How do you know when the question is in direct proportion, and when in inverse? How is the operation performed in inverse proportion? PART V. What is practice, and why so called? How many cases are there in practice? When the price consists of dollars, cents, and mills, how is the operation performed? When the price is the fractional part of a dollar or cent, how is the operation performed? When the price and quantity given are of several denominations, how is the operation performed?" When the price consists of pounds, shillings, pence, and farthings, how do you proceed? What is meant by aliquot parts? When both the price of the integer and the quantity are of different denommations, how do you proceed? What is tare and tret, and what is gross and neat? How do you work questions in tare and tret? What is interest? What is the general rate of interest? What is the sum of money loaned, called? What do you understand by the amount? How many kinds of interest are there? What is simple interest? How many cases are there in simple interest? When the given time is years and the principal dollars, how is the interest found? When there are cents and mills in the principal, how do you proceed? When the time is years and months, or months only, how is the interest found? When the time is months and days, or days only, how is the operation performed? How is the interest computed on bonds, notes, &c.? What is compound interest, and how is it performed? What is insurance? What is the instrument of agreement termed ? How are the questions in insurance performed? What is commission, and how performed? What is brokage, and how performed? What is stock, and how bought and sold? What is rebate or discount, and what the rule to work questions therein? What is the difference between discount and interest? What is bank discount, and how is the discount calculated? What do you mean by the equation of payments? How is the mean time found in the equation of payments? What is fellowship, and how many kinds are there? What is single fellowship, and how is the operation performed? What is compound fellowship, and what is the rule for working questions therein? What is profit and loss, and what is the rule of operation therein? What is barter, and how performed? What is exchange, and of how many kinds? What do you understand by par in exchange, and what by agio? How do you reduce the currency of different states to federal money? How do you reduce the currency of one state to another, where it is different in them? How are accounts kept in England, Ireland, and how in France, Spain, &c.? What is alligation, and how many cases are therein? How are the operations performed in the first case, second case, &c.? PART VI. What is a vulgar fraction, and how many kinds are there? What is a proper fraction, what is an improper fraction, what is a com pound fraction, and what is a mixed fraction? What are the numbers above the line called, and also those below? How do you reduce vulgar fractions to their lowest terms? How are mixed numbers reduced to an improper fraction? How is an improper fraction reduced to a whole or mixed number? How do you reduce fractions to others that shall have a common denominator? How do you find the least common denominator? How do you find the value of a fraction, in the known parts of an integer? How are vulgar fractions added, subtracted, multiplied, and divided? How do you perform the single rule of three in vulgar fractions, direct, and inverse? PART VII. What is involution? What do you understand by the power of a number? If there be decimals in the given number, how must it be pointed? How is the square root of a mixed number extracted? How do you find the side of a right angled triangle, the other two being given? How do you find the side of a square, in any given area? How do you find the diameter of a circle, when the area is given? How do you prove the square root? What is a cube? How do you extract the cube root in whole numbers? How do you extract the cube of a vulgar fraction? How do you point off in decimal numbers? How is the cube root of a mixed number extracted? How is the cube root proved? What is progression, and how many kinds? What is principally to be ob served in arithmetical progression? How do you find the last term; and sum of all the terms? How do you find the common difference? What is geometrical progression, and how does it differ from arithmetical ? What is principally to be observed in geometrical progression? How do you find the last term, and sum of all the series? What is position, and of how many kinds? How do you resolve questions in single position? How is single position proved? What is double position? What is the rule for working questions in double position? What do you understand by permutation? How is the number of variations found in this rule? What do we learn from the results of this rule ? What is combination? How do you find the greatest possible number of combinations in any given number? PART VIII. What are duodecimals? What are the denominations in duodecimals, and what are they termed? How are duodecimals added, subtracted, and multiplied? How do you prove multiplication of duodecimals? How is the solid content of bales, &c. found by duodecimals? How do you find a ship's tonnage? What is the carpenters' rule, and what its use? How do you find the superficial content of boards, &c.? How do you find the solid content of squared timber? How do you find the solid content of round timber? What things belong to carpenters' work? By what numbers do carpenters usually measure their work? How is brick-work estimated? What is the standard thickness of a brick wall? How do you reduce a wall of a different thickness to a standard one? How is masons' work measured? What kind of measure is used for materials? How is the solid content of walls calculated? What is superficial measure? How is plasterers' work divided? In what manner is plasterers' work measured? How is white-washing In what way is the area of an oblong piece of ground ascertained? How do you calculate a piece of ground lying in the shape of an oblique |