An Elementary Treatise on Algebra: For the Use of Students in High Schools and Colleges |
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Page iii
... equal degree , by requiring too little of the student . What success has attended an attempt to attain a proper medium , it is left for competent teachers to decide . This work commences in the inductive manner , because that mode is ...
... equal degree , by requiring too little of the student . What success has attended an attempt to attain a proper medium , it is left for competent teachers to decide . This work commences in the inductive manner , because that mode is ...
Page 2
... equal to , equals , or by some words of similar import ; for example , 6 + 4 = 10 means that the sum of 6 and 4 is equal to 10 , and is read 6 plus 4 equals 10 . Accordingly , 5 × 4 + 7 = -3 means , that , if 5 be multi- plied by 4 ...
... equal to , equals , or by some words of similar import ; for example , 6 + 4 = 10 means that the sum of 6 and 4 is equal to 10 , and is read 6 plus 4 equals 10 . Accordingly , 5 × 4 + 7 = -3 means , that , if 5 be multi- plied by 4 ...
Page 3
... 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 ...
... 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 ...
Page 5
... equal number of oxen , cows and sheep ; the oxen at $ 40 apiece , the cows at $ 15 , and the sheep at $ 5 ; the whole came to $ 660 . How many were there of each ? 5. A woman bought some peaches , pears and melons for $ 1.10 ; the ...
... equal number of oxen , cows and sheep ; the oxen at $ 40 apiece , the cows at $ 15 , and the sheep at $ 5 ; the whole came to $ 660 . How many were there of each ? 5. A woman bought some peaches , pears and melons for $ 1.10 ; the ...
Page 7
... equal number . How many coins of each kind would he require ? 19. A man paid £ 144 in guineas at 21s . and crowns at 5s . each . There were three times as many crowns as guineas . Required the number of each . 20. A man on a journey ...
... equal number . How many coins of each kind would he require ? 19. A man paid £ 144 in guineas at 21s . and crowns at 5s . each . There were three times as many crowns as guineas . Required the number of each . 20. A man on a journey ...
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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.