The Elements of Algebra |
From inside the book
Results 1-5 of 12
Page 23
... remainder , and so proceed till the division be completed , or till no term of the remainder be divisible by the first term of the divisor . ” The following example will illustrate the rule . Divide 2a2 + 4ab + 2b2 by a + b a + b ) 2 a2 ...
... remainder , and so proceed till the division be completed , or till no term of the remainder be divisible by the first term of the divisor . ” The following example will illustrate the rule . Divide 2a2 + 4ab + 2b2 by a + b a + b ) 2 a2 ...
Page 25
... remainder is consequently nothing : we shall now give examples in which there is a remainder . x − a ) x3 + a3 ( x2 + a x + a2 x3- α x2 + a x2 a x2- a2x a2x + a3 a2x - a3 2 a3 the remainder . The division cannot now be carried on by ...
... remainder is consequently nothing : we shall now give examples in which there is a remainder . x − a ) x3 + a3 ( x2 + a x + a2 x3- α x2 + a x2 a x2- a2x a2x + a3 a2x - a3 2 a3 the remainder . The division cannot now be carried on by ...
Page 26
... remainder Here the division may be continued for ever . Divide x + 2 by x + 1 . x + 1 ) x + 2 ( 1 + 1 x - 1 1 + & c . 23 x + 1 1 1+ T 118 I 118 118 C 1 2 100 remainder . Such expressions as 1 + x + x2 + x3 26 MULTIPLICATION AND DIVISION.
... remainder Here the division may be continued for ever . Divide x + 2 by x + 1 . x + 1 ) x + 2 ( 1 + 1 x - 1 1 + & c . 23 x + 1 1 1+ T 118 I 118 118 C 1 2 100 remainder . Such expressions as 1 + x + x2 + x3 26 MULTIPLICATION AND DIVISION.
Page 45
... remainder , it is said to be a common measure of the two , and to be the greatest when no num- ber greater than itself is contained in both of the numbers . Thus of the numbers 36 and 48 , 4 is said to be a com- mon measure , but 12 is ...
... remainder , it is said to be a common measure of the two , and to be the greatest when no num- ber greater than itself is contained in both of the numbers . Thus of the numbers 36 and 48 , 4 is said to be a com- mon measure , but 12 is ...
Page 47
... remainder c ; again divide b by c , and let the quotient be q and the remainder d , then divide c by d , let the quotient be r , and let there be no remainder . This process may be thus exhibited . b ) a p pb c ) bg qc d ) c ( r dr Then ...
... remainder c ; again divide b by c , and let the quotient be q and the remainder d , then divide c by d , let the quotient be r , and let there be no remainder . This process may be thus exhibited . b ) a p pb c ) bg qc d ) c ( r dr Then ...
Other editions - View all
Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - 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 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.