CHAP. III.

OF VULGAR ARITHMETIC.

SECT. I.

NOTATION OF NUMBERS.

ARITHMETIC is the most neceffary of all the fciences. From hence we may account for the perfection to which this part of literature is brought, above any other branch of mathematical science.

Notation, strictly speaking, is that part of arithmetic which teaches how to write any number by its proper charafters, or figures, and confequently in their due places; alfo to read, or discover, the true value of such number, when written.

All numbers, and the various combinations of them, are noted by these ten characters, tone, 2 two, 3 three, 4 four, 5 five, 6 fix, 7 feven, 8 eight, 9 nine, o cypher or nothing.

Each of thefe characters, when ufed alone, ftands for no more than its own intrinfic value: thus, 1 ftands only for one in number, 2 for only 2, &c. But when any of them are joined to other figures, they together ftand for more than their own real feparate value: thus, 1 and 2, joined together thus, 12, ftands for twelve; 6 and 5, joined together, ftands for 65, fixty-five, &c.

In order to discover the value of any compounded num ber it must be obferved, that a number placed in the first place towards the right hand, ftands for no more than its real intrinsic value, but increases in value in a tenfold proportion by every remove towards the left hand: thus, in the number 1799, the first figure 9 ftands for 9 only; the fecond figure being in the fecond place towards the left hand, its value is increased tenfold; thus it reprefents ninety, or ten times nine; which, with the foregoing 9, ftands for ninetynine. Again, the figure 7, which ftands in the third place towards the left hand, is increased to ten times as much as it would be if it stood in the next inferior place, viz. where the laft-mentioned 9 ftands: thus it reprefents feven hundred; which, with the two fore-mentioned figures, ftand for feven hundred and ninety-nine. The figure 1, which ftands in the fourth place, towards the left hand, is alfo increafed ten times. in value to what it would be if it ftood in the next inferior place, where the 7 is placed; in which cafe it would repréfent one hundred; whereas, in the prefent inftance, it stands for one thousand; and with the other figures represents one thoufand, feven hundred, and ninety-nine.

This defcription of the four foregoing figures may ferve to give the uninformed an idea of the value of figures, according to the different places they occupy in a compounded number. For every remove of a figure towards the left hand increases its value to ten times as much as before; as will more fully appear by the following table, called the Numeration

Table:

In order to read any number with facility and ease, it is neceffary that the learner have all the names of the numbers at the head of the table perfectly in his memory, that he may apply them to any other number he may have occasion for; calling the first figure, on the right hand, units; the fecond, -tens; the third, hundreds; the fourth, thousands; &c. as in the table.

Thus, the bottom figure in the table, ftanding under the place of units, is itfelf an unit, or a fingle one.

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