All solids, or things that have length, breadth and depth, are measured by this measure. N. B. The wine gallon contains 231 solid or cubic inches, and the beer gallon, 282. A bushel contains 2150,42 solid inches. 13 months, 1 day and 6 hours, 1 Julian year, mo. yr. Thirty days hath September, April. June, and November, February twenty-eight alone, all the rest have thirty-one. N. B. In bissextile, or leap vear, February hath 29 days. 12. Circular Motion. 30 seconds (") make 60 minutes, 30 degrees, 1 minute, 1 degree, 1 sign, 3. 12 signs, or 360 degrees, the whole great circle of the Zodiac. Explanation 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 5, is equal to 12. The sign of Division; as 8÷2=4, signifies that divided by 2, is equal to 4; or thus, =4, each of which signify the same thing : Four points set in the middle of four numbers, denote them to 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 numoer, 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, &c. 15 ARITHMETIC. ARITHMETIC is the art of computing by numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and Divi sion. 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 the second place, or NOTE. Although a cypher standing alone siguifies nothing; yet when it is placed on the right hand of figures, it increases their value in a tenfold proportion, by throwing them into higher places. Thus 2 with a cypher annexed to it, becomes 20, twenty, and with two cyphers, thus, 200, two hundred. 2. When numbers consisting of many figures, are given to be read, it will be found convenient to divide them into as many periods as we can, of six figures each, reckoning from the right hand towards the left, calling the first the period of units, the second that of millions, the third billions, the fourth trillions, &c. as in the following number: 80 7 3 6 2 5 4 6 2 7 89012506792 4. Period of 3 Period of 2. Period of 1. Period of Trillions. 8073 Billions. 625462 Millions. 789012 Units. 506792 and The foregoing number is read thus-Eight t seventy-three trillions; six handred and twenty-five thou sand, four hundred and sixty-two billions, seven eighty-nine thousand and twelve millions; five hundred and six thousand, seven hundred and ninety-two. N. B. Billions is substituted for millions of millions. Qtrillions for millions of millions of millions of millions &c. place of tens, it becomes so many tens, or ten imes its simple value, and in the third place, or place of hundreds it becomes an hundred times its simple value, and so on, as in the following TABLE: Millions, Tens, C. of Millions, X. of Millions, Units, C. of Thousands, Thousands, Hundreds, X. of Thousands, 1 - One. 21 3 21 Three hundred twenty-one Four thousand 321. 4 3 2 1 17 million 654 thousand 321. 1 8 987 million 654 thousand 321. 123 million 456 thousand 789. 987 million 654 thousand S48. To know the value of any number of figures. RULE. 1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds &c. as in the Nuineration 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. 54026, Fifty-four thousand and twenty-six 123461, One hundred and twenty-three thousand four hundred and sixty-one. 4666240, Four millions, six hundred and sixty-six thousand two hundred and forty. NOTE. For convenience in reading large numbers, they may he divided into periods of three gures eacn, as follows: 987, Nine hundred and eighty-seven. 987 000, Nine hundred and eighty-seven thousand. 987 000 000, Nine hundred and eighty-seven million. 987 654 521, Nine hundred and eighty-seven million, six hundred and fifty-four thousand, three hundred and twenty-one. To write 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. EXAMPLES. Write down in proper figures the following numbers : Thirty-six. Two hundred and seventy-nine. Thirty-seven thousand, five hundred and fourteen. Nue millions, seventy-two thousand and two hundred. 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 1C dollars |