higher number in the table confifts of two figures, I and o; the first whereof, ftanding in the place of tens, ftands for ten, being only a figure one: the other figure, being a cypher, and in the place of units, ftands for nothing, or no units: thefe two figures, therefore, exprefs only ten. The next number confifts of the figures 432; the four being in the place of hundreds, fignifies fo many hundreds; the three, as many tens; and the two, as many units; and is thus expreffed: four hundred and thirty-two. The fourth number in the table confifts of four figures, the first whereof stands in the place of thousands; this number, therefore, is thus expreffed eight thoufand, feven hundred, and fixty-five, The fifth number has its higheft figure in the place of tens of thousands, and is thus expreffed: feventy-eight thousand, nine hundred, and nine; it having a cypher in the place of tens, which stands for nothing. The fixth number confifts of hundreds of thousands, and is thus expreffed; one bun dred and twenty-three thoufand, four hundred, and fifty-fix. The highest place of the seventh number is that of millions ; it is expreffed thus: fix million, five hundred and forty-three thousand, two hundred, and ten. The eighth number confifts of tens of millions, and is thus expreffed: fixty-feven million, eight hundred and ninety thousand, nine hundred, and eighty-feven. The ninth number has its highest figure in hundreds of millions; it is expreffed thus: three hundred and twenty-one million, twelve thoufand, three hundred, and forty-five.

The fix other numbers are expreffed as follows:-The tenth number: feven thoufand, eight hundred and ninety millions, nine hundred and eighty-feven thoufand, fix hundred, and fifty-four. The eleventh number: forty-three thousand, two hundred and ten million, one hundred and twenty-three thousand, four hundred, and fifty-fix. The twelfth number: four hundred and fifty-fix thousand, seven hundred and eighty-nine million, ninety-eight thousand, feven hundred, and, fixty-five. The thirteenth number:

nine million of millions, eight hundred and feventy-x thoufand, 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 thoufand, one hundred and twenty-three millions, four hundred and fifty-fix thoufand, feven hundred, and eighty-nine. The fifteenth number: one hundred and twenty-three million of millions, four hundred and fiftyfix thoufand, feven hundred and eighty-nine millions, ninetyeight thoufand, feven hundred, and fixty-five.

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

This method alfo affords an eafier way of enumerating numbers, than by the foregoing table, as every three figures may have a common furname appropriated to them (inserted in italics at the head of the table), befides their names of units, tens, and hundreds: thus, when the learner can enumerate the first three figures in a number, and knows the proper furname to apply to each three figures, he may enumerate any number, however large. The first three figures on the right hand have no furname, as they ftand fimply for units, tens, and hundreds; but the next three figures have the furname of thoufands; the next three have the furname of millions; the next three, thousands of millions; and the other three figures have the furname of millions of millions. 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 furname of) million of millions; four hundred and fiftyfix (with its furname) thousands of millions; feven hundred and eighty-nine (with its furname) millions; ninety-eight (furname) thoufands; fever hundred, and fixty-five.

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

are,

are, nevertheless, very imperfectly acquainted with this most effential part.

Besides the foregoing ten characters used to exprefs numbers, there are alfo letters employed for the fame purpose, called Numerical Letters. This was the ancient method of expreffing numbers, and is fill made use of frequently, in the title-pages of books, and în funeral monuments in Roman hiftory, to exprefs the date of the year.

If a letter or letters of inferior value follow one of fuperior value, they are to be added thereto; thus, VI fignify fix, VII feven, VIII eight, and DCC feven hundred. But when a letter of inferior value is placed before one of fuperior value, it is then to be deducted therefrom: thus, IV fignify 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 fums together, 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 numbers of divers denominations.

Addition of numbers of one denomination confists in adding together fimple numbers or figures; in which it muft be ftri&ly 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 thoufands, and thofe 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:→→

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 hand, 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 manner till the whole be finished, and setting down the total amount of the last column under the fame.

Thus, in the firft example, I fay 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 1 is 18, and 2 is 20, the whole amount of the last column; wherefore I fet it down under the column, and the total is thus found to be 208.**

I

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 1 is 22; wherefore, 1 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 1 is 9. and 3 is 12, and 7 is 19, the amount of the fecond column'; wherefore I fet down the 9 under the column, and carry the remaining figure i to be added to the next column, faying, "t 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 1 is 27, the amount of the laft column, and to be fet 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 alfo the three following; in which the operation is purposely emitted, for the practice of the learner.

Gallons.

Yards.