The Elements of Algebra |
From inside the book
Results 1-5 of 10
Page 17
... complete re- sult ; but this would entail upon us the trouble of writing the multiplicand as often as there were terms in the mul- tiplier . In general therefore the multiplier is written under the multiplicand , and every term of the ...
... complete re- sult ; but this would entail upon us the trouble of writing the multiplicand as often as there were terms in the mul- tiplier . In general therefore the multiplier is written under the multiplicand , and every term of the ...
Page 54
... complete common measure is x2 + x . THE LEAST COMMON MULTIPLE OF TWO QUANTITIES . 54. A common multiple of two numbers is that num- ber which is divided by both ; and the least common mul- tiple that least number which is so divisible ...
... complete common measure is x2 + x . THE LEAST COMMON MULTIPLE OF TWO QUANTITIES . 54. A common multiple of two numbers is that num- ber which is divided by both ; and the least common mul- tiple that least number which is so divisible ...
Page 99
... complete square ; for then if the roots of both sides be taken , the equation will be reduced to a simple equation . But to find r . We see that in every complete square of a binomial , as x2 + 2ax + a2 , which is the square of x + a ...
... complete square ; for then if the roots of both sides be taken , the equation will be reduced to a simple equation . But to find r . We see that in every complete square of a binomial , as x2 + 2ax + a2 , which is the square of x + a ...
Page 100
... complete the square . Add to each member of the equation , the square of half the coeffi- cient of x ; and to extract the square root of the square so completed , add to x , half the coefficient of x in the original equation . Ex . Complete ...
... complete the square . Add to each member of the equation , the square of half the coeffi- cient of x ; and to extract the square root of the square so completed , add to x , half the coefficient of x in the original equation . Ex . Complete ...
Page 103
... Complete the square . ( 6 ) Extract the square root of both sides , and a simple equation remains ; whence x may be found . EXAMPLES . ( Ex . 1. ) Let x2 + 6x = 91 ; find x . 2 Add 9 or to both sides ; .. x2 + 6x + 9 = 91 + 9 = 100 ...
... Complete the square . ( 6 ) Extract the square root of both sides , and a simple equation remains ; whence x may be found . EXAMPLES . ( Ex . 1. ) Let x2 + 6x = 91 ; find x . 2 Add 9 or to both sides ; .. x2 + 6x + 9 = 91 + 9 = 100 ...
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.