A New Introduction to the Science of Algebra... |
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Page 9
... evident , therefore , that in order to measure a quan- tity , we must compare it with some known quantity of the same kind , assumed as the unit or measure of quantity . For example , if the quantity to be measured is a sum of money ...
... evident , therefore , that in order to measure a quan- tity , we must compare it with some known quantity of the same kind , assumed as the unit or measure of quantity . For example , if the quantity to be measured is a sum of money ...
Page 13
... evident that all the operations of arith- metic must be based upon these only . Under the first are comprehended addition and multiplica - ` tion , and under the second , subtraction and division . Addition consists in finding the sum ...
... evident that all the operations of arith- metic must be based upon these only . Under the first are comprehended addition and multiplica - ` tion , and under the second , subtraction and division . Addition consists in finding the sum ...
Page 16
... evident that the greater number cannot be taken from the less . 2. 322974-123748 = 199226 3. 1002641 - 783219 = - 4. 10000032 — 1364217 = 5. 666444-55455 = 6. From 3 millions 31 thousands and 1 , take 16 ARITHMETIC .
... evident that the greater number cannot be taken from the less . 2. 322974-123748 = 199226 3. 1002641 - 783219 = - 4. 10000032 — 1364217 = 5. 666444-55455 = 6. From 3 millions 31 thousands and 1 , take 16 ARITHMETIC .
Page 29
... evident , that as many times as the denominator is repeated , just so many times less each part becomes ; and hence , the numerator remaining the same MULTIPLICATION AND DIVISION OF FRACTIONS . 29 To divide a fraction by a whole number.
... evident , that as many times as the denominator is repeated , just so many times less each part becomes ; and hence , the numerator remaining the same MULTIPLICATION AND DIVISION OF FRACTIONS . 29 To divide a fraction by a whole number.
Page 33
... evident that this line cannot be greater than DF . Beginning therefore with DE , let it be applied to A B , and cut off from A B a part equal to DE as many times as possible ; suppose twice , with a remainder a B ; then cut off from DE ...
... evident that this line cannot be greater than DF . Beginning therefore with DE , let it be applied to A B , and cut off from A B a part equal to DE as many times as possible ; suppose twice , with a remainder a B ; then cut off from DE ...
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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.