measure--Of Multiplying a Monomial (120).—Of Dividing a Mono-

mial (121).—Rule for Polynomial or Compound Addition (122).—Rule

for Polynomial or Compound Subtraction (123).—What of Subtracting

a prior from a later Date (124).—Rule for Polynomial or Compound

Multiplication (125).-Rule for Polynomial or Compound Division

(126).—When the Divisor is a Polynomial (127).

DUODECIMALS-What 12ths of a Foot are called, 12ths of a Prime,

12ths of a Second, &c. (128).-Linear, Square, and Cubic Inches

expressed in Duodecimals (129).--Square and Cubic Measure, how

found (130).--Product of two Duodecimal Terms, what its index

(131).—To Multiply one Duodecimal Polynomial by another (132).—

In Dividing one Duodecimal Polynomial by another, how the Index

of a quotient term may be known (133).

ALIQUOT PARTS-How the Lower Orders of Units in a Polynomial Mul.

tiplier may be regarded (134).

CHAPTER VII.

RATIO AND PROPORTION.

PAGE 167.

The RATIO of one Quantity to another of the same kind-What the

Antecedent and Consequent together are called-Use of the (:),

colon, (135).—What to be observed in finding the Ratio between two

Quantities-What Quantities can have no Ratio to each other (136).

—Direct and Inverse Ratio (137).—Comparison of Fractions (138).--

When one Quantity varies directly as another (139).—When one

Quantity varies inversely as another (140).

PROPORTION-When four quantities are in Proportion-Antecedents

and Consequents of the Ratios-Extremes and Means-Fourth Pro-

portional (141).-Direct and Inverse Proportion-How a Proportion

is denoted (142).-An Inverse converted into a Direct Proportion

(143).—Product of the two Extremes equal to that of the two Means

(144).—To find a Fourth Proportional to three given Terms (145).—~

Rule for solving Questions in Proportion (146).

PARTITIVE PROPORTION-What this Division of Arithmetic is commonly

called (147).—To Divide a given Quantity into two or more Parts

which shall have a given Ratio, one to another (148).—When a Parti

tive Proportion has respect to Different Periods of Time (149).

MEDIAL PROPORTION-What this Division of Arithmetic is commonly

called (150).—To find the Proportion of two or more Ingredients,

at Different Rates, for a Compound of a given Mean Rate of

Value (151).—Different Proportions of the same Ingredients (152).

COMPOUND RATIO (153).—A Compound Proportion-What a Compound

Proportion is applicable to (154).-Rule for solving Questions in

Compound Proportion (155).—A Conjoined Proportion (156).—Rule

for solving Questions in Conjoined Proportion (157).

CHAPTER VIII.

PERCENTAGE, AND ITS APPLICATIONS. . . . . .

PAGE 198.

PERCENTAGE-Signification of the term Percentum (158).-Ratio of

Percentage (159).—How the Ratio of Percentage is usually expressed

(160).-Basis of Percentage-What Percentage is applied to (161).—

Taxes (162).—Duties (163).—Insurance (164).—Commission (165).—

Stock or Capital (166).-To find Percentage on any given Number

(167).-How to find the Basis of Percentage (168).—To find what

Percentum one given Number is of another (169).—To find a Num-

ber to which Percentage added at a given Rate, will make a given

Sum (170).-To find a Number from which Percentage subtracted at

a given Rate, will leave a given Remainder (171).

CHAPTER IX.

INTEREST.-EQUATION OF PAYMENTS, ETC. .

PAGE 211.

INTEREST-The Principal, the Amount (172).—Legal Interest (173).—

Conventional Interest-Usury (174).—Simple and Compound Inter-

est-Whether Compound Interest is sanctioned by Law-The term

Interest and alone (175).—To Calculate Interest on any given Princi-

pal (176).—Concise Method of computing Interest for Months and

Days (177).-Method of computing the Balance due on Notes or

Bonds on which Partial Payments have been made (178).—Method

frequently adopted for computing the Balance on Accounts (179).—

Rate Per cent., or Time of Interest, how found (181).

The PRESENT WORTH of a future Debt-Discount (182).—To find the

Principal, or Present Worth of a future Debt (183).-Proceeds of a

Note in Bank (184).--To find the Principal from which the Interest,

or Bank Discount, deducted, will leave a given Sum '185).

EQUATION OF PAYMENTS (186)To find the Proper Credit for the Sum

of two or more Payments due at Different Times, without Interest

(187). When Partial Payments are made on a Debt not due, and

not bearing Interest, to find the proper Extension on the Balance of

the Debt (188).—The Equation of an Account (189).-To find the

Mean Date at which an Account may be charged, or becomes due

with the same Time on its separate Items (190).—To find the Mean
Date at which an Account becomes due, with Different Periods of
Credit on its separate Items (191).-An Account Current-In what
its Equation consists (192).-To find the Date at which the Balance
of an Account Current becomes due, or subject to Interest (193).

CHAPTER X.

POWERS AND ROOTS OF NUMBERS.-INVOLUTION AND

EVOLUTION.

PAGE 244.

The FIRST POWER of a Number-The Second Power, or Square, of a
Number-The Third Power, or Cube, of a Number, &c. (194).-The
Second Root, or Square Root, of a Number-The Third Root, or Cube
Root, of a Number-Any Power or Root of Unity (195).--A Power,
or a Root, of a Fraction, how obtained (196).—A Power, or a Root of
a Mixed Number, how obtained (197).-Perfect and Imperfect Powers
--A Square Number--A Cube Number-What an Imperfect Power,
and its Root, are sometimes called (198).-Exponents of Powers and
Roots-How a Root is sometimes otherwise denoted (199).
INVOLUTION How the Involution of a Number may always be effected
-How a higher Power of a given Number may otherwise be ob-
tained (200).

EVOLUTION-Only Roots for which Arithmetical Rules are usually given

(201).—Extracting the Square Root, in what it consists--Principles

on which the Rule depends (202).—To extract the Square Root of a

given Number (203).—What to be done in Extracting the Square

Root of Decimals-Why the last Period must be complete-Number

of Decimal Figures to be made in the Root-When an exact Root

cannot be found (204).-Application of Square Root (205).-Ex-

tracting the Cube Root, in what it consists-Principles on which

the Rule depends (206).--To extract the Cube Root of a given num-

ber (207).—What to be done in Extracting the Cube Root of Deci-

mals-Why the last Period must be complete-Number of Decimal

Figures to be made in the Root-When an exact Root cannot be

found (208).-Application of the Cube Root (209).

CHAPTER XI.

PROGRESSIONS, AND THEIR APPLICATIONS TO COMPOUND INTEREST AND
ANNUITIES.
PAGE 263.

An ARITHMETICAL PROGRESSION-Extremes and Means (210).—What

the Last Term is equal to (211).-The Common Difference of the

Terms (212).-The Sum of the two Extremes (213).—An Arithme-

tical Mean (214).—The Sum of all the Terms (215).

A GEOMETRICAL PROGRESSION-Extremes and Means (216).—What the

Last Term is equal to (217).—Power of the Ratio found from the first

and last Terms (218).-Product of the two Extremes (219).—A

Geometrical Mean (220).-The Sum of all the Terms (221).-Sum

of an Infinite Number of decreasing Terms in Geometrical Pro-

gression (222).

Correspondence of Terms in COMPOUND INTEREST and Geometrical

Progression (223).-Rule for the Computation of Compound Inte-

rest (224).—To find the Principal from a given Amount at Compound

Interest (226).

An ANNUITY—A Perpetuity-An Annuity forborne, or in arrears—An

Annuity in reversion (227).—Amount of an Annuity at Simple Inte-

rest (228).-Amount of an Annuity at Compound Interest (229).-

Rule to find the Amount of an Annuity (230).—Rule to find the

Present Worth of an Annuity (231).-The Present Worth of a Per-

petuity (232). The Present Worth of an Annuity in reversion (233).

PERMUTATIONS (234)-Number of Permutations of different Things

(235).-Number of different Permutations of Things when some of

those Things are alike-When there are two or more Sets of like

Things (236).

COMBINATIONS (237).-Number of different Combinations that may be

formed out of a given number of Things (238).-Number of different

Combinations that may be formed by taking one from each of two or

more Sets of different Things (239).

CHAPTER XIII.

EXCHANGE, FOREIGN COINS AND CURRENCIES. PAGE 297.

EXCHANGE, in Commerce (240).-A Draft or Bill of Exchange (241).—
A Domestic or Inland Bill of Exchange-A Foreign Bill of Ex-
change-Set of Exchange (242).-Liability of the Drawer and En-
dorsers of a Bill of Exchange (243).-Par of Exchange (244).—
Course of Exchange-When the Exchange between two countries
will be at par, above par, or below par (245) -Nominal Value of the
Pound Sterling in Exchange between the United States and Eng-
land (246).—Arbitration of Exchange (247).-How the Relative
Values of Gold and Silver in any country are ascertained-Relative
Values of these Metals in the U. S.-in England-in France-in
Spain-in China (248).—Coins or Specie of a Country—Moneys of
Account (249).-Foreign Coins made current in any country (250).

CHAPTER XIV.

MATHEMATICAL PROBABILITIES, AND THEIR APPLICATION TO LIFE

ANNUITIES AND LIFE INSURANCE.

PAGE 308.

Of the THEORY OF PROBABILITIES, and the Nature of a Contingent

Event (251).-Measure of Probability (252).-Opposite Probabili-

ties (253)-Probability of the non-occurrence of a Contingent Event

(254).—Probability of one, indifferently, of two or more Contingent

Events (255).-Probability of the Concurrence of two or more Con-

tingent Events (256).—Probability of the first of two Contingent

Events, or, if the first fail, of the Second Event (257).—Absolute

Value of a Sum payable on the Occurrence of a Contingent Event

-Relative Value of a Sum payable on the Occurrence of a Contin-

gent Event (258).

A LIFE ANNUITY-A Temporary Life Annuity (259).—Present Value
of a Life Annuity (260).—Probability that a Person at any given
Age will attain any designated Higher Age (261).-Present Value
of an Annuity on any given Life found from that on a Life one Year