TABLE OF SIGNS WITH THEIR NAMES AND SIGNIFICATIONS. the parallel lines, equal; as 12d. 18. =3 + the perpendicular cross, plus, more, or addition; as - 6 + 4 = 10. the straight line, minus, less, or subtraction; as 10-46. > the oblique cross, multiplication; as 6 x 4 = 24. ÷ the horizontal line between two points, or between two numbers, denotes division; 24 ÷ 46, or 24 6. )(the inverted parenthesis, division; as 4)24(6.. :::: proportion; as 2:4 :: 4 : 8. = denotes square root; as √4 = 2, √16 = 4, etc. cubic root; as 8 = 2, √273, the fourth root, or biquadrate root; 813,256 4, etc. 64 = 4, etc. as 16 = 2, V the vinculum, drawn over several quantities, shows that they are to be considered as one; as 4+6-2, i. e. 8. .. the triangular points—therefore, or consequently. READ: 246; 6-2=4; 6 × 4 = 24; 24÷4=6; 8+ 2-3 × 4÷7=4; 36 = 9; 43 = 12. DEFINITIONS. Unil. One, or 1. Integer. A whole number; as 1, 3, 6, 20, 44, etc. Fraction. A broken number, or part of a unit: as,, one fourth; one half; 3, three fourths, etc. .9, nine tenths; .09, nine hundredths, etc. Decimal Fraction. A fraction whose denomination is tenths, hundredths, etc.: as, .6, six tenths; .06, six hundredths, etc. Vulgar Fraction. A fraction that may have any number for its denominator: as, 1, 4, 8, etc. Odd Number. One that cannot be divided by 2 without a remainder: as, 3, 5, 7, 9, etc. Even Number. One that may be divided by 2 and leave no remainder: as, 2, 4, 6, 8, etc. Prime Number. One that has no exact divisor except itself and unity as, 3, 5, 7, 11, etc. Composite Number. One that is the product of two other numbers, called factors: as, 16, the product of 4X4; 32, the product of 8X 4, etc. Abstract Number. One that denotes a thing, or number of things, in general. Applicate Number. One that denotes some particular thing, or things: as, 3 lbs., 3 yds., 10 feet, etc. TO THE TEACHER.-If in any case the teacher should find that it is not necessary for the scholar to do all the work in this book, he will, of course, tell him what may be omitted. TO THE SCHOLAR.-You must not expect always to find the answers expressed in this book; in many cases, the process of proving the work is so simple and profitable for you, that it is best you should find out by that means whether your work is correct. ARITHMETIC. From Arithmetica, (Latin.) ARITHMETIC is the science that treats of Numbers, and the various operations that may be performed with them. There are five principal or fundamental rules in Arithmetic, viz.: Notation or Numeration, Addition, Subtraction, Multiplication, and Division. NOTATION AND NUMERATION. 1. Notation teaches to form or write numbers. Notation from Nota, (Latin.) 2. Numeration teaches to read written numbers. Numeration from Numerus, (Latin.) 3. The figures we use in numbering are: 1, one; 2, two; 3, three; 4, four; 5, five; 6, six; 7, seven; 8, eight; 9, nine; and 0, naught, or cipher. 1, 2, 3, 4, 5, 6, 7, 8, 9, are called significant figures; Ō is called an insignificant figure. They were first used by the people of Arabia. They were introduced into Europe A. D. 991, and from Europe they were brought to this country by the first settlers. With these all other numbers are formed. The cipher is used to fill up places unoccupied by other figures. 4. Each figure has two values: First, Its own individual value. Secondly, A value according to the place it occupies. Thus-9, nine; 90, ninety; 900, nine hundred, etc. .9, nine tenths; .09, nine hundredths; .009, nine thousandths, &c. 5. Figures increase in value from the right to the left in a tenfold proportion; as, ten units make ten, ten tens make a hundred, ten hundreds make a thousand, etc. In decimals, ten thousandths make one hundredth, ten hundredths make one tenth, ten tenths make one unit, etc. What is Arithmetic? How many and what are the fundamental rules of arithmetic? What does notation teach? What numeration? What figures do we use in numbering [3]? Who first used these figures? What is the use of the cipher? How many values has each figure [4]? What are they? How do figures increase [5]? The United States currency might properly be denominated "The Decimal Currency;" for the ratio is the same: 10 mills make one cent, 10 cents make one dime, 10 dimes make one dollar, and 10 dollars make one eagle. (See the Table, page 16.) The scholar should particularly notice the point or separation between the integers and decimals. This must never be omitted when there are decimals. After Trillions, notation proceeds in the same manner with Quadrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, etc. 6. In learning the above table, the scholar should sayUnits, nine; units, tens, ninety-nine; units, tens, hundreds, nine hundred and ninety-nine, etc. The whole table reads thus-Nine trillions, nine hundred and ninety-nine billions, nine hundred and ninety-nine millions, nine hundred and ninety-nine thousands, nine hundred and ninetynine; and nine hundred and ninety-nine thousandths, nine hundred and ninety-nine millionths. 7. When the scholar has sufficiently studied the table, he should practice in reading other numbers. Name all the places for What is said about "The United States Currency"? whole numbers in the table, beginning with units. places. What comes after trillions? What is the 3d place in whole numbers called? The 6th? The 9th? The 12th? The 1st? The 4th? The 7th? The 10th? The 13th? The 2d? The 5th? The 8th? The 11th? What is the 1st place in decimals called? The 4th? The 2d? The 5th? The 3d? The 6th? For what does 6 stand in the 2d place? In the 5th place? In the 8th place? In the 11th place? In the 1st place? In the 4th? In the 7th? In the 10th? In the 13th? In the 3d? In the 6th? In the 9th? In the 12th? In the 1st place in decimals? In the 4th? In the 2d? In the 5th? In the 3d? In the 6th ? READ 9. 99. 49. 89. 289. 2289. 67894. 946742. 4867894. 94862678. 948948629. 4004. 80400. 80404. 404. 90001. 670006. READ-9.9 99.9 462.26 8644.264 94086. 94862.672 48648.4867 8. Now try if you can write numbers. WRITE-Four. Forty-four. Six hundred and forty-four. Nine thousand, four hundred and forty-four. Twenty-four thousand, four hundred and sixty-eight. WRITE-Six hundred and fifty, and four tenths. Ten thousand, four hundred and eighty-six, and twenty-six hundredths. Six dollars and twenty-five cents. Eight dollars and seventyfive cents. Twenty-four dollars and thirty-seven cents. Two hundred and twenty-eight dollars and thirty-seven cents. Eight thousand dollars, twenty-eight cents, and four mills. NOTE. I have given the French method of notation, as that has by common consent been adopted in this country. The English method divides the nota tion into periods of six figures. For more exercises in reading and writing numbers, use the BLACKBOARD. ADDITION. From Addo, (Latin.) ADDITION TABLE. DIRECTIONS FOR USING THIS TABLE.-Find one of the numbers which you wish to add, in the left-hand column, and then run your eye along to the right till you come directly under the number in the top line which you wish to add to it, and you will have the sum or answer, as 2 and 6 are 8. |
