The Principles of Elementary Algebra |
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Page 3
... equal to or is the same as all that follows the symbol , taken also in its totality . ( 2 ) > and < . The first denotes that all that pre- cedes the symbol , taken in its totality , is greater than all that follows the symbol , taken in ...
... equal to or is the same as all that follows the symbol , taken also in its totality . ( 2 ) > and < . The first denotes that all that pre- cedes the symbol , taken in its totality , is greater than all that follows the symbol , taken in ...
Page 11
... equal to the sum of the numbers formed by multiply- ing each number by the square of the other . It may be remarked that theorems like the foregoing cannot , in general , be proved by an arithmetical process . Repeated trials with ...
... equal to the sum of the numbers formed by multiply- ing each number by the square of the other . It may be remarked that theorems like the foregoing cannot , in general , be proved by an arithmetical process . Repeated trials with ...
Page 13
... equal in their totalities , although , in general , no transformation can change one into the other . That this condition of equality may exist , some rela- tion must hold amongst the quantitative symbols , and , usually , one of these ...
... equal in their totalities , although , in general , no transformation can change one into the other . That this condition of equality may exist , some rela- tion must hold amongst the quantitative symbols , and , usually , one of these ...
Page 16
... equal to one half the second . 9. The sum of the ages of A , B , and C is 108 years . A is twice as old as B , and twice C's age is equal to A's and B's together . Find their ages . 10. After paying 2 % taxes on my income I have $ 1078 ...
... equal to one half the second . 9. The sum of the ages of A , B , and C is 108 years . A is twice as old as B , and twice C's age is equal to A's and B's together . Find their ages . 10. After paying 2 % taxes on my income I have $ 1078 ...
Page 25
... equal to the difference between the sum of their squares and the sum of their cubes . 18. If the product of two numbers is 1 , the square of their sum exceeds the sum of their squares by 2 . 31. The distribution of ( x + a ) ( x + b ) ...
... equal to the difference between the sum of their squares and the sum of their cubes . 18. If the product of two numbers is 1 , the square of their sum exceeds the sum of their squares by 2 . 31. The distribution of ( x + a ) ( x + b ) ...
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Common terms and phrases
a₁ ab² arithmetic ax² b₁ becomes binomial binomial theorem c₁ coefficients complete square continued fraction convergent cube root decimal denominator denote diagonal difference dimensions Divide divisor elementary algebra equal equate coefficients equation EXERCISE expansion expression find the L. C. M. find the nth Find the value finite geometric geometric series given gives graph Hence imaginary independent term integer integral function inversions letters linear factors logarithms mantissa matrix miles monomial Multiply negative nth root nth term number of terms numerical quantity operation permutations positive integers proper fraction quadratic quantitative symbol R₁ rationalizing factor recurring series relation remainder result sides signs Similarly solution square root substituting subtract suffixes surd theorem tion triangle U₂ variable Whence zero
Popular passages
Page 90 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 254 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 336 - ... University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc. "Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions...
Page 254 - ... that the logarithm of the product of two numbers is the sum of the logarithms of the numbers.
Page 74 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.