An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 2
... quotient , which , when multiplied by a given divisor , produces a given dividend . " Division is denoted by placing the dividend be- fore the sign , and the divisor after it ; thus a- ÷ b , implies that the quantity a is to be divided ...
... quotient , which , when multiplied by a given divisor , produces a given dividend . " Division is denoted by placing the dividend be- fore the sign , and the divisor after it ; thus a- ÷ b , implies that the quantity a is to be divided ...
Σελίδα 45
... quotient will be + ; if unlike , the sign of the quotient will be - . The reason of this proposition follows immedi- ately from multiplication : + ab D Thus , if + ax + b + ab ; therefore → = + b : + a -ab + ax - b = -ab ; 8 + a -ab ...
... quotient will be + ; if unlike , the sign of the quotient will be - . The reason of this proposition follows immedi- ately from multiplication : + ab D Thus , if + ax + b + ab ; therefore → = + b : + a -ab + ax - b = -ab ; 8 + a -ab ...
Σελίδα 46
... quotient are those of the dividend not common to the divisor , when all the letters of the divisor are common to the dividend : for example , the product abc , divided by ab , gives c for the quotient , because the product of ab by c is ...
... quotient are those of the dividend not common to the divisor , when all the letters of the divisor are common to the dividend : for example , the product abc , divided by ab , gives c for the quotient , because the product of ab by c is ...
Σελίδα 47
... quotient must also be a , and if the unknown expo- nent of a be designated by x , then a will be the quotient , and from the nature of division , a = a " Xa * = a * + * ; from which there necessarily results the following equality ...
... quotient must also be a , and if the unknown expo- nent of a be designated by x , then a will be the quotient , and from the nature of division , a = a " Xa * = a * + * ; from which there necessarily results the following equality ...
Σελίδα 48
... quotient will be equal to 0 , or a * = ao , a result which it is necessary to explain . For this purpose , let us resume the division of a by am , which gives unity for the quo- am tient , or = 1 ; and as two quotients , arising from am ...
... quotient will be equal to 0 , or a * = ao , a result which it is necessary to explain . For this purpose , let us resume the division of a by am , which gives unity for the quo- am tient , or = 1 ; and as two quotients , arising from am ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² according added algebraic quantities arithmetical becomes binomial changing the signs coefficients common denominator completing the square compound quantity consequently cube root demonstrated difference divi divided dividend division equa equal exponent expression extracting the root factors find the values formula fourth fraction required greater greatest common divisor greatest common measure Hence improper fraction least common multiple less letter logarithm lowest terms lues magnitudes manner mixed quantity multiplied number of terms numbers or quantities observed operation positive prefixed Prob problem proper sign proportionals proposed equation quadratic quadratic equations quan quotient radical sign ratio Reduce remainder Required the square required to find result RULE shillings side simple equations square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number