,

36
29
31
6

set down 36 l. 29 l. 31 l. and 6 l. one un∣der another, in such order as you see here in the mar∣gent, drawing a line by the side of them as you see here done, and also a line under them.

This done, seeing that your first number to be set down to 36 l. is 8 s. 8 d. you must for the 8 s. (because two shillings, which we called a Decade, or the tenth part of a pound, is made the Integer, in the Scale of Money) set down 4, which is done by memorie, and after it make a comma. Then your next number to be set by 29 l. being 0 s. 2 d. for the 0 s.

36	4,
29	0,
31	8,
6

set down a Cypher, thirdly, for your number to be set by 31 l. being 16 s. 9 d. for the 16 s. set down 8 decades, with a comma

after it, and lastly, the number to be set by 6 l. being 2 s. 5 d. for the 2 s. I set down 1 decade with a comma after it, and then will your work stand, as here you see.

Then take your scale in hand, and seeing your first number of pence are 8 d. look in your scale of money for 8 d. and against it in the scale of 1000, you shall finde 333, which set to 36 l. 8 s. behinde the comma, then your next number of pence being 2 d. look in your scale for 2 d. and against it in the scale of 1000, you shall finde 082, which set to 29 l. 0 s. behinde the com∣ma.

36	4,	333
29	0,	083
31	8,	376
6	1,	208

Then your third number of pence being 9 d. look in your scale for 9 d. and against it in the scale of 1000, you shall finde 376, which set to 31 l. 16 s. and last∣ly, your last number of pence being 3 d. look in your scale for 5 d. and against it you shall finde 208, which set to 6 l. 2 s. and then will your whole work stand, as here you see.

Your sums being thus set down, which is done with more facilitie then you can imagine, till you make trial and be something perfect therein, you must then adde all the numbers to∣gether, as in Addition of Decimals, and you shall finde the sum of them to be 103|4,000, Now to know what this is in money, is as easie as it was to set the several sums down, for the figures 103, which stand behinde the down

right line, are 103 l. and the figure 4 which stands between the down right line and the com∣ma,

l.
36	4,	333
29	0,	083
31	8,	376
6	1,	208
103	4,	000

are 4 decades or 8 s. and being the rest to the right hand are all Cy∣phers, they signifie nei∣ther pence nor farthings, so is the total of this addition 103 l. 8 s. 0 d.

That the manner of working may appear more plain. I will give you another short Ex∣ample as difficult as I can invent, which I per∣formed by a Scale of Wood but of 8 inches long. Let the sums to be added together, be these following.

li.	t.	d.	q
332	17	4	1
159	6	8	1
217	5	3	3
709	9	4	1

First, set down your several sums of pounds one under another as before, and draw a line by the side of them,

332
159
217

and an∣other under them. So will they stand as here you see.

1 Your sums of pounds being thus orderly placed and lines drawn, repair to your Scale and seeing your first number of shillings, pence and farthings is 17 s. 4 d. 1 q. for your 17 s. set

down 8 Decads, which is 16 s. with a comma after it, then will there rest to be set down 1 s. 4 d. 1 q. or 16 d. 1 q. which if you seek in your scale of money, you shall find to stand against it in the scale of 1000 this number 677, which is the Decimal of 1 s. 4 d. 1 q.

2 Your second number of shillings pence and farthings is 6 s. 8 d. 1 q. for your 6 s. set down 3 decads, which is 6 s. and then there will re∣main 8 d. 1 q. which if you seek in your scale of money, you shall find to stand against it in the scale of 1000 this number 344, which is the deci∣mal of 8 d. 1 q.

3 Your third number of shillings, pence, and farthings, is 5 s. 3 d. 3 q. for your 5 s. set down 2 decads, which is 4 s. with a comma after it, then will there rest to be set down 1 s. 3 d. 3 q. or 15 d. 3 q. which if you seek in your scale of money, you shall finde to stand against it in the scale of 1000,

l.
332	8,677
159	3,344
217	2,656
709	4,677

this num∣ber 656, which is the De∣cimal of 15 d. 3 q. or 1 s. 3 d. 3 q. and the three sums to be added together will stand as here you see.

These sums being added together, according to the rule for Addition of Decimals, you shall finde the sum of them to be 709|4,677, now to know what this is in money, take notice that the 709 which stands to the left hand of the downright line are 709 pounds, and the figure 4,

which stands between the downright line and the comma, are 4 decads or 8 s. but (because the first figure next after the comma is above 5, viz. 6) you must add 1 s. to the 4 decads, making them 9 s.; then will there remain 177, wherefore if you look in the Scale of 1000 for 177, you shall find against it in the Scale of Money 4 d. 1 q. So is the whole sum of this Addition 709 l. 9 s. 4 d. 1 q. as by the preceding work doth appear.

¶ Here note, that when you had set down your 709 l. 4 decads or 8 s. there remained beyond the comma 677, which if you had sought in your Scale of 1000, you should have found a∣gainst it in the Scale of money 15 d. 1 q. or 1 s. 4 d. 1 q. (which is all one) as before, for it ap∣peareth plainly by the Scale that 500 in the line of 1000 is equal to one shilling.

I might proceed farther in giving you Exam∣ples in Weight and Measure answerable to the Scales, but that would only make the Reader spend his time to little purpose, for being before acquainted with Decimal Arithmetick, and (as by this time I suppose he is) with Numeration upon the Scales, he cannot be deficient in the ap∣plying of the other Scales of Weight and Measure to the same purpose for which they were contrived, I having so largely exemplified the use of the Scale of money.