New University AlgebraIvison, Blakeman, Taylor & Company, 1875 - 412 páginas |
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Página 37
... actual multiplication . The 3d , 4th , and 5th powers , however , may sometimes be easily written , without actual multiplication , by means of the formulas which follow : 1. ( a + b ) 3 2. ( ab 4 MULTIPLICATION . 37.
... actual multiplication . The 3d , 4th , and 5th powers , however , may sometimes be easily written , without actual multiplication , by means of the formulas which follow : 1. ( a + b ) 3 2. ( ab 4 MULTIPLICATION . 37.
Página 140
... mean that the couriers were together at 12 o'clock , at the point P , and at no other time or place . And this interpretation is also confirmed by the conditions of the problem . For , if d = 0 , then at 12 o'clock B must have been with ...
... mean that the couriers were together at 12 o'clock , at the point P , and at no other time or place . And this interpretation is also confirmed by the conditions of the problem . For , if d = 0 , then at 12 o'clock B must have been with ...
Página 159
... 2x3y + 3x2y2 + x1 . — 218. In a future section we shall give a formula , called the Binomial Formula , by means of which any power of a binomial may be obtained without the labor of multiplication . Th pr 158 4. ( 3a + 2b + c ) 3.
... 2x3y + 3x2y2 + x1 . — 218. In a future section we shall give a formula , called the Binomial Formula , by means of which any power of a binomial may be obtained without the labor of multiplication . Th pr 158 4. ( 3a + 2b + c ) 3.
Página 237
... means of a final equation in the quadratic form . Most of the examples of this kind are embraced in these three cases : 1st . Where one of the equations is simple , and the other quadratic . 2d . Where both of the equations are ...
... means of a final equation in the quadratic form . Most of the examples of this kind are embraced in these three cases : 1st . Where one of the equations is simple , and the other quadratic . 2d . Where both of the equations are ...
Página 258
... means of either one or two letters . It is left to the judgment and skill of the learner to discover the mode of solution , in each example , which is most simple . 1. It is required to divide the number 14 into two such parts , that 9 ...
... means of either one or two letters . It is left to the judgment and skill of the learner to discover the mode of solution , in each example , which is most simple . 1. It is required to divide the number 14 into two such parts , that 9 ...
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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.