# An Elementary Treatise on Algebra: Designed as First Lessons in that Science

Jacob Ernst, 1850 - 240 σελίδες

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### Περιεχόμενα

 INTRoduction 11 Simple problems for exercises 17 SECTION I 25 Subtraction 31 The product of minus by minus illustrated 37 Division 45 Division in compound quantities 51 Multiple and least common multiple 61
 Equations containing three or more unknown quantitiesRule 130 Negative results how understood 137 Expansion of a binomial 144 Expansion of a binomial 147 Evolution 150 How to extract roots of polynomials 153 Approximate rule for cube root 163 Equations of the second degree 170

 Complex fractions 68 Division illustrated by Equations 76 Subtraction of fractions 85 Transposition 93 Questions producing simple equations 101 How to propose convenient problems 107 Equations having compound fractions 116 Three methods of elimination 123
 SECTION IV 171 Rules for completing a square 180 Resolving a quadratic expression into two factors 186 191 Arithmetical progression 204 Examples in arithmetical progression 211 General problems that involve progression 220 Fellowship theoretically considered 237

### Δημοφιλή αποσπάσματα

Σελίδα 51 - 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.
Σελίδα 64 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Σελίδα 204 - Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 224 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Σελίδα 162 - The number of periods will indicate the number of figures in the root. Thus, the square root of 83,740,801 must contain...
Σελίδα 16 - If equal quantities be divided by the same, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Σελίδα 207 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Σελίδα 200 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.
Σελίδα 180 - It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.
Σελίδα 199 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.