SECT. II.

OF ADDITION.

ADDITION is that part of arithmetic which teaches how to add two or more numbers or fums together, in order to difcover the total, or value of the whole.

Addition of whole numbers is principally divided into two parts namely, Addition of numbers of one denomination ; and Addition of numbers of divers denominations.

....Addition of numbers of one denomination confifts in adding together fimple numbers or figures; in which it must be ftrictly observed,. that the units are to be fet directly under each other, in the fame column; the tens, in like manner, under each other; the hundreds alfo under each other; the thousands alfo, tens of thousands, and those of every degree, are all respectively to be placed in their refpective places, from the right hand, to which their rank entitles them; as in the following examples :→→

The feveral numbers to be added together being fet down in a regular order, as feen above, they are to be added together; beginning at the bottom figure on the right hand, and proceeding upwards, till you have added all the figures in one column together; then place the first figure on the right haud, or unit figure, of the fum fo found, under the fame column, carrying the remaining figure or figures, if any, to be added to the next column: having discovered the amount of the fecond column, place the unit figure alfo under,

the fame column, adding the other figure or figures to the next column, proceeding in this mauner till the whole be finished, and fetting down the total amount of the laft column under the fame.

Thus, in the first example, I say 2 and 4 is 6, and 9 is 15, and 7 is 22, and 3 is 25, and 2 is 27, and 1 is 28; this being the amount of the firft column, I fet down 8 (which is the figure in the place of units) under the fame column, and carry the remaining figure 2 to be added to the next column, faying, 2 and 2 is 4, and 5 is 9, and 4 is 13, and 1 is 14, and 3 is 17, and I is 18, and 2 is 20, the whole amount of the laft column; wherefore I fet it down under the column, and the total is thus found to be 208.

Proceeding in the fame manner, in the fecond example, I fay 5 and 4 is 9 (for the o ftands for nothing), and 3 is 12, and 9 is 21, and I is 22; wherefore, I fet down the 2 under the column, and carry the remaining 2 to be added to the next column; faying, 2 and 3 is 5, and 3 is 8, and'ı is 9, and 3 is 12, and 7 is 19, the amount of the second column; wherefore I fet down the 9 under the column, and carry the remaining figure 1 to be added to the next column, faying, I and 1 is 2, and 1 is 3, and 8 is 11, and 6 is 17, and 7 is 24, and 2 is 26, and I is 27, the amount of the last column, and to be fet under the fame; wherefore the total is 2792 (two thoufand feven hundred and ninety-two).

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In the fame manner the third example is wrought; as alfo the three following; in which the operation is purpofely omitted, for the practice of the learner.

Here it must be noted, that when the amount of any column, in any fum has a cypher in the place of units, fuch: cypher is to be placed under the column; as in the firit of: the three laft examples.

The three laft examples are proved-which is done in this manner after the total is found according to the foregoing rules, and placed in the firft of the three bottom lines, the top line of the fum is to be feparated by a line drawn under it, the remaining part of the fum caft up, and the amount of it placed under the aforefaid total; this last amount, and the top line of the fum, are then to be added together; and if the amount of these two lines be equal to the total in the first bottom line, the fum is rightly caft up; otherwise not.

All other fums in addition are to be proved in a fimilar manner, whether they be of one denomination or of divers denominations,

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Addition-of divers denominations confifts in adding together numbers of different denominations, whether they be money, weights, or measures.

Before the learner proceeds to addition of money, it is neceffary that he have the following tables by heart; called the Pence Table, and the Shilling Table.

In addition of divers denominations, thofe numbers which are of the fame denomination are always placed in the fame column, and their name or mark generally at the top: thus, in addition of money, the pounds are placed in one column, with an at the top for libra, the Latin word for pounds; the fhillings in another column, with an s at the top for folidi, the Latin word for fhillings; the pence alfo by themfelves, in another column, with a d at the top for denarii, the Latin for pence; and fometimes the farthings are placed in a separate column, with a gr. at the top for quadrans; but the most general rule is, to place them immediately after the pence," as a fraction of a penny: thus, for one fourth part of a penny, or one farthing; for one half, or a halfpenny: for three fourths of a penny, or three farthings: as in the following examples :--

In addition of numbers of divers denominations, this is the general rule: To begin at the right hand column, or the column of the least denomination; adding all the numbers in the faid column together, and obferving how many units there be in it of the next higher denomination, and how much overplus: the overplus is to be fet down under the line, and the units of the next denomination are to be added to the next column. The next column being caft up, it must

alfo be noted how many units there are in it of the next higher denomination, and how much overplus: the overplus is to be placed under its own column, and the units of the next denomination added to the next column, as before; and fo on to every new column.

Thus, in the firft of the three foregoing examples, I begin with the unit figures of the lowest denomination, which is pence, faying, 1 and 2 is 3, and 1 is 4, and 4 is 8, and 9 is 17, and 2 is 19, and 9 is 28; to which I add the tens in the fame column, faying, 28 and 10 is 38, and 10 is 48, and 10 i58; now, by the pence table, I know that 50 pence is 4 hillings and 2 pence, therefore 58 pence is 4 fhillings and 10 pence: thus, I must set down the 10 pence, which is the overplus, under the fame column; and the 4 fhillings, which are 4 units of the next higher denomination, I carry to be added to the next denomination, saying, 4 and 9 is 13, and 7 is 20, and 5 is 25, and 7 is 32, and 6 is 38, and 7 is 45; to which I add the tens, faying, 45 and 10 is 55, and io is 65, and 10 is 75: now, by the fhilling table, I find that 75 fhillings is 3 pounds 15 fhillings; the 15 fhillings are to be fet under the column of fhillings, and the 3 pounds, being units of the next denomination, viz. pounds, are to be added thereto and the pounds, being the laft and highest denomination, are to be added together as fimple numbers of one denomination, and the total placed under the fame: thus the total is found to be 52l. 155. 10d.

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In the next example I begin with the farthings, being of the lowest denomination, faying, 2 farthings and 2 is 4, and 3 is 7, and 1 is 8, and 2 is 10; 10 farthings is 2 pence and 2 farthings; the 2 farthings is to be fet under the line as overplus, and the 2 pence is to be added to the column of pence, which, added up, amounts to 43 pence, which is 3 fillings and 7 pence; the 7 pence is to be fet under the column of pence, and the 3 fhillings is to be added to the column of shillings; in which column, with the 3 added,

there is 75 fillings, or 3 pounds 15 fhillings; the 15 fhil