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 páginas |
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Página 56
... Whence it follows that the greatest common divisor of A and B will divide R , and is therefore a common divisor of B and R. For like reasons , referring to the second equa- tion , the greatest common divisor of B and R will also divide ...
... Whence it follows that the greatest common divisor of A and B will divide R , and is therefore a common divisor of B and R. For like reasons , referring to the second equa- tion , the greatest common divisor of B and R will also divide ...
Página 89
... whence , by addition , we have 81 = 81 , and the value of x is therefore vcrified . 155. It should here be observed that an equation of the first degree , containing but one unknown quantity , can not have more than one root . For ...
... whence , by addition , we have 81 = 81 , and the value of x is therefore vcrified . 155. It should here be observed that an equation of the first degree , containing but one unknown quantity , can not have more than one root . For ...
Página 90
... 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 not zero , and a is not zero . Hence , An ...
... 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 not zero , and a is not zero . Hence , An ...
Página 91
... whence , by division , x = 4 . х 3. When the equation contains but a single numerical term , we may simply indicate the multiplication of this term , in the clearing of fractions , until the final step in the reduction is reached . x ...
... whence , by division , x = 4 . х 3. When the equation contains but a single numerical term , we may simply indicate the multiplication of this term , in the clearing of fractions , until the final step in the reduction is reached . x ...
Página 95
... whence х х 3 + 4 = 21 ; 4x + 3x = 21x12 , 7x = 21 × 12 , x = 36 , Ans . 2. A and B have each the same annual income . A's yearly ex- penses are $ 800 and B's $ 1000 , and A saves as much in 5 years as B saves in 7 years ; how much is ...
... whence х х 3 + 4 = 21 ; 4x + 3x = 21x12 , 7x = 21 × 12 , x = 36 , Ans . 2. A and B have each the same annual income . A's yearly ex- penses are $ 800 and B's $ 1000 , and A saves as much in 5 years as B saves in 7 years ; how much is ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Página 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.
Página 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...
Página 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...
Página 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Página 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.
Página 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Página 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.
Página 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.