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nine million of millions, eight hundred and feventy-fix thousand, five hundred and forty-three' million, two hundred and ten thousand, one hundred, and twenty-three. The fourteenth number : forty-three million of millions, two hundred and ten thonfand, one hundred and twenty-three millions, four hundred and fifty-fix thousand, feven bundred, and eighty-nine. The fifteenth number : one hundred and twenty-three million of millions, four hundred and fiftyfix thousand, leven Hundred and eighty-nine miikons, Binety. eight thousand, feven hundred, and lixty-five.

I have, in the table, distinguillred every three figures by a point, or comma, beginning at the right hand, as is generally done in public offices, and by men of extenfire bufiness.

This method alfó affords an eafier way of enumerating pembers, than by the foregoing table, as every three figures may have a common surname appropriared to them finserted in italics at the head of the table), befides their naines of units; tens, and hundreds : thus, when the learner can end. merate the first three figures in a number, and knows the proper surname to apply to each three figures, he may enumerate any number, however large. The first three figures on the right hand have no surname, as they stand fimply for units, tens, and hundreds; but the next three figures have the furname of thoufands ; tbe next three have the surname of millions ; the next three, thon fands of millions ; and the other three figures have the furname of millions of millioss. Thus, to repeat the highest number in the table, beginning at the left hand, I fay, one hundred and twenty-three (to which I add its firrname of) million of millions ; four hundred and fiftyfix (with its furname) thousands of millions ; feven brandred and eighty-nine (with its surname) millions; ninety-eight (furnaine) thoufands; feven hundred, and fixty-five.

I have been more particular in the description of the Numeration Table, as it is generally found the most difficult of all the tables in Arithmetic to a learner; and several persons who have arrived to a tolerable proficiency in this fcience,

are,

are, nevertheless, very imperfeâly acquainted with this most

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essential part.

Besides the foregoing ten characters used to express nimbers, there are also letters employed for the same purpose, called Numerical Letters. This was the ancient method of exprefling numbers, and is fill made use of frequently, in the title-pages of books, and in funeral monunents in Roman hiftory, to express the date of the year.

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I, stands for one.

CCCCCIO353, ten hunV, five.

dred thousand, or, a milX, ten.

lion. L, fifty.

The letters MDCCCVIII C, an hundreds

express the number 1808, the D, or 15, five hundred.

date of the present year M, or CII, a thousand. M standing for one thousand, 155, five thousand. D for five hundred, CCC CCIɔɔ, ten thousand. three hundred more, which is 1555, fifty thousand.

eight hundred, and VIII eight; CCCCI393, a hundred together one thousand, eight thousand.

hundred, and eight, 1503, five hundred

thousand.

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If a letter or letters of inferior value follow one of superior value, they are to be added thereto: thus, VI signify fix, VII feven, VIII eight, and DCC seven hundred. But when a letter of inferior value is placed before one of superior value, it is then to be deducted therefrom : thus, IV lignify four, IX nine, XL forty, CD four hundred, &c.

SECT.

SECT. II.

OF ADDITION.

ADDITION is that part of arithmetic which teaches how to add two or more numbers or sums togetlier, in order to discover 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 oubers of divers denominations.

Addition of numbers of one denomination consists in adding together fimple numbers or figures; in which it muft be ftrially observed, that the units are to be set directly under each other, in the fame column; the tens, in like manner, under each other; the hundreds also under each other; the thousands also, tens of thousands, and those of every degree, are all refpectively to be placed in their respective places, from the right hand, to which their rank entitles them; as in the following examples : Yos. fo

Gallons. 171

124731
239

642943
33
713

726574
812973

861413
54
135

963672

347365
208
2792

4479671

21

12

2

17 49

604 870

22

100

The several numbers to be added together being set down iu a regular order, as seen above, they are to be added together; beginning at the bottom figure on the right hand, and procecding upwards, till you have added all the figures in one column together; then place the first figure on the right hand, or unit figure, of the sum so found, under the same column, carrying the remaining figure or figures, if any, to be added to the next column: having discovered the amount of the second coluon, place the unit figure also under

the fame column, adding the other figure or figures to the next column, proceeding in this manner till the whole be finished, and setting down the total amount of the last column under the same.

Thus, in the first example, I fay 2 and 4 is 6, and g is 159 and 7 is 22, and 3 is 25, and 2 is 27, and 1 is 28; this being the amount of the first column, I ser 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, saying, 2 and 2 is 4; and 5 is 9, and 4 is 13, and 1 is '14, and 3 is 179 and's is 18, and 2 is 20, the whole amount of the last columns wherefore I set it down under the column, and the total is thus found to be 208.

Proceeding in the same manner, in the second exaniple, I fay 5 and 4 is 9 (for the o stands for nothing), and; is 12, and 9 is 21, and 1 is 22 ; wherefore, I set down the 2 under the column, and carry the remaining 2 to be added to the next column; saying, 2 and 3 is 5, and 3 is 8, and I is 9, and 3 is 12, and 7 is 19, the amount of the fecond column"; wherefore I set down the'g under the column, and carry the remaining figure i to be added to the next column, saying, " , and 1 is 2, and 1 is 3; and 8 is ri, and 6 is'17, and 7 is 245 and 2 is 26, and 1 is 27, the amount of ihe last column, and to be set under the fame ; wherefore the total is 2792 (two thousand seven hundred and ninety-two).

In the fame manner the third example is wrought; as also the three following; in which the operation is purposely omitted, for the practice of the learner. Gallons. Yards.

£.
17964017
12 794368

16729420
43706123
64368901

12090736 94218740 20107036

67342617 29991815 45736298

74298064 58997252 12469927

29020721 55122753 72970617

41739402 Total 228447.47

Total 24122001 282036083 215652779

024491540 Proof 300000700 Proof 228147147

Proof

241220960 Vob.l. R

Here

Total 300000 700

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

The three last examples are provedwhich is done in this manner : after the total is found according to the foregoing rules, and placed in the first of the three bottom lines, the top line of the fum is to be separated by a line drawn under it, the remaining part of the sum caft up, and the amount of it placed under the aforesaid total; this last amount, and the top line of the sum, 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 sum is rightly cait up; otherwise not.

All other sums in addition are to be proved in a similar manner, whether they be of one denomination or of divers denominations.

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 necessary that he have the following tables by heart; calice the Pence Table, and the Shilling Table.

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2

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Shilling Table.

£.de
20. shillings is
30

I 10
40
50

2 10

3 70

3 10 so

4 o 90

4 10 100

5

S 10." 120

6

60

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110

2

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