New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications, for Colleges and High SchoolsIvison, Phinney & Company, 1863 - 420 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 28
... successively by the above rules . Thus , a— { b — c― ( d — e ) } = a— { b — c ― d + e } = a — b + c + d — e Or , in a different order , a― { b — c― ( d — e ) } = a — b + c + ( d — e ) —a — b + c + d — e EXAMPLES FOR PRACTICE . 61 ...
... successively by the above rules . Thus , a— { b — c― ( d — e ) } = a— { b — c ― d + e } = a — b + c + d — e Or , in a different order , a― { b — c― ( d — e ) } = a — b + c + ( d — e ) —a — b + c + d — e EXAMPLES FOR PRACTICE . 61 ...
Σελίδα 32
... successively added ; and the minus sign before a multiplier shows that the multiplicand is to be successively subtracted . To exhibit the law which governs the sign of a product , ac- cording to this principle , we present the four ...
... successively added ; and the minus sign before a multiplier shows that the multiplicand is to be successively subtracted . To exhibit the law which governs the sign of a product , ac- cording to this principle , we present the four ...
Σελίδα 55
... successive operations will appear as follows : ( 1. ) B ) A ( q Bq ( 2. ) R ) B ( 9 ' Rq ' ( 3. ) R ' ) R ( q " R'q " R ' 0 R To investigate the mutual relations of A , B , R , and R ' , we ob- serve that in division the product of the ...
... successive operations will appear as follows : ( 1. ) B ) A ( q Bq ( 2. ) R ) B ( 9 ' Rq ' ( 3. ) R ' ) R ( q " R'q " R ' 0 R To investigate the mutual relations of A , B , R , and R ' , we ob- serve that in division the product of the ...
Σελίδα 88
... successively . EXAMPLES FOR PRACTICE . Clear the following equations of fractions : x 1 . la 2x + 3x 2 . 7 3 . a X- a 3х - 10 . X- -5 = - 3 4 2x + 3 14 + 21 с x + a 2x - 3a 2 Ans . 6x + 8x - 9x = 120 . Ans . 18x - 6x - 9-2x - 10 . d Ans ...
... successively . EXAMPLES FOR PRACTICE . Clear the following equations of fractions : x 1 . la 2x + 3x 2 . 7 3 . a X- a 3х - 10 . X- -5 = - 3 4 2x + 3 14 + 21 с x + a 2x - 3a 2 Ans . 6x + 8x - 9x = 120 . Ans . 18x - 6x - 9-2x - 10 . d Ans ...
Σελίδα 90
... successively in ( 1 ) , ar = b , ar ' = b . whence , by Ax . 7 , we shall have ar = ar ' ; or , by transposing and factoring , a ( r ) = 0 . ( 2 ) ( 3 ) ( 4 ) ( 5 ) But equation ( 5 ) is impossible , since , by supposition , r — r ' is ...
... successively in ( 1 ) , ar = b , ar ' = b . whence , by Ax . 7 , we shall have ar = ar ' ; or , by transposing and factoring , a ( r ) = 0 . ( 2 ) ( 3 ) ( 4 ) ( 5 ) But equation ( 5 ) is impossible , since , by supposition , r — r ' is ...
Περιεχόμενα
66 | |
74 | |
81 | |
83 | |
89 | |
103 | |
118 | |
124 | |
130 | |
136 | |
145 | |
151 | |
157 | |
164 | |
172 | |
182 | |
189 | |
197 | |
204 | |
274 | |
283 | |
290 | |
298 | |
306 | |
308 | |
317 | |
323 | |
331 | |
340 | |
346 | |
353 | |
359 | |
370 | |
376 | |
388 | |
398 | |
405 | |
416 | |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
added algebraic quantity arithmetical progression binomial factors clearing of fractions coefficients cube root degree denote derived polynomial dividend division dollars EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the logarithm Find the sum find the values following RULE formula fourth geometrical progression geometrical series given equation given number given quantities greater greatest common divisor identical equation imaginary indicated inequality irreducible fraction last term least common multiple less letters minus sign monomial Multiply negative quantity nth root number of terms obtain OPERATION partial fractions permutations positive roots problem proportion quadratic quadratic equation quotient radical sign rational Reduce remainder represent required root result second member second term square root Sturm's Theorem subtracted suppose surd taken third three numbers tion transformed equation transposing trial divisor unknown quantity whence whole number X₁ zero
Δημοφιλή αποσπάσματα
Σελίδα 209 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Σελίδα 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
Σελίδα 178 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Σελίδα 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Σελίδα 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Σελίδα 77 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Σελίδα 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Σελίδα 266 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Σελίδα 169 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.