A Treatise on Elementary and Higher Algebra |
From inside the book
Page 41
... quently , we shall have " + A1ær −1 + Av2 - 2 + Azur -3 , etc . , ... + An = 0 ; which is called an equation of the n degree . - ― - - - " It is easy to see that the product ( x − a ) ( x —b ) ( x — c ) ( x − d ) × , etc. , becomes ...
... quently , we shall have " + A1ær −1 + Av2 - 2 + Azur -3 , etc . , ... + An = 0 ; which is called an equation of the n degree . - ― - - - " It is easy to see that the product ( x − a ) ( x —b ) ( x — c ) ( x − d ) × , etc. , becomes ...
Page 62
... quently put the divisor to the right of the dividend , and hav- ing drawn a right line between the dividend and divisor , and another right line below the divisor , they put the quotient under the last line ; thus , if a is the dividend ...
... quently put the divisor to the right of the dividend , and hav- ing drawn a right line between the dividend and divisor , and another right line below the divisor , they put the quotient under the last line ; thus , if a is the dividend ...
Page 87
... corre- sponds to 3 , the second coefficient in the quotient ; conse- quently , +3 +9 is the quotient arising from the division of 381 by 3x - 9 . 2002 Ex . 2. - To divide 6x6 - 12x DIVISION . 87 Horner's Synthetic Division.
... corre- sponds to 3 , the second coefficient in the quotient ; conse- quently , +3 +9 is the quotient arising from the division of 381 by 3x - 9 . 2002 Ex . 2. - To divide 6x6 - 12x DIVISION . 87 Horner's Synthetic Division.
Page 99
... quently ± shall be less than any finite quantity ; conse- xn 1 + x = 1 − x + x2 -- may be rejected , and we shall have - 1 1 + x x2 + x1 — 2+ etc. , ( B ) , the law of contin- uation of the series being such that if we multiply any ...
... quently ± shall be less than any finite quantity ; conse- xn 1 + x = 1 − x + x2 -- may be rejected , and we shall have - 1 1 + x x2 + x1 — 2+ etc. , ( B ) , the law of contin- uation of the series being such that if we multiply any ...
Page 117
... quently we get 1 + 0 + 0m m + m2 m m 2m hence y2 + 2my + m2 is the required transformation ; and we have ( y + m ) 2 = y2 + 2my + m2 , a well - known x2 = result . Ex . 5. To transform a3 when xy- m . - In this instance n = 3 , and for ...
... quently we get 1 + 0 + 0m m + m2 m m 2m hence y2 + 2my + m2 is the required transformation ; and we have ( y + m ) 2 = y2 + 2my + m2 , a well - known x2 = result . Ex . 5. To transform a3 when xy- m . - In this instance n = 3 , and for ...
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Common terms and phrases
algebraic arithmetical progression ascending powers becomes binomial called changing the sign clear clearly coefficients common logarithm compound quantity conse consequently corresponding cube root cx² decimal places denote derived function difference divide dividend division equa equal ratios equal roots evident EXAMPLES exponent expressed extract the square factors find the number follows fraction given equation gives greater greatest common divisor Hence imaginary roots inequality integer least common multiple less logarithm monomial multiplicand multiplier negative roots nth root number of terms numbers or quantities odd number polynomial positive integer positive roots proportion proposed equation quadratic quently quotient real roots remainder remaining roots represent result right member rule second term solution square root subtract supposed surds thence third term tion unknown letter whole number
Popular passages
Page 374 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 307 - Multiply the complete divisor by the second term of the root, and subtract the product from the remainder.
Page 152 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from, home, it lasted the woman 30 days ; how many days would the man be in drinking it alone ? Ans.
Page 141 - II. Divide the greater number by the less, writing the quotient between the verticals, the product under the dividend, and the remainder below. III. Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 347 - 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 161 - ... multiply each numerator by all the denominators, except its own, for a new numerator, and under it write the common denominator.
Page 215 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Page 375 - A, B, C, D, E play together on this condition, that he who loses shall give to all the rest as much as they already have. First A loses, then B, then C, then D, and at last also E. All lose in turn, and yet at the end of the 5th game they all have the same sum, viz. each $32. How much had each when they began to play ? Ans.
Page 209 - The first term, the last term (or the extremes) and the ratio given, to find the sum of the series. RULE. Multiply the last term by the ratio, and from the product subtract the first term ; then divide the remainder by the ratio, less by 1, and the quotient will be the sum of all the terms.
Page 173 - ... proportion, the sum of the extremes is equal to the sum of the means. Thus...