A New Introduction to the Science of Algebra... |
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Page viii
... root 63 65 66 67 • Extraction of the cube root 70 CHAPTER IV . Ratios and proportions 72 Arithmetical proportions 73 Arithmetical progressions 75 Geometrical proportion 78 Geometrical progression 81 Rule of Three 83 Application of the ...
... root 63 65 66 67 • Extraction of the cube root 70 CHAPTER IV . Ratios and proportions 72 Arithmetical proportions 73 Arithmetical progressions 75 Geometrical proportion 78 Geometrical progression 81 Rule of Three 83 Application of the ...
Page x
... root of polynomials Extraction of the cube root of polynomials 202 • 203 207 General rule for extracting the roots of all powers Demonstration of the rules for extracting the root of num- 211 bers • Square root Cube root 213 66 216 ...
... root of polynomials Extraction of the cube root of polynomials 202 • 203 207 General rule for extracting the roots of all powers Demonstration of the rules for extracting the root of num- 211 bers • Square root Cube root 213 66 216 ...
Page 13
... root of the number 6 . 3 4 6 signifies the cube root of the number 6 . 5 6 √2 , v2 , v 2 , & c . signifies the 4th , 5th , 6th , & c . root of the number 2 . THE FOUR RULES OF ARITHMETIC . ( 6. ) As quantity admits of no other changes ...
... root of the number 6 . 3 4 6 signifies the cube root of the number 6 . 5 6 √2 , v2 , v 2 , & c . signifies the 4th , 5th , 6th , & c . root of the number 2 . THE FOUR RULES OF ARITHMETIC . ( 6. ) As quantity admits of no other changes ...
Page 63
... root ; thus , 2 is the 2d or square root of 4 , the 3d or cube root of 8 , the 4th root of 16 , & c . The degree of the power to which a number is INVOLUTION AND EVOLUTION . 63 32 CHAPTER III Involution and evolution.
... root ; thus , 2 is the 2d or square root of 4 , the 3d or cube root of 8 , the 4th root of 16 , & c . The degree of the power to which a number is INVOLUTION AND EVOLUTION . 63 32 CHAPTER III Involution and evolution.
Page 66
... roots of any given powers . The root of any number , is such a number as multiplied into itself a certain number of times , will produce that num- ber ; thus , = 25 ; 5 is the square or 2d root of 25 , since 52 , or , 5 × 5 4 is the cube or ...
... roots of any given powers . The root of any number , is such a number as multiplied into itself a certain number of times , will produce that num- ber ; thus , = 25 ; 5 is the square or 2d root of 25 , since 52 , or , 5 × 5 4 is the cube or ...
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Common terms and phrases
2ab+b² 2d power 4th power a²b² a²x added algebraic quantity antecedents Arith arithmetical progression ax² cent Clearing of fractions coefficient common denominator common difference contained continued fraction cube root decimal fraction dividend division dollars evident EXAMPLES exponent expression Extract the cube Extract the square extracting the root factors Find the greatest Find the sum find the value fourth geometrical progression given number gives greater greatest common divisor hence improper fraction last term least common multiple less letters logarithms lowest terms mean terms multiplicand Multiply nator nth root number of terms obtain operation polynomial Prod quan quotient ratio remainder required to find result simple fraction square root subtractive terms tens third power tion tity Transposing and reducing unity unknown quantity Va² vulgar fraction whence whole number writing written
Popular passages
Page 268 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Page 136 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 167 - B with $96. A lost twice as much as B; and, upon settling their accounts, it appeared that A had three times as much remaining as B. How much did each lose ? Ans. A lost $96, and B lost $48.
Page 73 - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 78 - In any proportion, the product of the means is equal to the product of the extremes.
Page 91 - If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, may he travel 360 miles ? Ans.
Page 277 - A and B 165 miles distant from each other set out with a design to meet; A travels 1 mile the first day, 2 the second, 3 the third, and so on.
Page 88 - If 248 men, in 5 days, of 11 hours each, can dig a trench 230 yards long, 3 wide...
Page 161 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Page 267 - A and B set off at the same time, to a place at the distance of 150 miles. A travels 3 miles an hour faster than B, and arrives at his journey's end 8 hours and 20 minutes before him.