A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the Higher Parts Usually Taught in Colleges; Containing Moreover, the New Method of Cubic and Higher Equations as Well as the Development and Application of the More Recently Discovered Theorem of SturmD. Appleton and Company, 1850 - 420 σελίδες |
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Σελίδα 6
... formulas for the 20 cases of arithmetical progression , 221 Geometrical ratio , ..................... . 224 Table of all the formulas of geometrical progression ,. 230 Harmonical proportion ,. 234 CHAPTER VII . Method of indeterminate ...
... formulas for the 20 cases of arithmetical progression , 221 Geometrical ratio , ..................... . 224 Table of all the formulas of geometrical progression ,. 230 Harmonical proportion ,. 234 CHAPTER VII . Method of indeterminate ...
Σελίδα 7
... formula found , ...... Numerical calculation of logarithms ,. Exponential Theorem , ... Application of logarithms , .. Exponential equations resolved by logarithms ,. Compound interest and annuities by logarithms . CHAPTER X. GENERAL ...
... formula found , ...... Numerical calculation of logarithms ,. Exponential Theorem , ... Application of logarithms , .. Exponential equations resolved by logarithms ,. Compound interest and annuities by logarithms . CHAPTER X. GENERAL ...
Σελίδα 14
... formulas . ( a + b ) * = a2 + 2ab + b2 . - ( a - b ) 2 = a2 2ab + b2 . 2 1 ( a + b ) + 1 ( a —b ) : ( a + b ) 2 + ( a - b ) 2 = 2a2 + 262 . = α . 1⁄2 ( a + b ) — 1 ( a —b ) = b . - ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) Expression ( ...
... formulas . ( a + b ) * = a2 + 2ab + b2 . - ( a - b ) 2 = a2 2ab + b2 . 2 1 ( a + b ) + 1 ( a —b ) : ( a + b ) 2 + ( a - b ) 2 = 2a2 + 262 . = α . 1⁄2 ( a + b ) — 1 ( a —b ) = b . - ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) Expression ( ...
Σελίδα 150
... one for- mula , both ( A ) and ( B ) . √a ± √b = = { a + √ a2 — b ± 2 = .1om b ( C ) 2 2 ( 118. ) We will now show the use of formulas ( A ) and ( B ) by the following EXAMPLES . 1. What is the square root of 7 150 SURD QUANTITIES .
... one for- mula , both ( A ) and ( B ) . √a ± √b = = { a + √ a2 — b ± 2 = .1om b ( C ) 2 2 ( 118. ) We will now show the use of formulas ( A ) and ( B ) by the following EXAMPLES . 1. What is the square root of 7 150 SURD QUANTITIES .
Σελίδα 151
... formula ( A ) , gives a } + √a2 - b 6 + √36 2 - 2 - 20 +4 = √ 5 . 2 2 Therefore , b 6 = √36 2 20 6 4 - = 1 . 2 √6 + √20 = √5 + 1 . 3. What is the square root of 2 ( x + 1 ) + 4 √x ? Ans . √2x + √2 . 4. What is the square root ...
... formula ( A ) , gives a } + √a2 - b 6 + √36 2 - 2 - 20 +4 = √ 5 . 2 2 Therefore , b 6 = √36 2 20 6 4 - = 1 . 2 √6 + √20 = √5 + 1 . 3. What is the square root of 2 ( x + 1 ) + 4 √x ? Ans . √2x + √2 . 4. What is the square root ...
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A₁ algebraic approximative fractions arithmetical progression becomes binomial Binomial Theorem cleared of fractions common denominator consequently continued fraction cube root cubic equation D₁ degree denoted dividend equa equal EXAMPLES expansion exponent expression Extracting the square factors fifth root figure Find a root find the value formula fourth geometrical geometrical progression geometrical series given gives greatest common divisor greatest common measure Hence left-hand member letters logarithms method multiply NEGATIVE PRODUCTS Nlog nth root number of terms numerator and denominator obtain OPERATION partial denominators polynomial POSITIVE PRODUCTS quadratic equation quotient rational real roots reciprocal recurring equation recurring series Reduce remainder right-hand member Rule under Art scale of relation second term square root Sturm's Theorem subscript numbers Subtracting suppose surd THEOREM three roots tion transposing and uniting unknown quantity X₁