Esplanation of Characters used in this Book. Equal to, as 12d. 1s. signifies that 12 pence are equal to 1 shilling. + More, the sign of Addition, as 5+7=12, signifies that 5 and 7 added together, are equal to 12. - Minus, or less, the sign of Subtraction, as 6-2=-4, signifies that 2 subtracted from 6, leaves 4. X Multiply, or with, the sign of Multiplication ; as 4x3=12, signifies that 4 multiplied by 3, is equal to 12. • The sign of Division; as 8:2=4, signifies that 8 divided by 2, is equal to 4 ; or thus, i=4, each of which signify the same thing. : : Four points set in the middle of four numbers, denote them tù be proportional to one another, by the rule of three ; as 2:4::8:16 ; that is, as 2 to 4, so is 8 to 16. ✓ Prefixed to any number, supposes that the square root of that number is required. ✓ Prefixed to any number, supposes the cube root of that number is required. ✓ Denotes the biquadrate root, or fourth power, &e. , 3 ARITHMETIC, ARITIMETIC is the art of computing by numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and DiviBion. NUMERATION. Numeration is the art of numbering. It teaches to express the value of any proposed number by the following characters, or figures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or cypher Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any figure in the place of units, represents only its simple value, or so many ones, but in ihe second place, or Note..--Although a cypher standing alone signifies noiliing; yet when it is placid on the right land of figures, it iicrcases their value in a ientold proportion, by throwing them into higher pinces. Tous ? with a typher anexed to it becomes 20, iweniy, and with two cyphers, thus, 200, two hundred. 2. When sumbers consisung of many rigures, are given to live read, it will be found convenirt to divide them into as many periods as we car, of -ix hgures each, reckonmg from the right hand towards the feil, calling the first the period of units, the second iliat of millions, the ihiid billioos, ile vult trillions, &c. as in the following number: 8 0 7 3 6 2 5 4 6 2 7 9 9 0 1 2 5 0 6 7 9 3 4. Period of 3. Period of 2. Period of 1. Period of Trilliin. Billions. Millr018. L'uits. 8073 789012 506792 The foregoing number is iead thus-Eight thousand and seventy-three trillions; six hundred and twenty-five thousad, for hundred and sixiy-two bil. lion8, seven biridred and tighty-nine thousand arid twelve millions ; five hundred and six thousanu seven huidred and infly.io. N. B. Billions is substituted for millions of ruillions. place of tens, it becomes so many tens, or ten times its simple value, and in the third place or place of hundreds, it becomes a hundred times its simple value, and so on, as in the following TABLE. Tens, 1 One. 3 2 1 - Three hundred & twenty-one. 14 3 2 1 - Four thousand 321. 5 4 3 2 1 - Fifty-four thousand 321. 6 5 4 3 2 1 - 654 thousand 321. 7 6 5 4 3 2 1 . million 654 thousand 321. 18 7 6 5 4 3 2 1 - 87 million 654 thousand 321. 9 8 7 6 5 4 3 2 1 - 987 million 654 thousand 321. 1 2 3 4 5 6 m 89 - 123 million 456 thousand 789. 9 8 7 6 5 4 3 4 8 - 987 million 654 thousand 348, To know the value of any number of figures. RULE. 1. Numer ate from the right to the left hand, each figare in its proper place, by saying, units, tens, hundreds, &c. as in the Numeration Table. 2. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading to the right. EXAMPLES. Read the following numbers. 365, Three hundred and sixty-five. 5461, Five thousand four hundred and sixty-one. 1234, One thousand two hundred and thirty-four. 54025, Fifty-four thousand and twenty-six. 128461, One hundred and twenty-three thousand four hundred and sixty-one. 4656240, Four millions, six hundred and sixty-six thousand two hundred and forty. Note. For convenience in reading large numbers, they may be divided into periods of three figures each, as follows: 987, Nine hundred and eignty-seven. 987-000, Nine hundred and eighty-seven thousand. 987 000 000; Nine hundred and eighty-seven million. 987 654 321, Nine hundred and eighty-seven million, six hundred aid fifty-four thousand, three hundred and twenty-one. To urile numbers. RULE. Begin on the right hand, write units in the units place, tens in the tens place, hundreds in the hundreds place, and so on, towards the left hand, writing each figure according to its proper value in numeration ; taking care to supply those places of the natural order with cyphers which are omitted in the question. EXAMPI.ES. Write down in proper figures the following numbers : Eight hundred millions, forty-four thousand and fiftyfive. SIMPLE ADDITION, IS putting together several smaller numbers, of the same denomination, into one larger, equal to the whole or sum total ; as 4 dollars and six dollars in one sum is 10 dollars RULE. &c Having placed units under units, tens under tens, draw a line underncath, and begin with the units ; afier adding up every figure in that column, consider how many tens are contained in their sum ; set down the remainaer under the units, and carry so many as you have tens, to the next column of tens; proceed in the same manner through every column, or row, and set down the whole amount of the last row. |