76. The time, rate per cent., and amount being given, how find the principal?

77. The principal, time, and interest being given, how find the rate per cent.?

78. The principal, interest, and rate per cent. being given, how find the time?

79. What is a partial payment? Indorsement?

80. What is discount?

How find it?

Present worth of a debt?

81. What is a bank? Bank discount? Days of grace?

Bank note? Nego

82. What is a promissory note? Bank note?

tiable note?

83. What is a notary-public? A protest?

84. What is exchange? How many kinds?

85. What is domestic exchange? Foreign exchange? 86. What is a set of exchange? Course of Exchange? 87. What is equation of payments?

What is direct ratio? Inverse or reciprocal?
What is proportion?

90.

91.

What is ratio?

Define each kind?

92.

What is the antecedent? Consequent?

93.

94.

95.

96.

97.

Which are the extremes? The means?

Of what does allegation treat?

How many kinds of allegation? Define each.

98. What is involution? Evolution?

99.

100.

ΙΟΙ.

I02.

What is a surd?

What is the square root of a number?
What is the cube root of a number?
What is arithmetical progression?

103. What is geometrical progression?

4. A unit or a collection of units. The power of a number is the product produced by repeating a number any number of times as a factor. A root is a factor repeated to produce power.

5. A whole number.

6. An abstract number is one used without reference to any particular thing. A concrete number is one that has reference to a particular thing.

7. A character indicating an operation to be performed. The sign of aggregation is a parenthesis, or bar, which shows that the numbers enclosed by it are to be considered together subject to the same operation.

8. A rule is a prescribed method of performing an operation. A problem is something to be done. An axiom is any truth that is self-evident.

9. The process of investigating principles, and solving problems, independently of set rules.

IO.

Notation is a method of writing or expressing numbers by characters. Numeration is a method of reading numbers expressed by characters.

II. Two: the Roman anu Arabic.

12. Upon five principles: first, repeating a letter repeats its value; second, if a letter of any value is placed after one of greater value, it is added to the greater; third, if a letter of any value is placed before a greater, it is to be taken from the greater; fourth, if a letter of any value is placed between letters of higher value, it is to be taken from their united values; fifth, if a bar or dash is placed over a letter, it increases its value a thousand-fold.

13. The simple value of a figure is its value when taken alone, while the local value depends upon the place it occupies with other figures.

14. Notation and numeration, addition, subtraction, multiplication, and division.

15. The minuend is the number to be subtracted from. The subtrahend is the number which is subtracted.

16. One that can be produced by multiplying two or more numbers together.

17. The several numbers, which, being multiplied together, produce the number.

18. The number itself, or the root.

The second power,

or square, is the number multiplied by itself. The third power, or cube, of a number, is the product arising from using the number three times as a factor.

19. It is I divided by that number.

20.

Multiply each partial remainder except the first, by all the preceding divisors, and add these products to the first remainder. It will be noticed that after the first division, the remainder cannot be of the same denomination as the first number divided; and as each succeeding division increases the value of the remainders, therefore each remainder must be multiplied by all the preceding divisors to reduce it to its former denomination.

21. One that cannot be resolved into factors. Numbers are prime to each other when they have no common divisor.

22. One that will divide two or more numbers without a remainder. The greatest common divisor is the greatest number that will divide two or more numbers without a remainder.

23. A multiple is a number that is exactly divisible by a given number. A common multiple is one that is exactly divisible by two or more numbers. The least common multiple is the least common multiple that is exactly divisible by two or more given numbers.

25. The quotient of the numerator divided by the denominator.

26. The denominator shows into how many parts a number is divided; the numerator shows how many parts are taken.

27. A proper fraction is one whose numerator is smaller than its denominator. An improper fraction is one whose numerator is equal to or greater than its denominator. A mixed number is one expressed by an integer and fraction written together. A complex fraction is one that has a fraction in its numerator, or denominator, or both.

28. For convenience; if not inverted they must be reduced to a common denominator, and one numerator divided by the other.

29. Find the greatest common divisor of the given numerators, and the least common multiple of the denominators.

30. Find the least common multiple of the numerators, and the greatest common divisor of the denominators.

31. Fractions whose denominators are increased or decreased in ten-fold ratio.

32. Write the multiplier with the order of its figures reversed, and with units' place under that figure of the multiplicand which is the lowest decimal to be retained in the product. Find the product of each figure of the multiplier

by the one above in the multiplicand and those to the left, increasing this multiplication by as many units as would have been carried had the rejected part of the multiplicand been used. Write these partial products with the lowest figure in the same column and add together, pointing off the required number of decimal figures.

33. Compare the left hand figure of the divisor with the units of like order in the dividend, and determine how many figures will be required in the quotient. For the first contracted divisor, take as many figures from the left of the divisor as there are places required in the quotient, and in each following division reject one place from the right of the last preceding divisor, using the remainder for a new dividend.

34. A decimal in which a figure or set of figures are continually repeating.

35. The figure or set of figures continually repeated. 36. A fraction whose numerator is 1, and whose denominator is a whole number, plus a fraction whose numerator is also 1, and whose denominator is a similar fraction, etc.

37. The first has a denominator understood, showing that a unit is divided into ten equal parts, or sub-divided in a ten-fold ratio; the second has a denominator showing that a unit is divided into any number of equal parts.

38. The medium of circulation.

39. From the initial letters of the United States, U. S. joined together as a monogram.

40.

Such a part as will exactly divide that number. 4I. A written statement of articles bought or sold, together with price of each and the whole cost.

42. A concrete number, whose value is expressed in two or more different denominations.

43. That by which extent, dimension, capacity, or amount is ascertained. Measures are of seven kinds: