A Treatise on Elementary and Higher Algebra |
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Page viii
... Examples . PAGE 353 362 388 Appendix to Simple Equations ..... SECTION XIV . QUADRATIC EQUATIONS . Simple or Pure ... Examples 429 To the Reversion of Series . 435 Development of the Roots of Equations of the nth Degree 439 ...
... Examples . PAGE 353 362 388 Appendix to Simple Equations ..... SECTION XIV . QUADRATIC EQUATIONS . Simple or Pure ... Examples 429 To the Reversion of Series . 435 Development of the Roots of Equations of the nth Degree 439 ...
Page ix
... . RESOLUTION OF WHOLE NUMBERS INTO THEIR FACTORS Illustrated by Examples ... 535 537 SECTION XXII . PERMUTATIONS AND COMBINATIONS . 544 ELEMENTARY HIGHER AND ALGEBRA . SECTION I. DEFINITIONS AND NOTATION CONTENTS . ix.
... . RESOLUTION OF WHOLE NUMBERS INTO THEIR FACTORS Illustrated by Examples ... 535 537 SECTION XXII . PERMUTATIONS AND COMBINATIONS . 544 ELEMENTARY HIGHER AND ALGEBRA . SECTION I. DEFINITIONS AND NOTATION CONTENTS . ix.
Page 10
... EXAMPLES . 1 . ab ab 2 . 3 . - 7x2y 5 √ a2 + b2 + y2 9x1y 7 √ a2 + b2 + y2 3ab - 29a3y 11 √ a2 + b2 + y2 5ab - 31xy 19 Va + b2 + y2 9ab ― 42x'y √ a2 + b2 + y2 19ab - 118x2y 43 Va2 + b2 + y2 4 . 4 √ m2n + pq2 6 V m3n + pq2 3 √m23n ...
... EXAMPLES . 1 . ab ab 2 . 3 . - 7x2y 5 √ a2 + b2 + y2 9x1y 7 √ a2 + b2 + y2 3ab - 29a3y 11 √ a2 + b2 + y2 5ab - 31xy 19 Va + b2 + y2 9ab ― 42x'y √ a2 + b2 + y2 19ab - 118x2y 43 Va2 + b2 + y2 4 . 4 √ m2n + pq2 6 V m3n + pq2 3 √m23n ...
Page 11
... EXAMPLES . 2 . 3 . 4 . 5b √xy 1 16m3n 15m3 n 6 √x2 - y2 V x2 · 12 ( x2 — y2 ) 1 - - -- — 20 ( x2 — y2 ) 1 - — 2b x * y * - - 3b √xy +90 Nay 1 45 Vx2 y3 2bcd 17 √x - y y3 - - 9 b x y sum = 6bcd - - 54 √ x2 — y2 - 0 - 22m3 n - 40m 3 ...
... EXAMPLES . 2 . 3 . 4 . 5b √xy 1 16m3n 15m3 n 6 √x2 - y2 V x2 · 12 ( x2 — y2 ) 1 - - -- — 20 ( x2 — y2 ) 1 - — 2b x * y * - - 3b √xy +90 Nay 1 45 Vx2 y3 2bcd 17 √x - y y3 - - 9 b x y sum = 6bcd - - 54 √ x2 — y2 - 0 - 22m3 n - 40m 3 ...
Page 12
... EXAMPLES . 1 . 3x2 + 7x2 + 9x + 2 11x3 + 13x2 + 4x3 - 20.03 6x2 8205+ - ---- 41 + 26x2 - 11 - 15x3 4x2 + - + 3 x + 25 ∞ ∞ 8 2 . √x2 + y2 - √x2 - y2 + pq - w 6 √x2 + y2 - √ x2 - y2 — pq + d 13 √x2 + y2 + 5 √x2 — y2 + 14pq + 7d + ...
... EXAMPLES . 1 . 3x2 + 7x2 + 9x + 2 11x3 + 13x2 + 4x3 - 20.03 6x2 8205+ - ---- 41 + 26x2 - 11 - 15x3 4x2 + - + 3 x + 25 ∞ ∞ 8 2 . √x2 + y2 - √x2 - y2 + pq - w 6 √x2 + y2 - √ x2 - y2 — pq + d 13 √x2 + y2 + 5 √x2 — y2 + 14pq + 7d + ...
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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
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