Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted to the Courses of Mathematical Instruction in the U.S.Wiley and Long, 1835 - 353 σελίδες |
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Σελίδα 13
... affected by changing the order of its terms , provided the signs of all the terms be preserved . For example , the polynomial 4a3 - 3a2b + 5ac2 = 5ac2-3a2b + 4a3 - 3a2b + 5ac2 + 4a3 . This is evident , from the nature of arithmetical ...
... affected by changing the order of its terms , provided the signs of all the terms be preserved . For example , the polynomial 4a3 - 3a2b + 5ac2 = 5ac2-3a2b + 4a3 - 3a2b + 5ac2 + 4a3 . This is evident , from the nature of arithmetical ...
Σελίδα 14
... affected with like exponents , are called similar terms . Thus , in the polynomial 7ab + 3ab - 4ab2 + 5a3 , the terms Tab and 3ab , are similar ; and so also are the terms - 4a32 and 5a3b3 , the letters and exponents in each being the ...
... affected with like exponents , are called similar terms . Thus , in the polynomial 7ab + 3ab - 4ab2 + 5a3 , the terms Tab and 3ab , are similar ; and so also are the terms - 4a32 and 5a3b3 , the letters and exponents in each being the ...
Σελίδα 15
... affected with like exponents . 29. When a polynomial contains several similar terms it may often be reduced to a simpler form . Take the polynomial 4a2b - 3a2c + 7a2c - 2a2b . It may be written ( Art . 23 ) , 4a2b - 2ab + 7a c - 3a c ...
... affected with like exponents . 29. When a polynomial contains several similar terms it may often be reduced to a simpler form . Take the polynomial 4a2b - 3a2c + 7a2c - 2a2b . It may be written ( Art . 23 ) , 4a2b - 2ab + 7a c - 3a c ...
Σελίδα 16
... affects only the co - efficients , and not the exponents . EXAMPLES . 1. Reduce the polynomial 4a3b - 8a2b — 9a3b + 11a2b to its sim- plest form . Ans . -2a2b . Ans . -3abc2 . 2. Reduce the polynomial 7abc - abc2-7abc2-8abc2 + 6abc2 to ...
... affects only the co - efficients , and not the exponents . EXAMPLES . 1. Reduce the polynomial 4a3b - 8a2b — 9a3b + 11a2b to its sim- plest form . Ans . -2a2b . Ans . -3abc2 . 2. Reduce the polynomial 7abc - abc2-7abc2-8abc2 + 6abc2 to ...
Σελίδα 24
... affected with the sign — - 2d . The words subtraction and difference do not always convey the idea of diminution , for the difference between a and b being a + b , exceeds a . This result is an algebraic difference , and can be put ...
... affected with the sign — - 2d . The words subtraction and difference do not always convey the idea of diminution , for the difference between a and b being a + b , exceeds a . This result is an algebraic difference , and can be put ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Algebra: Translated from the French of M. Bourdon; Revised and ... Charles Davies Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Elements of Algebra: Translated From the French of M. Bourdon; Revised and ... Charles Davies Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
affected algebraic quantities arithmetical arithmetical means binomial co-efficient common factor contain contrary signs cube root decimal divide dividend division double product entire number enunciation equa equal equations involving example expression extract the square figure Find the greatest find the square find the values formula fourth fraction given number gives greater greatest common divisor greyhound Hence inequality irreducible fraction last term least common multiple less letter logarithm manner monomial multiplicand multiply necessary negative nth root number of terms number of units obtain operation ounces of silver perfect square performed preceding problem proposed equation proposed polynomials quotient radical reduced remainder result second degree second member second term square root substituted suppose take the equation tens third tion twice the product unity unknown quantity verified vulgar fraction whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 152 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 1 5| days, but B would have been 28 days in performing A's journey How far did each travel ? Ans.
Σελίδα 96 - 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 will it take each person to perform the same work alone.
Σελίδα 116 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Σελίδα 95 - A person bought a chaise, horse, and harness, • for £60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each?
Σελίδα 119 - 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.
Σελίδα 33 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Σελίδα 70 - A fish was caught whose tail weighed 9Z6. ; his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together : what was the weight of the fish?
Σελίδα 27 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Σελίδα 246 - That is : The first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one.
Σελίδα 26 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.