The Principles of Elementary Algebra |
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Page 5
... corresponds an algebraical negative number , the relation between corresponding numbers being that their algebraic sum is zero or nothing . Negative numbers are important in their relations to concrete arithmetic , and especially where ...
... corresponds an algebraical negative number , the relation between corresponding numbers being that their algebraic sum is zero or nothing . Negative numbers are important in their relations to concrete arithmetic , and especially where ...
Page 36
... corresponding posi- tive exponent . Thus , α b = ab1 ; 1 + = + 1 1 x2 ; = 1 + x ̄1 + x ̄2 ; etc. -2 х 39. The most important cases of division , where any special process is required , are those involving a variable in an integral ...
... corresponding posi- tive exponent . Thus , α b = ab1 ; 1 + = + 1 1 x2 ; = 1 + x ̄1 + x ̄2 ; etc. -2 х 39. The most important cases of division , where any special process is required , are those involving a variable in an integral ...
Page 39
... corresponds to a greater quantity in arithmetic ; so that , when the divi- dend is of a higher degree than the divisor , and the division is not exact , we may obtain a quotient and a remainder , or we may expand the remainder into an ...
... corresponds to a greater quantity in arithmetic ; so that , when the divi- dend is of a higher degree than the divisor , and the division is not exact , we may obtain a quotient and a remainder , or we may expand the remainder into an ...
Page 55
... corresponding imaginary ; the relation between these being that the square of the first is a2 , and of the other it is -x2 . This generalization introduces us to a new set of num- bers , the symbolic numbers or imaginaries . All whole ...
... corresponding imaginary ; the relation between these being that the square of the first is a2 , and of the other it is -x2 . This generalization introduces us to a new set of num- bers , the symbolic numbers or imaginaries . All whole ...
Page 62
... the variable . 60. When the roots of an integral function or of the corresponding equation are all real and all rational , they can generally be found . Also , the methods of factoring now at our disposal 62 FACTORS AND ROOTS .
... the variable . 60. When the roots of an integral function or of the corresponding equation are all real and all rational , they can generally be found . Also , the methods of factoring now at our disposal 62 FACTORS AND ROOTS .
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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.