Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA.S. Barnes & Burr, 1860 - 400 σελίδες |
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Σελίδα 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 ...
Σελίδα 14
... , the processes of Algebra become chains of thought , in which each link fulfils the double office of a distinct and connecting propos tion . ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND PRELIMINARY REMARKS 14 INTRODUCTION .
... , the processes of Algebra become chains of thought , in which each link fulfils the double office of a distinct and connecting propos tion . ELEMENTS OF ALGEBRA . CHAPTER I. DEFINITIONS AND PRELIMINARY REMARKS 14 INTRODUCTION .
Σελίδα 31
... becomes 8a2 - ( 3ab2b2 + 2bc ) . Sa2b 4b2c + 6b3 , - ( Sa2b4b2c 6b3 ) ; 7a38a2b- ( 4bc6b3 ) . 6a2b2 + 5a2b3 , ( 6a2b25a2b3 ) . Also , - 9a2c3 - Sa + b2 . -C . · - 9a2c3 ( 8a4b2 + c ) ; may be written - or , it may be written - 9a2c3b2 ...
... becomes 8a2 - ( 3ab2b2 + 2bc ) . Sa2b 4b2c + 6b3 , - ( Sa2b4b2c 6b3 ) ; 7a38a2b- ( 4bc6b3 ) . 6a2b2 + 5a2b3 , ( 6a2b25a2b3 ) . Also , - 9a2c3 - Sa + b2 . -C . · - 9a2c3 ( 8a4b2 + c ) ; may be written - or , it may be written - 9a2c3b2 ...
Σελίδα 53
... becomes 0 , we shall have m terms in the quotient , and the result may be writ ten thus : am - α bm b = am - 1 + am - 2b + am - 362 + • + abm - 2 + bs . 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 - α bm b = am - 1 + am - 2b + am - 362 + • + abm - 2 + bs . CHAPTER III . OF ALGEBRAIC FRACTIONS . 62. AN ALGEBRAIC CHAP . II . ] 53 DIVISION .
Σελίδα 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 b 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 b becomes greater than any ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes binomial called co-efficient common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Δημοφιλή αποσπάσματα
Σελίδα 99 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Σελίδα 364 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Σελίδα 118 - X 6 62 + 3 x 3; and taken 3 tens times, 32 + 2 (3 X 6) + 6s gives 3 x 6 + 32 ; and their sum is, 33 + 2 (3 x 6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Σελίδα 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 39 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Σελίδα 200 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a, dividend.
Σελίδα 242 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 215 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.