New University AlgebraIvison, Blakeman, Taylor & Company, 1875 - 412 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 com- mon divisor of B and R. For like reasons , referring to the second equation , 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 com- mon divisor of B and R. For like reasons , referring to the second equation , the greatest common divisor of B and R.will also divide ...
Página 89
... whence , by addition , we have 2 81 = 81 ; the value of x is therefore verified . 155. It should here be observed that an equation of the first degree , containing but one unknown quantity , cannot have more than one root . For ...
... whence , by addition , we have 2 81 = 81 ; the value of x is therefore verified . 155. It should here be observed that an equation of the first degree , containing but one unknown quantity , cannot have more than one root . For ...
Página 95
... whence , X X + = 21 ; 3 4 4x + 3x = 21 × 12 , 7x = 21 × 12 , x = 36 , Ans . 2. A and B have each the same annual income . A's yearly expenses are $ 800 and B's $ 1000 , and A saves as much in 5 years as B saves in 7 years ; how much is ...
... whence , X X + = 21 ; 3 4 4x + 3x = 21 × 12 , 7x = 21 × 12 , x = 36 , Ans . 2. A and B have each the same annual income . A's yearly expenses are $ 800 and B's $ 1000 , and A saves as much in 5 years as B saves in 7 years ; how much is ...
Página 96
... whence , 6x = 12 ; x2 , the less , x + 6 = 8 , the greater . These examples illustrate the three essential steps in the solu- tion of any problem requiring but one equation ; and we may derive from them the following GENERAL RULE . I ...
... whence , 6x = 12 ; x2 , the less , x + 6 = 8 , the greater . These examples illustrate the three essential steps in the solu- tion of any problem requiring but one equation ; and we may derive from them the following GENERAL RULE . I ...
Página 99
... whence , 15a and 15x8a + 336 - 8x , 7x = 7a - 336 , - x = α 48 $ 1440 , Ans . 21. A prize having been captured by a privateer , the sum of $ 7560 was awarded to the officers , and the residue was divided equally among the crew ...
... whence , 15a and 15x8a + 336 - 8x , 7x = 7a - 336 , - x = α 48 $ 1440 , Ans . 21. A prize having been captured by a privateer , the sum of $ 7560 was awarded to the officers , and the residue was divided equally among the crew ...
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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.