Number of Real Roots of Equations (190-206), .

212

SECTION II.

Limits of the Real Roots of an Equation (207-210),

224

Inferior limit of the difference between two roots (220, 221), 238

CHAPTER IX.

Continued Fractions (222-233),

Approximation to value of ratio (231),

Approximate roots of equation (232, 233),

EXPONENTIAL EQUATIONS

AND

LOGARITHMS.

SECTION I.

EXPONENTIAL EQUATIONS (1—3), .

SECTION II.

Nature and PROPERTIES OF Logarithms (4—15),

SECTION III.

COMMON LOGARITHMS AND THEIR USES (16- 32),

Ꭺ Ꮮ Ꮐ Ꭼ Ᏼ Ꭱ Ꭺ .

ALGEBRA.

CHAPTER I.

Fundamental Processes of Algebra.

SECTION 1.

Definitions and Notation.

1. Algebra, according to the usual definition, is that branch of mathematics in which the quantities considered are represented by the letters of the alphabet, and the operations to be performed upon them are indicated by signs. In this sense it would embrace almost the whole science of mathematics, elementary geometry alone being excepted. It is, consequently, subject in common use to some limitations, which will be more easily understood, when we are farther advanced in the science.

2. The sign is called plus or more, or the positive sign, and placed between two quantities denotes that they are to be added together.

Thus 35 is 3 plus or more 5, and denotes the sum of 3 and 5. Likewise ab is the sum of a and b, or of the quantities which a and b represent.