High School Arithemtic

divisor and quotient-Why the number of decimal places in the dividend can-
not be taken less than the number in the divisor-Why the Os are prefixed, in
supplying deficiencies in the quotient.

The quotient of a less integer divided by a greater, how represented (153)--

If the less integer be then divided by the greater, decimally.

CHAPTER VII-PAGE 123.

TABLES OF MONEY, WEIGHTS, AND MEASURES.-REDUCTION OF MONOMIALS,

POLYNOMIALS, AND CURRENCIES.

Measuring Units (154)-Different Orders of measuring units (155)—Measuring

units in Federal Money,-their scale of increase (156)-Measuring units in other

kinds of quantity-English or sterling Money (157)—Troy Weight (158)—Avoir-

dupois Weight (159)-Apothecaries Weight (160)-Dry Measure (161)—Beer

Measure (162)-Wine Measure (163)-Linear or Long Measure (164)-Cloth

Measure (165)-Square Measure (166)—Cubic or Solid Measure (167)-Circular

Measure (168)-Measure of Time (169)—Names of the months-Number of

days in each month-The solar year (170)—how much longer than the common

civil year-How this error in the account of time is corrected-Rule adopted

to preserve the civil in agreement with the solar years.

REDUCTION OF MONOMIALS AND POLYNOMIALS

PAGE 129.

A monomial quantity (171)—A polynomial quantity (172)—Terms of a-polyno

mial-What monomials and polynomials have usually been called.

Reduction Descending (173).

RULE XXXIII. To reduce a quantity to a LOWER DENOMINATION (174).

What each lower term in a Polynomial must be added to, in reducing to a lower

denomination-Integers in the successive products, in reducing a monomial

fraction to a lower denomination.

Reduction Ascending (175).

RULE XXXIV. To reduce a quantity to a HIGHER DENOMINATION (176).

What each higher term in a Polynomial must be added to, in reducing to a

higher denomination-Remainders which occur, in reducing a monomial integer

to a higher denomination.

Another method of Reducing a Polynomial to a Fraction of a higher denomi-

nation (177).

A polynomial reduced-to the Denomination of either of its terms (178)-Cubic

Measure reduced to Gallons, Bushels, &c. (179).

The coin or specie of a country (180)―The gold coins of the United States-

the silver-the copper-The coins of one country as money in other countries
(181) The Currency of a country (182)-The fineness of gold, how expressed
(183) Standard Purity and Weight of United States' coins (184)—Alloy of the
gold coins-of the silver coins-the copper coins-Weight of the eagle--of the
dollar-of the cent-Use of the alloy in the gold and silver coins.

The Federal currency of the United States, when established (185) -Currency

of the States at that time-States in which $1-6 s., 8s. 7 s., 43 s.-States in

which 1 s. = 163 cts.., 12} cts., 133 cts., 21 & cts.-How the shilling is valued in the

new States.

The English pound sterling (186)—Its intrinsic value-Its marketable value.

RULE XXXV. (1) To reduce Federal to English Money; (2) To reduce English

to Federal Money (187).

CHAPTER VIII.-PAGE 141.

ADDITION, SUBTRACTION, ETC., of MONOMIALS AND POLYNOMIALS.-DUO-

DECIMALS.

Whether any dissimilar Monomials may be added or subtracted (188).

RULE XXXVI. To add or subtract DISSIMILAR MONOMIALS in the same kind

of measure (189).

n Multiplication, how the multiplier is to be considered (190)—in Division,

when the answer required is the number of times the dividend contains the

divisor, or the part the dividend is of the divisor (191).

ADDITION, &C., OF POLYNOMIALS.-PAGE 143.

How Polynomials in the same kind of measure, might be added, &c. (192)—

When Polynomials are added, &c., under the Polynomial form, what the oper-

ations are usually called.

RULE XXXVII. For Polynomial or Compound Addition (193).

RULE XXXVIII. For Polynomial or Compound Subtraction (194).

Subtracting a prior from a later date (195)-Of the interval of time thus found

(196)

RULE XXXIX. For Polynomial or Compound Multiplication (197).

RULE XL. For Polynomial or Compound Division (198).

When the divisor and dividend are both polynomials.

DUODECIMALS,

And their Application to Square and Cubic Measure.-PAGE 153.

Duodecimals (199)- Primes, seconds, thirds, &c.-How these denominations

are denoted-Primes in linear measure (200)-Seconds in square measure (201)

-Thirds in cubic measure (202)-Square measure, how found (203)-Cubic

measure, how found (204)—Product of two duodecimal terms (205)—Reduction, ̧

Addition, &c., of Duodecimals (206)-What distinct case occurs here.

RULE XLI. For Duodecimal or Cross Multiplication (207).

CHAPTER IX.-PAGE 159.

ALIQUOT PARTS.-ANALYSIS.-CANCELLATION.-RATIO.-PROPORTION.

ALIQUOT PARTS.

An aliquot part of a quantity (208)-ANALYSIS in Arithmetic (209)-CANCEL-
LATION in Arithmetic (210)-In the Analysis of questions, how the given num-
bers may often be placed (211).

RATIO.-PAGE 163.

The Ratio of one quantity to another (212)-What the antecedent and conse-

quent together are called-Whether the antecedent and consequent must be in

the same denomination, in finding their ratio (213)-What quantities have no

ratio to each other-Sign of Ratio (214)-Ratio expressed by a fraction-Direct

and Inverse Ratio (215)-Ratio of Reciprocals (216)-The term ratio when

used alone-The ratio of two Fractions having a common denominator (217)- - Of

'wo Fractions having a common numerator.

PROPORTION.-PAGE 165.

Proportion, in what it consists (218)-Four quantities in proportion-The
antecedents in a proportion-the consequents. The two extremes-the two means
Fourth proportional-A direct proportion (219)—An inverse proportion—The
term proportion when used alone.

VARIATION (220)-When one term varies directly as another-When one term

varies inversely as another-What variation is sometimes called-Sign of Pro-

portion (221)-Inverse converted into Direct proportion (222)-Product of the

Extremes equal to that of the Means (223).

RULE XLII. To find a FOURTH PROPORTIONAL to three given terms (224).

An inverse fourth proportional, how found-The first and second terms, how

used-When the third term is a polynomial-The fourth term found in what

kind of quantity, and in what denomination.

Why the fourth term in a proportion is equal to the product of the second

and third, divided by the first-Why the first and second terms must be used in

the same denomination.

Of the application of Proportion (225)-Proportion involved in multiplication