A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the Higher Parts Usually Taught in Colleges : Containing Moreover, the New Method of Cubic and Higher Equations, as Well as the Development and Application of the More Recently Discovered Theorem of SturmO. Hutchinson, 1842 - 360 σελίδες |
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Σελίδα 3
... real roots , of any algebraic equation , with much more ease than could be done by any previously discovered methods . The method of finding the numerical values of the roots of cubic and higher equations , as fully explained under the ...
... real roots , of any algebraic equation , with much more ease than could be done by any previously discovered methods . The method of finding the numerical values of the roots of cubic and higher equations , as fully explained under the ...
Σελίδα 177
... ROOTS OF QUADRATIC EQUATIONS . ( 154 ) . We have seen that all quadratic ... real values of a , it follows that the sign of the expression a2 + b ... roots of quadratic equations,
... ROOTS OF QUADRATIC EQUATIONS . ( 154 ) . We have seen that all quadratic ... real values of a , it follows that the sign of the expression a2 + b ... roots of quadratic equations,
Σελίδα 285
... roots . Hence , if a + √ - b is a root of this equation , then also will a ... real root . ( 252. ) If we divide both members of the identical equa- tion 2 ... roots occur in pairs,
... roots . Hence , if a + √ - b is a root of this equation , then also will a ... real root . ( 252. ) If we divide both members of the identical equa- tion 2 ... roots occur in pairs,
Σελίδα 302
... real roots , and n - 2 imaginary roots . ( 271. ) If n is odd , the equation an + 1 = 0 , or X " = - 1 , gives x = 1-1 = -1 , so that there is one real root and n ... imaginary roots 302 GENERAL PROPERTIES OF EQUATIONS . Binomial equations,
... real roots , and n - 2 imaginary roots . ( 271. ) If n is odd , the equation an + 1 = 0 , or X " = - 1 , gives x = 1-1 = -1 , so that there is one real root and n ... imaginary roots 302 GENERAL PROPERTIES OF EQUATIONS . Binomial equations,
Σελίδα 311
... root of equation ( 15 ) , " x = am + a2n x = a2m + an S giving the roots of equation ( 17 ) , ( 18 ) The roots given ... real . Now , in order that ( 5 ) and ( GENERAL PROPERTIES OF EQUATIONS . 311.
... root of equation ( 15 ) , " x = am + a2n x = a2m + an S giving the roots of equation ( 17 ) , ( 18 ) The roots given ... real . Now , in order that ( 5 ) and ( GENERAL PROPERTIES OF EQUATIONS . 311.
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A₁ algebraic annuity arithmetical progression assume becomes BINOMIAL THEOREM cleared of fractions common logarithms consequently cube root cubic equation D₁ degree denote dividend equa Equating the coefficients exponent expression Extracting the square factors figure Find a root find the value formula four quantities fourth geometrical progression given gives greatest common divisor greatest common measure Hence imaginary roots infinite series left-hand member m₂ method multinomial theorem multiply Napierian Nlog nth root nth term number of terms numerator and denominator obtain OPERATION polynomial proportion quadratic equation quotient real roots recurring equation Reduce remainder Required the sum result right-hand member root of equation Rule under Art scale of relation second term square root STURM'S THEOREM Subtracting suppose surd Taking the logarithm third three roots tion transposing and uniting uniting terms unknown quantity values substituted
Δημοφιλή αποσπάσματα
Σελίδα 199 - If we have a : c : : a' : c', a : c : : a" : c", a : c : : a'
Σελίδα 34 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
Σελίδα 67 - A farmer had two flocks of sheep, each containing the same number. Having sold from one of these 39, and from the other 93, he finds twice as many remaining in the one as in the other. How many did each flock originally contain 1 Prob.
Σελίδα 195 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 116 - Divide it by twice the root just found, and add the quotient both to the root and to the divisor. Multiply the divisor thus increased, into the term last placed in the root, and subtract the product from the dividend.
Σελίδα 48 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Σελίδα 176 - A person being asked his age, answered, " My mother was 20 years old when I was born, and her age multiplied by mine, exceeds our united ages by 2500.
Σελίδα 95 - Substitution. water. How much gold, and how much silver, did this crown contain ? Ans. 14,77... Ibs. of gold, and 5,22.. .Ibs. of silver. 151. Problem. To solve any number of equations of the...
Σελίδα 205 - Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then...
Σελίδα 61 - Any term may be transposed from one side of an equation to the other by changing its sign.