New University AlgebraIvison, Blakeman, Taylor & Company, 1875 - 412 páginas |
Dentro del libro
Resultados 1-5 de 58
Página 31
... suppose it were required to multiply any quantity , as a , by cd . Now it is evident that a taken c minus . d times , is the same as a taken c times , diminished by a taken d times ; or a × ( c — d ) = ac ad . In the first term of this ...
... suppose it were required to multiply any quantity , as a , by cd . Now it is evident that a taken c minus . d times , is the same as a taken c times , diminished by a taken d times ; or a × ( c — d ) = ac ad . In the first term of this ...
Página 41
... Suppose both dividend and divisor to be arranged according to the descending powers of some letter . Then it follows , from ( 75 , 1 ) , that the first term of the dividend must be the product of the first term of the divisor by the ...
... Suppose both dividend and divisor to be arranged according to the descending powers of some letter . Then it follows , from ( 75 , 1 ) , that the first term of the dividend must be the product of the first term of the divisor by the ...
Página 54
... suppose A to be a quantity which is exactly divisible by another quantity , D , and let q represent the quotient . Then , A D - q . If we now multiply the dividend by m , we shall have in which qm is entire . it will also divide Am . Am ...
... suppose A to be a quantity which is exactly divisible by another quantity , D , and let q represent the quotient . Then , A D - q . If we now multiply the dividend by m , we shall have in which qm is entire . it will also divide Am . Am ...
Página 55
... Suppose two polynomials to be arranged according to the powers of the same letter , and let A represent the greater and B the less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till ...
... Suppose two polynomials to be arranged according to the powers of the same letter , and let A represent the greater and B the less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till ...
Página 89
... the first degree , containing but one unknown quantity , cannot have more than one root . For , whatever the equation may be , suppose it to EXAMPLES FOR PRACTICE . Find the value of x in 8 * REDUCTION . 89 REDUCTION OF SIMPLE EQUATIONS.
... the first degree , containing but one unknown quantity , cannot have more than one root . For , whatever the equation may be , suppose it to EXAMPLES FOR PRACTICE . Find the value of x in 8 * REDUCTION . 89 REDUCTION OF SIMPLE EQUATIONS.
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Términos y frases comunes
a²x added algebraic quantity arithmetical arithmetical progression binomial factors coefficients cube root decimal places degree denominator denote difference dividend division dollars equal equation containing EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the square Find the sum find the values following RULE.-I formula geometrical progression given equation given number given quantity greater greatest common divisor identical equation inequality irreducible fraction least common multiple less letter miles minus sign monomial Multiply negative quantity nth root number of terms o'clock obtain OPERATION problem quadratic Quadratic Equation quan quotient radical sign rational Reduce remainder represent required root result second member second term shillings solution square root Sturm's Theorem subtracted suppose surd third three numbers tion transformed equation trial divisor unknown quantity whence whole numbers X₁ zero
Pasajes populares
Página 167 - 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.
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 176 - ... 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 167 - 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 141 - But the relations of these quantities will not be changed, if we suppose the path of motion to be a curve, instead of a straight line. The above formula will therefore apply to the hands of a clock moving around the dial-plate, or to the planets moving in the circle of the heavens. It will thus afford a direct solution to the following problems : 1. The hour and minute hands of a clock are together at 12 o'clock ; when are they next together ? The circumference of the dial-plate is divided into 12...
Página 36 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.
Página 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Página 36 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Página 264 - 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 266 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.