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 SturmH.H. Hawley & Company, 1847 - 420 σελίδες |
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ algebraic approximative fractions arithmetical progression becomes binomial Binomial Theorem cleared of fractions common denominator consequently continued fraction cube root cubic equation D₁ degree denoted dividend equa equal EXAMPLES expansion exponent expression Extracting the square factors fifth root figure Find a root find the value formula fourth geometrical geometrical progression geometrical series given gives greatest common divisor greatest common measure Hence left-hand member letters logarithms m₁ method multiply NEGATIVE PRODUCTS Nlog nth root number of terms numerator and denominator obtain OPERATION partial denominators polynomial POSITIVE PRODUCTS quadratic equation quotient r₁ rational real roots reciprocal recurring equation recurring series Reduce remainder right-hand member Rule under Art scale of relation second term square root Sturm's Theorem subscript numbers Subtracting suppose surd THEOREM three roots tion transposing and uniting unknown quantity X₁ Y₁
Δημοφιλή αποσπάσματα
Σελίδα 34 - ... then divide the first term on the left of the dividend by the first term on the left of the divisor...
Σελίδα 69 - 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 199 - 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 29 - 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.
Σελίδα 223 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Σελίδα 201 - Find a number consisting of three digits, such, that the sum of the squares of the digits, without considering their position, may be 104 ; but the square of the middle digit exceeds twice the product of the other two by 4 ; farther, if 594 be subtracted from the number sought, the three digits are inverted.
Σελίδα 34 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Σελίδα 134 - Seek how often the divisor is contained in the dividend (except the right hand figure) and place the answer in the root for the second figure of it, and likewise on the right hand of the divisor. Multiply the divisor with the figure last annexed by the figure last placed in the root, and subtract the product from the dividend. To the remainder join the next period for a new dividend.
Σελίδα 234 - 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 134 - 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.