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REMARKS

ON THE METHOD OF USING THIS WORK, AND CONDUCTING

EXAMINATIONS IN ALGEBRA.

The following remarks may be useful to the less experienced Teacher using this work, who would make it fully efficient for the purposes intended.

1. The definitions and propositions numbered (1), (2), (3), &c., and the Rules I, II, III, &c., should be accurately memorized and recited by the Student.

2. The accompanying examples, illustrations, or demonstrations, should be required of the Student, and discussed with him on the part of the Teacher, with reference to the principles involved in them.

3. The oral exercises in the earlier parts of the work, should be exacted; and the Student should often be examined on the exercises under the Rules, with his book closed.

4. In the solution of Equations and Problems, he should explain each part of the operation, as exemplified in different parts of the work.

5. The Analysis of Contents (see the next page) will be convenient for reviews on the theory of the science; and such reviews should be frequent. The Student will thus become familiar with the phraseology, principles, and order of the science.

6. The Student's acquisitions will depend very much on the exactness, as well as on the frequency, with which he is examined. The requisitions made on him should be adapted to his capabilities,-which, it should be remembered, are liable to be sometimes overrated, and sometimes underrated, by Authors and Teachers.

ANALYSIS OF CONTENTS.

This Analysis is designed to be used in oral examinations, in reviews. The
Teacher will name the topic as presented in this table; the Learner will respond
according to his knowledge of the subject.

For example: the Teacher will say, "Science and Art; " the Learner will re-
spond, "Science is knowledge reduced to a system; Art is knowledge applied to
practical purposes."

Calculations on the same Polynomial in two or more ( )'s, (32).

Algebraic SUBTRACTION, (33).-How to Subtract a Monomial from

another Quantity, (34).-How to Subtract a Monomial from a Dissimilar

Quantity, (35).

RULE II. For the Subtraction of Algebraic Quantities, (36).

How to denote the Subtraction of a negative Monomial-of a Polyno-

mial, (37).—Change of signs in a Polynomial without affecting its Value,

(38).

Algebraic MULTIPLICATION- —When the Multiplier is positive-When the

Multiplier is negative, (39).—Product of Two Monomials, (40).—Exponent,
in the Product, of a Letter occurring in both the Monomials multiplied to-
gether, (41)-Sign of the Product-Reason for this when both the Quanti-
ties are negative-When One of them is positive and the Other negative.
(42).-Product when Either of the Two Factors is 0, (43).

RULE IV. To Multiply a Polynomial into a Polynomial, (45).

Algebraic DIVISION, (46).—How to find the Quotient of Two Monomials,
(47).-Value of any Quantity with exponent 0, (48).—Sign of the Quotient,*
and Principle which determines it, (49)-Quotient of 0 divided by any
Quantity, and of any Quantity divided by 0, (50).

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