One is written
Two is written
Three is written
Four is written
Five is written
Six is written
Seven is written

Eight is written

Nine is written

123456899

7

These nine figures are sometimes called the 9 digits. By

But as it

And so on to ten tens, which were written with ten crosses. was found inconvenient to express numbers so large as seven or eight, with marks as represented above, the X was cut in two, thus X, and the upper part was used to express one half of ten, or five, and the numbers from five to ten were expressed by writing marks after the V, to express the number of units added to five.

Six was written
Seven was written-
Eight was written

Nine was written

VI

VII

VIII

VIIII

The intermediate numbers between the tens were expressed by writing the excess above even tens after the tens.

Eleven was written

Twelve was written

Twenty-seven was written

XI

XII, &c.
XXVII, &c.

To express ten Xs, or ten tens, that is, one unit, of the third order, or one hundred, three marks were used, thus, C. And to avoid the inconvenience of writing seven or eight Xs, the C was divided, thus E, and the lower part L used to express five Xs, or fifty.

To express ten hundreds, four dashes were used, thus, M. This last was afterwards written in this form CƆ and sometimes CIƆ, and was then divided, and Ɔ was used to express five hundreds.

These dashes resemble some of the letters of the alphabet, and those letters were afterwards substituted for them.

The resembles the I; the V resembles the V; the X resembles the X; the L resembles the L; the C was substituted for the [; the resembles the D; and the M resembles the M.

these nine characters all numbers whatever may be express

ed.

To express ten, we make use of the first character 1. But to distinguish it from one unit, it is written in a new place, thus 10; the 0, which is called zero or a cipher, being placed on the right. The zero 0 has no value, it is used only to occupy a place, when there is nothing else to be put in that place.

Twenty-four

*XXIIII

One thousand

M

One thousand, eight hundred, and twenty-six MDCCCXXVI

A man has a carriage worth seven hundred and sixty-eight dollars; and two horses, one worth two hundred and seventy-three dollars, and the other worth two hundred and forty-seven dollars; how many dollars are the whole worth?

These numbers may be written as follows:

Operation.
DCCLXVIII dolls.

CCLXXIII dolls.
CCXXXXVII dolls.

MCCLXXXVIII dolls.

1

To add these numbers together it is easy to see that it will be the most convenient to commence on the right, and count the Is first. We find eight of them, which we should write thus VIII, but observing that

*It is usual to write four IV, instead of IIII, and nine IX, instead of VIIII, and forty XL, instead of XXXX, and ninety XC, instead of LXXXX, &c. in which a small character before a large, takes out its value from the large. This is more convenient when no calculation is to be made. But when they are to be used in calculation, the method given in the text is best.

Eleven is written thus, 11, with two 1s.

The 1 on the

eft expresses one ten; and the one on the right expresses one unit, or one added to ten. Twelve is written 12; the

1 on the left signifies one ten, and the 2 on the right signifies two units, and the whole is properly read ten and two.

there are more Vs we set down only III, reserving the V and counting it with the other Vs. Counting the Vs we find two, and the one which we reserved makes three. Three Vs are equivalent to one X and one V. We write the V and reserve the X. Counting the Xs, we find seven of them, and the one which was reserved makes eight. Eight Xs are equivalent to LXXX. We write the three Xs and reserve the L. Counting the Ls, we find two of them, and the one which was reserved makes three. Three Ls are equivalent to CL. We write the L and reserve the C. Counting the Cs, we find six of them, and the one which was reserved makes seven. Seven Cs are equivalent to DCC. We write the CC and reserve the D. Counting the Ds we find one, and the one which was reserved makes two. Two Ds are equivalent to M. The whole sum therefore is MCCLXXXVIII dollars.

The general rule for addition, therefore is, to begin with the characters which express the lowest numbers and count all of each kind to gether without regard to their value, only observing that five Is make one V, and that two Vs make one X, and that five Xs make one L, &c., and setting them down accordingly.

A man having one hundred and seventy-eight dollars, paid away Seventy-nine dollars for a horse; how many had he left?

Operation.
CLXXVIII dolls.
LXXVIIII dolls.

To perform this operation we begin at the right hand, and take the Is from the Is, the Vs from the Vs, &c. But a difficulty immeLXXXXVIIII dolls. diately occurs, for we cannot take IIII from III; it is necessary therefore to take the IIII from VIII, that is, from IIIIIIII, which leaves IIII; these we set down. Since we have used the V in the upper line, it will be necessary to take the V in the lower line from one of the Xs, that is from VV. V from VV, leaves V, which we set down. Having used one of the Xs, there is but one left. We cannot take XX from X, we must therefore use the L, which is equivalent to five Xs, which, added to the one X, make XXXXXX; from these we take XX and there remain XXXX, which we set down. Since the L in the upper line is already used, it is necessary to take the L in the lower line from the C which is equivalent to LL; one L taken from these, leaves L, which we set down. The whole remainder therefore is LXXXXVIIII dolls.

Hence the general rule for taking one number from another, expressed by the Roman characters, is, to begin with the characters expressing the lowest numbers, and take those of the same kind from each other, when practicable, but if any of the numbers to be subtracted exceed those from which they are to be taken, a character of the next highest order must be taken, and reduced to the order required and joined with the others from which the subtraction is to be made. This process is called subtraction,

The following is the manner of writing the numbers from nine to ninety-nine, inclusive.

The first column contains the figures, the second shows the proper mode of expressing them in words and the way in which they are always to be understood, and the third contains the names which are commonly applied. The common names are expressive of their signification, but not so much so as those in the second column.

Two tens and one.
Two tens and two.
Two tens and three.
Two tens and four.
Two tens and five.
Two tens and six.
Two tens and seven.
Two tens and eight.
Two tens and nine.
Three tens.

Three tens and one.
Three tens and two.
Four tens.
Four tens and one.
Five tens.

Five tens and one.

Six tens.

Six tens and one.

Seven tens.

Seven tens and one.

Eight tens.
Eight tens and one.

Sixteen.
Seventeen.
Eighteen.
Nineteen.
Twenty.

Twenty-one.
Twenty-two.
Twenty-three.
Twenty-four.
Twenty-five.
Twenty-six.
Twenty-seven.
Twenty-eight.
'Twenty-nine.
Thirty.
Thirty-one.

Thirty-two.
Forty.

Forty-one.
Fifty.
Fifty-one.
Sixty.
Sixty-one.
Seventy.
Seventy-one.

Eighty
Eighty-one.

Nine tens and nine or ninety-nine is the largest number that can be expressed by two figures. If one be added to nine tens and nine, it makes ten tens, or one hundred. To express one hundred we use the first figure again; but in order to show that it has a new value, it is put in another place, which is called the hundreds' place. The hundreds' place is the third place counting from the right. One hundred is written, 100; two hundred is written, 200; three hundred is written, 300. The zeros on the right have no value; their only purpose is to occupy the two first places, so that the figures 1, 2, 3, &c. may stand in the third place.. The figures in the second place, we observe, have the same value whether the first place be occupied by a zero or by a figure for example, in 20 and in 23 the 2 has precisely the same value; it is two tens or twenty in both. In the first there is nothing added to the twenty, and in the second three is added to it.

It is the same with figures in the third place. They have the same value, whether the two first places are occupied by zeros or figures. In 400, 403, 420, and 435, the 4 has the same value in each, that is four hundred. The value of every figure, therefore, depends upon its place as counted from the right towards the left. A figure standing in the first place signifies so many units; the same figure standing in the second place signifies so many tens; and the same figure standing in the third place signifies so many hundreds. For example, 333, the three on the right signifies three units, the three in the second place signifies three tens or thirty, and the 3 in the third place signifies three hundreds. The number is read three hundreds, three tens, and three, or three hundred and thirty-three. We have seen

that all the numbers from ten to twenty, from twenty to thirty, &c. are expressed by adding units to the tens; in the same manner all the numbers from one hundred to two hundred, from two hundred to three hundred, &c. are expressed by adding tens and units to the hundreds.—For example, to express five hundred and eighty-two, we write five hundreds, eight tens, and two units thus, 582.