An Elementary Treatise on Algebra: For the Use of Students in High Schools and Colleges |
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Page 107
... formula , show by what operations they were obtained , and furnish rules for the solution of all questions of the same kind . 1. Two men , A and B , are to share $ 420 , of which B is to have 3 times as much as A. Required the share of ...
... formula , show by what operations they were obtained , and furnish rules for the solution of all questions of the same kind . 1. Two men , A and B , are to share $ 420 , of which B is to have 3 times as much as A. Required the share of ...
Page 110
... formula may be translated into the following rule , viz : Divide the price of the whole by the sum of the prices of a pound of each sort ; the quotient will be the number of pounds of each . If in the formula we substitute the numbers 7 ...
... formula may be translated into the following rule , viz : Divide the price of the whole by the sum of the prices of a pound of each sort ; the quotient will be the number of pounds of each . If in the formula we substitute the numbers 7 ...
Page 111
... formula we substitute the numbers 7 , 6 , 10 and 92 , for a , b , c , and d respectively , we have x = 92 7 + 6 + 10 24 lbs . , particular answer . 13. A farmer found he had a times as many cows as oxen , and b times as many sheep as ...
... formula we substitute the numbers 7 , 6 , 10 and 92 , for a , b , c , and d respectively , we have x = 92 7 + 6 + 10 24 lbs . , particular answer . 13. A farmer found he had a times as many cows as oxen , and b times as many sheep as ...
Page 112
... formula we derive the following rule for any simi- lar case , in which two workmen are employed . Divide the product of the numbers expressing the times in which each would perform it , by the sum of those numbers . Let the learner find ...
... formula we derive the following rule for any simi- lar case , in which two workmen are employed . Divide the product of the numbers expressing the times in which each would perform it , by the sum of those numbers . Let the learner find ...
Page 115
... formula gives the following rule . To find the interest when the principal , rate , and time are known , multiply together the principal , time , and rate . 24. The principal being $ 256.25 , the time 4 years , and the rate 6 per cent ...
... formula gives the following rule . To find the interest when the principal , rate , and time are known , multiply together the principal , time , and rate . 24. The principal being $ 256.25 , the time 4 years , and the rate 6 per cent ...
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Common terms and phrases
3d power a b c a² b² a² b³ abc2 added algebra ALGEBRAIC QUANTITIES arithmetical bought bushels cents change the signs coefficient contain cows decimal difference Divide dividend division equal example exponent expressed Extract Find the 3d Find the 4th Find the third following RULE formula fraction gallons given gives greater greatest common divisor Hence integral quantity last term least common multiple less Let the learner letter logarithm manner monomial mth power Multiply number of terms numerator and denominator obtain Operation polynomials preceding prime factors progression by quotient proportion quan question ratio remainder Required the number result rods second power second root SECTION separated shillings square Substitute subtracted Suppose tens third power third root tities twice unknown quantity whole number yards
Popular passages
Page 50 - 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 46 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Page 23 - A shepherd in time of war was plundered by a party of soldiers, who took \ of his flock and \ of a sheep ; another party took from him \ of what he had left and \ of a sheep ; then a third party took \ of what now remained and J of a sheep.
Page 226 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 258 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 260 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 1 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Page 223 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 1 - If equal quantities be divided by the same or 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.
Page 137 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.