PROBLEMS: with the Methods of tracing the Figures on the Ground.. 236 Of measuring angles with the Protractor, Line of Chords, and Sector 241 ARITHMETIC. 1. A RITHMETIC is the science of numbers, or the art of computing by means of the ten numeral digits, or figures; o cipher, 1 one, a two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine. All numbers may be denoted by those figures variously combined. And the rule which teaches their different values according to their different places, is called NOTATION, or NUMERATION. LET the number 444444444444 be proposed: then the different values of the same figure 4 will be as follows: The first figure on the right stands for four units, being its simple value; the next for four lens, or forty, or ten times its simple value; the third for four hundreds, or a hundred times VOL. 1. j's simple value; the fourth for four thousands, or a thousand times its simple value, &c. and the four together or 4444 denote four thousand four hundred and forty four. Hence it appears that the values increase from the right to the left in a decuple proportion, each figure standing for ten times the value of the preceding one. It is also evident that in reading of numbers there is a constant repetition of hundreds, tens, and units, at every three figures: thus, the three first on the right denote four hundred and forty-four; the next three, four hundred and forty four thousands; the next three, four hundred and forty-four millions; and the next three, four hundred and forty-four thousands of millions, &c. Therefore in reading of large numbers, if we divide them into periods of six figures each, the first period to the right will be units, tens, hundreds, and thousands; the next period will be millions; the next millions of millions, or bi-millions, or billions; the next tri-millions or trillions, &c. &c. For example, let 12$02110007815104906709 be a proposed number: 12802 410007815104 906 7 0 Then dividing it into periods as above, it will be read thus: twelve thousand eight hundred and two trillions, four hundred ten thousand and seven billions, eight hundred and fifteen thousand one hundred and four millions, nine hun-· dred and six thousand, se.eu hundred and nine. 3. The digits 1, 2, 3, 4, 5, 6, 7, 8, 9, are called significant figures, because each has a value by itself, but the cipher or zero o stands for nothing if alone; when annexed however, on the right hand to other figures, or any number, it increases the value ten times: thus 7 denotes only seven, but 70 is seven tens |