The Principles of Elementary Algebra |
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Page 11
... reduced by transformations , as to depend upon the smallest possible cycle of such operations . 21. As algebra is generalized arithmetic , every alge- braic relation , which is arithmetically interpretable , ex- presses some general ...
... reduced by transformations , as to depend upon the smallest possible cycle of such operations . 21. As algebra is generalized arithmetic , every alge- braic relation , which is arithmetically interpretable , ex- presses some general ...
Page 12
... Reduce to a single number- i . 1-2 ( -1 + 1 − 2 ) } . ii . 34-5 ( 6-7 [ 89 ] ) } . iii . } { } − } ( t − } [ } − 1 · 1 % — AD ) } . 3. Condense as much as possible- i . 2a 3a ( a · - - − a ) } . ii . a - b { 1 - b ( 1 − a · - a . 1 - ...
... Reduce to a single number- i . 1-2 ( -1 + 1 − 2 ) } . ii . 34-5 ( 6-7 [ 89 ] ) } . iii . } { } − } ( t − } [ } − 1 · 1 % — AD ) } . 3. Condense as much as possible- i . 2a 3a ( a · - - − a ) } . ii . a - b { 1 - b ( 1 − a · - a . 1 - ...
Page 23
... reduces to ( p + q + r ) 3 − p3 — q3 — r3 = 3 ( p + r ) ( r + q ) ( I + p ) , which is true by Art . 29 , ( 4 ) . 30. Expansion of Symmetrical Homogeneous Expres- sions . This form of expression is of frequent occurrence , and its ...
... reduces to ( p + q + r ) 3 − p3 — q3 — r3 = 3 ( p + r ) ( r + q ) ( I + p ) , which is true by Art . 29 , ( 4 ) . 30. Expansion of Symmetrical Homogeneous Expres- sions . This form of expression is of frequent occurrence , and its ...
Page 43
... reduces the division to x2 ( 1 + 2 z2 . 28 + 24 — 25 ) ÷ ( 1 + z2 − z3 ) . - - 15. Find the simplest division that will give the series x + 3x2 + 2 x3- x1 — 3x5 2x + x2 + ... 16. What expression added to ( a + b + c ) ( ab + be + ca ) ...
... reduces the division to x2 ( 1 + 2 z2 . 28 + 24 — 25 ) ÷ ( 1 + z2 − z3 ) . - - 15. Find the simplest division that will give the series x + 3x2 + 2 x3- x1 — 3x5 2x + x2 + ... 16. What expression added to ( a + b + c ) ( ab + be + ca ) ...
Page 54
... a is real . Thus every imaginary number can be reduced to depend upon the symbol V - 1 , which is called the imaginary unit , and is usually symbolized by i . If , then , a denotes any real number , 54 FACTORS AND FACTORIZATION .
... a is real . Thus every imaginary number can be reduced to depend upon the symbol V - 1 , which is called the imaginary unit , and is usually symbolized by i . If , then , a denotes any real number , 54 FACTORS AND FACTORIZATION .
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a₁ ab˛ arithmetic ax˛ 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.