The Elements of Algebra |
From inside the book
Results 1-5 of 19
Page 54
... respectively , and the quotients q and p which arise from these divisions , have common divisor ; therefore pqD is the least common multiple of a and b . no b But pqD = pDx qD D a x = D > or the least common multiple of two quantities ...
... respectively , and the quotients q and p which arise from these divisions , have common divisor ; therefore pqD is the least common multiple of a and b . no b But pqD = pDx qD D a x = D > or the least common multiple of two quantities ...
Page 58
... respectively express the second , third , fourth , fifth , and nth powers of a . And to find the cube of a3 we write ( a2 ) 3 , but ( a2 ) 3 = a2 × aa × a2 = ao = a2 × 3 ; i . e . we multiply the index 2 by 3 . So to find the mth power ...
... respectively express the second , third , fourth , fifth , and nth powers of a . And to find the cube of a3 we write ( a2 ) 3 , but ( a2 ) 3 = a2 × aa × a2 = ao = a2 × 3 ; i . e . we multiply the index 2 by 3 . So to find the mth power ...
Page 64
... respectively . And hence also , whenever we meet with a quantity as a having a fractional index , we must remember that the numerator of the fraction expresses the power to which the quantity is to be raised , and the denominator the ...
... respectively . And hence also , whenever we meet with a quantity as a having a fractional index , we must remember that the numerator of the fraction expresses the power to which the quantity is to be raised , and the denominator the ...
Page 100
... respectively 3 5 x + 4 , x- - 4 , Ꮖ and + 9 ་ It may be observed that both the positive and negative signs are prefixed to the root of the second member of the equa- tion , the reason for which may be thus shewn ; make 2 p2 + q = m2 ...
... respectively 3 5 x + 4 , x- - 4 , Ꮖ and + 9 ་ It may be observed that both the positive and negative signs are prefixed to the root of the second member of the equa- tion , the reason for which may be thus shewn ; make 2 p2 + q = m2 ...
Page 101
... respectively represent these two values ; P - p .. + q p 9+ Therefore , a + ß β - -- Ρ 2 - 4 p , or the sum of the values of x is equal to the coefficient of the second term with its sign changed : this proposition is true of equations ...
... respectively represent these two values ; P - p .. + q p 9+ Therefore , a + ß β - -- Ρ 2 - 4 p , or the sum of the values of x is equal to the coefficient of the second term with its sign changed : this proposition is true of equations ...
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.