EXPLANATION OF CHARACTERS. = S IGNIFIES equality : as 20 shillings = I pound, signifies, that 20 shillings are equal to one pound. + Signifies plus, or addition : as, 4+2=6. - Signifies minus, or subtraction: as, 6-2=4. X Into, signifies multiplication : as, 3 X 2 = 6. By, or ) ( signifies division : as, 6÷2=3, or 2)6(3. Division may also be denoted by placing the dividend over a line, and the divisor under it: thus=6+2=3. :: .. Signifies arithmetical proportion: thus 24::6-8; here the meaning is, that 4-2=8-6=2. :::: Signifies geometrical proportion : thus 2:4::3:6, which is to be read, as 2 to 4, so is 3 to 6. Signifies arithmetical progression. Signifies continual geometrical proportion, or geometrical progression. ... Signifies therefore. Signifies the second power, or square. 73 Signifies the third power, or cube. 1TM Signifies any power. ✓ or, Signifies the square root. B \ Signifies any root of any power. NOTE. The number, or letter, belonging to the above signs of powers and roots, is called the index, or exponent. A line, or vinculum, drawn over several numbers, signifies, that the numbers under it are to be considered jointly: thus, 20-7+8=5; but without the vincu lum, 20-7+8=21. ab=aXb = the product of a and b. ARITHMETIC. 0000000円 ARITHMETIC is the art of computing by numbers, and has five principal or fundamental rules for its operations; viz. Notation, Addition, Subtraction, Multiplication, and Division. ΝΟΤΑΤΙΟΝ.* Notation teacheth how to express any proposed number, either by words or characters. To * As it is absolutely necessary to have a perfect knowledge of our excellent method of notation, in order to understand the reasoning made use of in the following notes, I shall endeavour to explain it in as clear and concise a manner as possible. First, then, it may be observed, that the characters, by which all numbers are expressed, are these ten; 0, 1, 2, 3, 4, 5, 6, 7, 8,9; 0 is called a cypher, and the rest, or rather all of them, are called figures or digits. The names and signification of these characters, and the origin or generation of the numbers they stand for, are as follow: o nothing; I one, or a single thing called an unit; 1+1=2two; 2+1=3 three; 3+1=4 four; 4+1=5 five; 5+1=6 six; 6+1=7 seven; 7+1=8eight; 8+1=9 nine; and 9+1=ten; which has no single character; and thus by the continual addition of one, all numbers are generated. 2. Beside To read NUMBERS. To the simple value of each figure join the name of its place, beginning at the left hand and reading toward the right. 2. Beside the simple value of the figures, as above noted, they have, each, a local value, according to the following law : Viz. In a combination of figures, reckoning from right to left, the figure in the first place represents its primitive simple value; that in the second place, ten times its simple value; that in the third place, a hundred times its simple value; and so on; the value of the figure in each succeeding place being ten times the value of it in that immediately preceding it. 3. The names of the places are denominated according to their order. The first is called the place of units; the second, tens; the third, hundreds; the fourth, thousands; the fifth, ten thousands; the sixth, hundred thousands; the seventh, millions; and so on. Thus in the number 3456789; 9 in the first place signifies only nine; 8 in the second place signifies eight tens, or eighty; 7 in the third place is seven hundred ; 6 in the fourth place is six thousand; 5 in the fifth place is fifty thousand; 4 in the sixth place is four hundred thousand; and 3 in the seventh place is three millions; and the whole number is read thus, three millions, four hundred and fifty six thousand, seven hundred and eighty nine. 4. A cypher, though it signifies nothing of itself, yet it occupies a place, and, when set on the right hand of other figures, increases their value in the same ten-fold proportion; thus, 5 signifies only five, but 50 is five tens or fifty, and 500 is five hundred, &c. To write NUMBERS. RULE. Write down the figures in the same order their values are expressed in, beginning at the left hand, and writing toward the right; remembering to supply those places of the natural order with cyphers, which are omitted in the question. EXAMPLES. 5. For the more easily reading of large numbers, they are divided into periods, and half periods, each half period consisting of three figures; the name of the first period being units; of the second, millions; of the third, billions; of the fourth, trillions, &c. Also the first part of any period is so many units of it, and the latter part, so many thousands. The following Table contains a summary of the whole doctrine. =I Periods. Quadril. Trill. Billions. Millions. Units. }}}}}}}}}} Half Per. th. un. th. un. th. un. th. un. cxt cxu 2=II As often as any character is repeated, so many 3=III times is its value repeated. 4=IIII or IV A less character before a greater dimin5=V ishes its value. 6=VI A less character after a greater increases its |