The number of years fince any event happened, may be discovered by fubtracting the date of the year the event hap.

pened from that of the prefent year. Thus :

Subtraction of divers denominations is performed upon the fame principle as fubtraction of numbers of one denomination. Obferving, that when an unit is borrowed of the next higher denomination, it must be confidered according to its true intrinfic value, and must be repaid to the lower figure of the fame denomination; as will be feen in the following examples :

In the first of thefe examples, beginning with the farthings, I fay, 3 farthings from 2 I cannot, but borrowing an unit from the next denomination, or I penny from the 9 pence (and which added to the 2 farthings makes 6 farthings), I say, 3 farthings from 6 farthings and there remains 3 farthings, which I fet under the farthings; then for the unit I borrowed of the pence, I add 1 to the 6, saying 6 and 1 is 7; now 7 from 9 and there remains 2; then 10 from 14 and there remains 4; laftly, 10 from 17 and there remains 7; thus the remains is 71. 45. 24d. which is proved in the example.

In the fecond example, I say, 1 farthing from 3 and there remains 2 farthings, or an halfpenny; which I fet down in its proper place, viz. under the denomination of farthings; then 9 from 7 I cannot, wherefore borrowing 1 fhilling from the 14, and adding it to the 7 pence, which makes 19 pence, I fay, 9 from 19 and there remains 10; then I that I borrowed

rowed and 19 is 20, 20 from 14 I cannot, wherefore I borrow 1 pound from the pounds, which, added to the 14, makes 34 fillings; therefore, I fay, 20 from 34 and there remains 14; then 1 that I borrowed and 1 is 2, 2 from 3 and there remains ; and 1 from 2 and there remains 1: thus, the anfwer to this fum is 117. 145. 1947; and its proof, under the anfwer, fhews that it is right.

If the money paid be paid at feveral times, the fums fo paid are to be added together, and the total fubtracted from

Thefe examples, and all others of other denominations, are wrought in the fame manner as fubtraction of money; having respect to the table belonging to the denomination: thus, in the firft example of avoirdupois weight, I fay, take 21 pounds from 20 I cannot, wherefore I borrow 1 quarter of an hundred from the 3 quarters, and add it to the 20, which makes 48 pounds; then I fay, 21 from 48 and there remains 27; next, 1 that I borrowed and 2 is 3, 3 from 3 I cannot, wherefore I fet down o, as before hinted; laftly, 10 from 12, and there remains 2.

The figures at the head of the columns fhew the number of units which each unit of the next higher denomination contains.

SECT. IV.

OF MULTIPLICATION.

MULTIPLICATION is, perhaps, the moft neceffary rule in arithmetic for bufinefs, on account of its dispatch in refolving feveral long questions.

Multiplication teaches how, from two given numbers, to find a third, that shall contain either of the two given numbers as often as the other contains units: thus, 3 times 4 is 12; here 3 and 4 are the two given numbers, and 12 is the third number, or product, which contains 3 as often as 4 contains units, viz. 4 times; or it contains 4 as often as 3 contains units, 3 times.

VOL. I

There are three ends principally to be answered by multiplication

First. It ferves to bring the greater denominations of money, weights, or meafures, into fmall ones; as, pounds into fhillings, pence, and farthings; hundred weights into pounds, ounces, or drams; miles iuto yards, feet, barley-corns, &c. Secondly. Having the length and breadth of a plain furface, we find its contents.

Thirdly. Having the rate or value of any one thing, we know the rate or value of any number of fuch things, however great.

But before the learner can begin this rule, it is abfolutely neceffary that he have the following table perfectly by heart:

The ufe of this table is, to find the product of any two numbers: thus, to find the product of 6 times 7, I look in the brace which has 6 at the point, and in the line which has 7 at the beginning, opposite to which is the product, which is 42.

Beginning with the first brace, I fay-2 times 2 is 4, 2 times 3 is 6,2 times 4 is 8 2 times gris ro, 2 times 6 is 124 2 times 7 is 14, 2 times 8 is 16, 2 times 9 is 18,2 times ro is 20,22 times 11 is 22, 2 timès 1zásr241 to pretesti gita Da

Then, proceeding in the fame manner, I begin with the fecond brace, faying, 3 times 3 is 9,3 times 4 is 2,3 times 5 is 15, 3 times 6 is 18, 3 times 7 is 21, 3 times 18 is 24, 3* times g is 27, 3 times 10 is 30, 3 times is 335 3 times (125

Again, I begin with the third brace, faying, 4 times 4 is 16, 4 times 5 is 20, 4 times 6 is 24, 4 times is 28,4 times 8 is 32, 4 times 9 is 36, 4 times ro is 40,4 times s449 4 times 12 is 48.

Then, I fay, 5 times 5 is 25, 5 times 6 is 30, 5 times 7 is 35, 5 times 8 is 40,5 times is 45,5 times rois 50,05 times 11 is 55, 5 times 12 is 60,10 21 15 cílanco riqi um 9.'1

Then, 6 times 6 is 36, 6 times 7 is 42, 6 times 8 is 48, 6: times 9 is 54, 6 times 10 is 60, 6 times 1 is 66,b6stimes 12. is 723 kur kasino

1 10 21

Then, 7 times 7 is 49, 7 times 8 is 56, 7 times 9 is 63, 7 times rois 70, times 11 is 77, 7 times 12 is 84. rito. Then, 8 times 81is 64, 8 times 9 is 2, 8 times 10 is. So, 8 timės 1 ï is 88, 8 times 12 is 96.

9

Again, 9 times 9 is 8r; 9 times 10 is 90, 9 times 11 is 99, times 12 is 108.

Then, 10 times 10 is 100, 10 times 11 is 110, 10 times 12

And 11 times 11 is 121, 11 times 12 is 132.

Laftly, 12 times 12 is 144.

T 2

In