The Principles of Elementary Algebra |
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... FRACTIONS . ∞ AND 0 .... 74 VI . RATIO , PROPORTION , VARIATION OR GENERALIZED PROPORTION 90 VII . INDICES AND SURDS . 100 VIII . CONCRETE QUANTITY . GEOMETRICAL INTERPRETA- TIONS . THE GRAPH . 114 IX . THE QUADRATIC .. 136 X ...
... FRACTIONS . ∞ AND 0 .... 74 VI . RATIO , PROPORTION , VARIATION OR GENERALIZED PROPORTION 90 VII . INDICES AND SURDS . 100 VIII . CONCRETE QUANTITY . GEOMETRICAL INTERPRETA- TIONS . THE GRAPH . 114 IX . THE QUADRATIC .. 136 X ...
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... fractions ; ( 3 ) Numerical quantities which cannot be exactly expressed as integers or fractions , but whose values may be expressed to any required degree of approximation . Such are the square roots of the non - square numbers , the ...
... fractions ; ( 3 ) Numerical quantities which cannot be exactly expressed as integers or fractions , but whose values may be expressed to any required degree of approximation . Such are the square roots of the non - square numbers , the ...
Page 1
... fractions ; ( 3 ) Numerical quantities which cannot be exactly expressed as integers or fractions , but whose values may be expressed to any required degree of approximation . Such are the square roots of the non - square numbers , the ...
... fractions ; ( 3 ) Numerical quantities which cannot be exactly expressed as integers or fractions , but whose values may be expressed to any required degree of approximation . Such are the square roots of the non - square numbers , the ...
Page 71
... fractions . 69. Two numbers whose G. C. M. is 1 are prime to one another ; and a number which is prime to every number , except unity , smaller than itself is a prime number , or simply a prime . The following are the primes less than ...
... fractions . 69. Two numbers whose G. C. M. is 1 are prime to one another ; and a number which is prime to every number , except unity , smaller than itself is a prime number , or simply a prime . The following are the primes less than ...
Page 73
... + 5 x − 2 a complete square ? 8. What is the least multiplier that will make 144 a multiple of 64 ? That will make x3 — 5 x2 + 5 x − 1 a multiple of x2 - 4x + 3 ? CHAPTER V. FRACTIONS . SYMBOLS AND 0 . - 71. G. C. M. AND L. C. M. 73.
... + 5 x − 2 a complete square ? 8. What is the least multiplier that will make 144 a multiple of 64 ? That will make x3 — 5 x2 + 5 x − 1 a multiple of x2 - 4x + 3 ? CHAPTER V. FRACTIONS . SYMBOLS AND 0 . - 71. G. C. M. AND L. C. M. 73.
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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.