# An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

Durrie & Peck, 1847 - Algebra - 332 pages

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### Contents

 Introductory Observations on the Mathematics in general l 1 Notation Positive and Negative Quantities Axioms c 21 Subtraction 27 Multiplication 31 W Division 41 Algebraic Fractions 49 Roduction of Equations by Transposition Multiplication and Division Solution of Problems 65 Involution Notation Addition Subtracton Multiplication and 83
 Ratio and Proportion 173 Variation or General Proportion 206 Arithmetical and Geometrical Progression 213 Mathematical Infinity 227 Division by Compound Divisors 233 Involution of Compound Quantitles by the Binomial Theorem 242 Evolution of Compound Quantities 253 Infinite Series 259

### Popular passages

Page 59 - FRACTIONS, MULTIPLY THE NUMERATORS TOGETHER, FOR A NEW NUMERATOR, AND THE DENOMINATORS TOGETHER, FOR A NEW DENOMINATOR.
Page 31 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Page 188 - But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 231 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 290 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Page 134 - Two travellers A and B set out to meet each other, A leaving the town C, at the same time that B left D.
Page 216 - If the first term of an increasing arithmetical series is 3, the common difference 2, and the number of terms 20 ; what is the sum of the series 1 Ans.
Page 185 - When there ka series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c. are all equal ; the quantities are said to be in continued proportion.
Page 42 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the 'dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factor a and bd .will produce the dividend. The first of these, being a divisor, maybe set aside.
Page 224 - There are three numbers in geometrical progression, the greatest of which exceeds the least by 15; and the difference of the squares of the greatest and the least,. is to the sum of the squares of all the three numbers as 5 to 7. What are the numbers 1 Ans.