New University AlgebraIvison, Blakeman, Taylor & Company, 1875 - 412 páginas |
Dentro del libro
Resultados 1-5 de 32
Página viii
... DERIVED POLYNOMIALS COMPOSITION OF DERIVED POLYNOMIALS . EQUAL ROOTS ..... TRANSFORMATIONS ... DETACHED COEFFICIENTS .. SYNTHETIC DIVISION .. SURD AND IMAGINARY ROOTS .. RULE OF DES CARTES ... CARDAN'S RULE FOR CUBICS ... SECTION IX ...
... DERIVED POLYNOMIALS COMPOSITION OF DERIVED POLYNOMIALS . EQUAL ROOTS ..... TRANSFORMATIONS ... DETACHED COEFFICIENTS .. SYNTHETIC DIVISION .. SURD AND IMAGINARY ROOTS .. RULE OF DES CARTES ... CARDAN'S RULE FOR CUBICS ... SECTION IX ...
Página 32
... the principles already established we derive the following RULE.-I. Multiply the coefficients of the two terms together for the coefficient of the product . II . Write all the letters of both terms for 32 ENTIRE QUANTITIES .
... the principles already established we derive the following RULE.-I. Multiply the coefficients of the two terms together for the coefficient of the product . II . Write all the letters of both terms for 32 ENTIRE QUANTITIES .
Página 79
... derive a general rule for the division of frac- tions , from the following example : a 1. Divide by b C OPERATION . a с ÷ = ab - 1 ÷ cd1 = = b d ab - 1 ad = cd - 1 bc By inspecting this result , we find that the new numerator may be ...
... derive a general rule for the division of frac- tions , from the following example : a 1. Divide by b C OPERATION . a с ÷ = ab - 1 ÷ cd1 = = b d ab - 1 ad = cd - 1 bc By inspecting this result , we find that the new numerator may be ...
Página 81
... derived from the following observations : 1. If a fraction be multiplied by its own denominator , the product will be the numerator . 2. If a fraction be multiplied by any multiple of its denomina- tor , the product must be entire ...
... derived from the following observations : 1. If a fraction be multiplied by its own denominator , the product will be the numerator . 2. If a fraction be multiplied by any multiple of its denomina- tor , the product must be entire ...
Página 88
... derived from its numerator must be changed . NOTES . — 1 . The pupil should observe that in multiplying any fraction it will be most convenient to divide the multiplier by the denominator and multiply the numerator by the quotient . 2 ...
... derived from its numerator must be changed . NOTES . — 1 . The pupil should observe that in multiplying any fraction it will be most convenient to divide the multiplier by the denominator and multiply the numerator by the quotient . 2 ...
Contenido
94 | |
103 | |
105 | |
112 | |
118 | |
124 | |
125 | |
130 | |
136 | |
141 | |
145 | |
150 | |
151 | |
157 | |
164 | |
172 | |
174 | |
182 | |
189 | |
197 | |
265 | |
274 | |
283 | |
290 | |
298 | |
306 | |
313 | |
320 | |
328 | |
336 | |
343 | |
353 | |
359 | |
370 | |
376 | |
388 | |
398 | |
405 | |
416 | |
Otras ediciones - Ver todas
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.