Quadrans, which in Latin signifies the fourth part of any thing.

Suppose a Tradesman wishes to know the amount of seven Bills, drawn from his books; he writes down the several sums as below;

Total of this last and the 1st. line £. 530 07

2

In this operation the several denominations must be placed under one another, observing that units come under units, tens under tens, &c.: then beginning with the column of Farthings, on the right hand, say 3 and 1 are 4, and 2 are 6, and 3 are 9, and 1 are 10. Now here are 10 farthings, and as 4 farthings are 1 penny, 8 will be 2 pence, and there will be 2 farthings over: or 10 qrs. will be equal to 2d. 2 qrs. Then in the column of farthings write the 2, and carry on the 2 pence to be added to the column of pence, saying, 2 and 4 are 6, and 8 are 14, and (going first up the units) 7 are 21, and 9 are 30, and 6 are 36, and 1 are 37. Write this number on one side of your paper, and then count up the figures in the tens column, thus, 1 and 1 are 9, and write down 2 under the 3 of the 37, which will make 57 pence. But as 12 pence make 1 shilling, 24 pence will be 2 shillings, 36 pence 3 shillings, 48 pence 4 shillings, and 57 pence, being 9 pence more than 48, the whole sum will be 4 shillings and 9 pence.

This sum 9 must therefore be written in the units' place of the pence column (filling up the tens' place, either with a dot or a nought, for uniformity's sake), and carrying the 4 shillings to the column of shillings, begin with the units' place, saying, 4 and 3 are 7, and 9 are 16, and 2 are 18, and 8 are 26, and 3 are 29, and 8 are 37: then write on one side the 7, and carrying the 3 to the ten's column, say, 3 and 1 are 4, and 1 are 5, and 1 are 6, and 1 are 7, and 1 are 8: This 8 written on the left hand of the 7 will make 87 shillings: but as 20 shillings are 1 pound, 40 shillings will be 2 pounds, 60 shillings 3 pounds, and 80 shillings 4 pounds, 87 shillings will therefore be 4 pounds 7 shillings. The 7 shillings are then to be written in the units' place of the shillings column, (filling up the tens' place with a nought or a dot as before), and the 4 pounds must be carried on, to be added to the units' place of the column of pounds, saying, 4 and 2 are 6, and 5 are 11, and 9 are 20, and 5 are 25, and 2 are 27, and 9 are 36, and 4 are 40. This column consisting of integers of the highest denomination, it is to be added up, as the simple integers given in the former examples; by which the sum of the several Bills will be found to be £. 530.. 07s. ogd... 2qrs. which was required to be done. Το prove the of Addition of sums of money, or any other complex numbers and quantities, the same methods are used, as those pointed out for checking addition of integers.

accuracy

Again, if it be required to add together a number of quantities expressing what is called Averdupois weight; it must be observed, that

The following example will show how addition of such quantities is performed; where T. means Tons, Cwt. Hundred weight, Qrs. Quarters, Lbs. Pounds weight, Oz. Ounces, Dr. Drams.

The column of Drams amounts to 60, equal to 3 ounces and 12 Drams, which last sum is written in the column, and the 3 Ounces being carried to the next column, make it amount to 54 Ounces, equal to 3 Pounds and 6 Ounces over. These 6 ounces are written in the column, and the 3 Pounds are carried to the following column, making it 103 Pounds, or 3 Quarters and 19 Pounds. Writing down 19 in the Pounds Column, the 3 Quarters are carried on and added to the column for that denomination, which thus amounts to 13 Quarters, equal to '3 Hundred weight, and 1 Quarter over. Enter this Quarter in the proper column, and proceed with the 3 Hundreds to the column of that denomination, which will then amount to 65 Hundreds, equal to 3 Tons and 5 Hundreds; which last sum being written in its due place, the 3 Tons added to the column of Tons, will give a total of 802 Tons. To ascertain this addition, cut off, by a line, the first row of quantities, and add the remaining 4 rows together, producing a total which when

added

added to the first row, will, if the operation be correct, give a total equal to that found by the addition of all the five rows of quantities.

In the practice of keeping accounts, it frequently happens that the whole of an account can not be contained in one page or folio of the book; when this is the case, the custom is to sum up the contents of that page or folio, and write it down at the bottom of the coluinn, with the words Carried forward opposite to the sum; and the same sum or total is entered at the top of the money column of the subsequent page or folio, with the words Brought forward, leading to it. In this manner each preceding page is summed up, and the amount made the first article in the following page, until the account is closed, when the amount of the last page, as comprehending all the particular totals of the preceding pages, is to be considered as the total amount of the whole account.

OF SUBTRACTION.

Subtraction means that branch of calculation by which we find the difference between two given quantities; or agrecably to the meaning of the term, by which we draw a less sum from a greater, and so discover what quantity will be left as a remainder.

Although Subtraction be an operation, directly opposite to Addition, yet the numbers must be placed under one another as before; that is, the small number must be written under the great, and beginning at the units or first figures on the right hand, which may for instance be 8 and 5, we say if from 8 units, such as pounds, yards, &c, we take away 5, there will remain 3: or the difference between 5 and 8 is 3. Again, when one figure of the least number

happens

happens to be greater than the corresponding figure in the great number, as in subtracting 37 from 65; as it is impossible to take 7 units out of 5, we borrow, as it is called, 1 ten from the place of tens in the great number, and add it to the 5, thereby making 15; from which if we subtract or take away 7, the remainder will be 8. This 8 is accordingly written under the place of units, and the operation proceeds in this way. By borrowing the ten from the place of tens, the figure 6, may be supposed to be reduced to 5: we have then to subtract the 3 of the less number from the 5 of the greater, and the remainder or difference will be 2; that is in all 98. Or instead of taking 1 away from the 6, if we repay or add 1 to the 3, standing under it, we shall' have 4, which again being subtracted from 6 will leave 2 as before.

The Subtrahend or less number being written under the Minuend or greater, observing to place units under units, tens under tens, &c, we begin at the right hand, saying, if from 7 men 5 be taken away, 2 will remain behind: this 2 therefore is written in the column of units. Again, if from 8 be taken 6, 2 will remain: Then from the third figure of the greater sum 1, we should take away 3; but this is impossible; we must therefore borrow 1 from the next figure on the left hand 2, which, if the 1 be considered as occupying the place of units, will become a ten, which 10 being added to the 1 will make 11. From this sum 11 we can subtract, as was first proposed, the 3, and the remainder will be 8, which is also written in its due place. Having borrowed 1 from the 2 in the fourth place of figures, this 2 comes to be reckoned as 1, and from it, as has just been done, we subtract the 5, by borrowing another ten from the