New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications. For Colleges and High SchoolsIvison, Phinney, Blakeman, & Company, 1864 - 420 σελίδες |
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Σελίδα 12
... equal . Thus , in a = b + c , the sign ,, indicates that is equal to b plus c . An expression of equality between two quantities is called an equation . 16. The Sign of Inequality is the angle , > 12 . ALGEBRAIC QUANTITIES . Symbols of ...
... equal . Thus , in a = b + c , the sign ,, indicates that is equal to b plus c . An expression of equality between two quantities is called an equation . 16. The Sign of Inequality is the angle , > 12 . ALGEBRAIC QUANTITIES . Symbols of ...
Σελίδα 13
... equal to the ratio of c to d ; and the expression ab :: c : d signifies the same , and may be read , a is to b as c is to d . · 21. The Sign of Variation is the character ∞ . It signifies that the two quantities between which it is ...
... equal to the ratio of c to d ; and the expression ab :: c : d signifies the same , and may be read , a is to b as c is to d . · 21. The Sign of Variation is the character ∞ . It signifies that the two quantities between which it is ...
Σελίδα 15
... equal quantities be added to equal quantities , the sums will be equal . 2. If the same quantity or equal quantities be subtracted from equal quantities , the remainders will be equal . 3. If equal quantities be multiplied by the same , or ...
... equal quantities be added to equal quantities , the sums will be equal . 2. If the same quantity or equal quantities be subtracted from equal quantities , the remainders will be equal . 3. If equal quantities be multiplied by the same , or ...
Σελίδα 16
... equal quantities are equal . 9. Like roots of equal quantities are equal . 10. The whole of a quantity is greater than any of its parts . 11. The whole of a quantity is equal to the sum of all its parts . EXERCISES IN ALGEBRAIC NOTATION ...
... equal quantities are equal . 9. Like roots of equal quantities are equal . 10. The whole of a quantity is greater than any of its parts . 11. The whole of a quantity is equal to the sum of all its parts . EXERCISES IN ALGEBRAIC NOTATION ...
Σελίδα 19
... equal . Thus , 5a is not equal to 5a , for the former expression signifies that a is taken additively five times , and the latter signifies that a is taken subtract- ively five times . 3. Two quantities having the same absolute value ...
... equal . Thus , 5a is not equal to 5a , for the former expression signifies that a is taken additively five times , and the latter signifies that a is taken subtract- ively five times . 3. Two quantities having the same absolute value ...
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added algebraic quantity arithmetical progression binomial factors clearing of fractions coefficients cube root degree denote derived polynomial division dollars EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the logarithm Find the sum find the values following RULE formula geometrical progression 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 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 Tx+U University Algebra unknown quantity whence whole number X₁ zero
Δημοφιλή αποσπάσματα
Σελίδα 204 - ... 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.
Σελίδα 36 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 61 - 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.
Σελίδα 396 - VARIATIONS of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of variations of the signs, p the number of permanences ; we shall have m=n+p. Moreover, let n' denote the number of positive roots, and p' the number...
Σελίδα 173 - 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.
Σελίδα 359 - From this we might conclude that every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and can have no more.
Σελίδα 72 - 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.
Σελίδα vii - Fractional exponents are used to denote both involution and evolution in the same expression, the numerator indicating the power to which the quantity is to be raised, and the denominator the required root of this power. Thus, the expression a* signifies the 4th root of the 3d power of a, and is equivalent to Va'.
Σελίδα 31 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Σελίδα 93 - Divide 48 into two such parts, that if the less be divided by 4, and the greater by 6, the sum of the quotients will be 9. Ans. 12 and 36. 11. An estate is to be divided among 4 children, in the following manner : The first is to have $200 more than 1 of the whole.