A New Introduction to the Science of Algebra ... |
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Page 76
... progression . The first and last terms are the extremes , and the number by which each term is greater or less than that which preceded it , is called the common difference . We proceed now to give certain ... progression , 76 ARITHMETIC .
... progression . The first and last terms are the extremes , and the number by which each term is greater or less than that which preceded it , is called the common difference . We proceed now to give certain ... progression , 76 ARITHMETIC .
Page 82
... progression is equal to the product of the last term by the ratio minus the first term , divided by the ratio less 1 . Hence , the sum of the series ; 2 : 6 : 18 : 54 : 162 : 486 : 1458 , is ( 1458 × 3 ) -2 ... progression 82 ARITHMETIC .
... progression is equal to the product of the last term by the ratio minus the first term , divided by the ratio less 1 . Hence , the sum of the series ; 2 : 6 : 18 : 54 : 162 : 486 : 1458 , is ( 1458 × 3 ) -2 ... progression 82 ARITHMETIC .
Page 83
... progression is , the last term 243 64 665 and the sum of the terms what is ... arithmetic , the Rule of Three . * Suppose it be required to find the fourth ... arithmetic , all the operations which we should perform upon the number itself ...
... progression is , the last term 243 64 665 and the sum of the terms what is ... arithmetic , the Rule of Three . * Suppose it be required to find the fourth ... arithmetic , all the operations which we should perform upon the number itself ...
Page 270
... progression be a decreasing one , we have only to make q negative , and the formula will become , or , l = a + ( n − 1 ) × — q , - l — a— ( n − 1 ) q From these formulas is derived the principle laid down in arithmetic ( 62 ) , namely ...
... progression be a decreasing one , we have only to make q negative , and the formula will become , or , l = a + ( n − 1 ) × — q , - l — a— ( n − 1 ) q From these formulas is derived the principle laid down in arithmetic ( 62 ) , namely ...
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Common terms and phrases
2ab+b² 2d power 4th power a²b² a²x a²x² added additive terms algebraic quantities Arith arithmetical progression ax² cent Clearing of fractions coefficient common denominator common difference contained cube root dividend division dollars equa 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 letter logarithms lowest terms merator mixed quantity monomial multiplicand nth root number of terms obtain polynomial Prod proportion quan quotient ratio remainder required to find result RULE simple fraction square root subtractive terms tens third power tion tity Transposing and reducing unity unknown quantity vulgar fraction whence whole number writing written
Popular passages
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 184 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 186 - ... of the sum of the shares of the other three, the share of the second ^ of the sum of the other three, and the share of the third...
Page 70 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 63 - To divide a Decimal by 10, 100, 1000, &c., remove the decimal point as many places to the left as there are ciphers in the divisor...
Page 187 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Page 73 - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 62 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.
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.