Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA. S. Barnes & Burr, 1860 - 400 páginas |
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Página 13
... become to that extent , merely mechanical . But when we look back and see on what the reasoning is based , and how the processes have been conducted , we shall find that every step was taken on the supposition that we were actually ...
... become to that extent , merely mechanical . But when we look back and see on what the reasoning is based , and how the processes have been conducted , we shall find that every step was taken on the supposition that we were actually ...
Página 14
... the other ; and thus , the processes of Algebra become chains of thought , in which each link fulfils the double office of a distinct and connecting propos tion . LIBRARY . ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND 14 INTRODUCTION .
... the other ; and thus , the processes of Algebra become chains of thought , in which each link fulfils the double office of a distinct and connecting propos tion . LIBRARY . ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND 14 INTRODUCTION .
Página 31
... becomes Also , may be written - or , it may be written - · 7a3 8a2 8a2 - - 9a2c3 9a2c3 ( Sa2b4b2c6b3 ) ; 8a2b- ( 4b2c - ( 4b2c6b3 ) . · 6a2b2 + 5a2b3 , - ( 6a2b25a2b3 ) . - 8a + b2 -C . ( 8a + b2 + c ) ; ( 8a + c ) . 9a2c3 + b2 These ...
... becomes Also , may be written - or , it may be written - · 7a3 8a2 8a2 - - 9a2c3 9a2c3 ( Sa2b4b2c6b3 ) ; 8a2b- ( 4b2c - ( 4b2c6b3 ) . · 6a2b2 + 5a2b3 , - ( 6a2b25a2b3 ) . - 8a + b2 -C . ( 8a + b2 + c ) ; ( 8a + c ) . 9a2c3 + b2 These ...
Página 53
... becomes 0 , we shall have m terms in the quotient , and the result may be writ- ten thus : am bm = + am - 2b + am - 3f2 + - a b + abm - 2 + - b . CHAPTER III . OF ALGEBRAIC FRACTIONS . 62. AN ALGEBRAIC CHAP . II . ] 53 DIVISION .
... becomes 0 , we shall have m terms in the quotient , and the result may be writ- ten thus : am bm = + am - 2b + am - 3f2 + - a b + abm - 2 + - b . CHAPTER III . OF ALGEBRAIC FRACTIONS . 62. AN ALGEBRAIC CHAP . II . ] 53 DIVISION .
Página 70
... becomes greater and greater , it is evident that the value of the fraction will become less and less . When the value of b becomes very great , the value of the fraction becomes very small ; and finally , when ỏ becomes greater than any ...
... becomes greater and greater , it is evident that the value of the fraction will become less and less . When the value of b becomes very great , the value of the fraction becomes very small ; and finally , when ỏ becomes greater than any ...
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Términos y frases comunes
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient contrary signs cube root decimal places deduce denote the number derived polynomial Divide dividend entire number example exponent extract the square figures Find the factors Find the square find the values following RULE formula fourth fractional unit given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots remainder required root required to find result second degree second member second term simplest form square root substituted subtract suppose supposition take the equation taken third unknown quantity whence whole number write
Pasajes populares
Página 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 290 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 117 - The first ten numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Roots.
Página 136 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.
Página 200 - RULE I. Separate the given number into periods. of three figures each, beginning at the right hand ; the left hand period will often con tain less than three places of figures.
Página 100 - 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 will it take each person to perform the same work alone.
Página 62 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator. EXAMPLES FOR PRACTICE.
Página 154 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Página 222 - Consequently, teueя the index of the radical is divisible by the exponent of the power to which it is to be raised, perform the division, leaving the quantity under the radical sign unchanged.