An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts to Simplify Some of the More Difficult Parts of the Science, Particularly the Demonstration of the Binomial Theorem in Its Most General Form, [etc.]Hogan and Thompson, 1839 |
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Σελίδα vi
... appears to be preferable , as it affords the student an early opportunity of applying the principles that he has acquired to useful and interesting inquiries , an exer- cise which is generally found to be peculiarly pleasing and ...
... appears to be preferable , as it affords the student an early opportunity of applying the principles that he has acquired to useful and interesting inquiries , an exer- cise which is generally found to be peculiarly pleasing and ...
Σελίδα vii
... appears to be more simple and satisfactory than any which I have had an opportunity of seeing . In the practical application of this theorem to the expansion of a binomial , it is always best to separate the case in which the exponent ...
... appears to be more simple and satisfactory than any which I have had an opportunity of seeing . In the practical application of this theorem to the expansion of a binomial , it is always best to separate the case in which the exponent ...
Σελίδα 13
... appear . It is sometimes found convenient , when the coefficients are large numbers , to represent them , as well as the quantities which they multiply , by letters ; choosing always , agreeably to art . ( 1 ) , the leading letters of ...
... appear . It is sometimes found convenient , when the coefficients are large numbers , to represent them , as well as the quantities which they multiply , by letters ; choosing always , agreeably to art . ( 1 ) , the leading letters of ...
Σελίδα 34
... appears that aa — 2 is the greatest common measure of the terms of the proposed fraction , and , consequently , by dividing both numerator and denominator by this common measure , the frac- a2 + x2 a + x tion is reduced to its lowest ...
... appears that aa — 2 is the greatest common measure of the terms of the proposed fraction , and , consequently , by dividing both numerator and denominator by this common measure , the frac- a2 + x2 a + x tion is reduced to its lowest ...
Σελίδα 35
... appears less simple than the original one , but it is in reality more so , the numerator and denominator of the former being , re- spectively , x + y times that of the latter . That this process alters the form merely , and not ...
... appears less simple than the original one , but it is in reality more so , the numerator and denominator of the former being , re- spectively , x + y times that of the latter . That this process alters the form merely , and not ...
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a²x² arithmetical progression ax² ax³ becomes bers BINOMIAL THEOREM bx² Clear the equation coefficients column common logarithms completing the square compound interest consequently cube root cubic equation cx² decimals difference Divide dividend division equal EXAMPLES expansion exponent extracting the root factors figure Find a number find the values Find two numbers fourth fraction gallons geometrical geometrical progression hence imaginary improper fraction integral last term logarithms method multiplied negative number of solutions number of terms numerator and denominator obtained positive preceding quadratic QUESTION quotient rational Reduce remainder represented Required the sum required to find result second term simple equation square root substituting subtracting surd third transposing transposition unknown quantity values of x whence whole number
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Σελίδα 83 - В can perform a piece of work in 8 days, A and С together in 9 days, and В and С together in 10 days ; in how many days can each alone perform the same work ? Let...
Σελίδα 146 - PROBLEM I. To reduce a rational quantity to the form of a surd. RULE. Raise the quantity to a power...
Σελίδα 116 - The plate of a looking-glass is 18 inches by 12, and it is to be surrounded by a plain frame of uniform width/ having a surface equal to that of the glass.
Σελίδα 99 - The sum of the first and third of four numbers in geometrical progression is 148, and the sum of the second and fourth is 888.
Σελίδα 99 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Σελίδα 75 - There is a number consisting of two digits, which is equal to four times the sum of those digits; and if 18 be added to it, the digits will be inverted. What is the number?
Σελίδα 67 - Ans. 16 and 24. 42. It is required to find a number such, that if it be increased by 7, the square root of the sum shall be equal to the square root of the number itself, and 1 more. Ans. 9.
Σελίδα 52 - An equation of the third, fourth, &c. degree, is one in which the highest power of the unknown quantity is the third, fourth, &c.
Σελίδα 114 - It is required to find two numbers, such, that their sum, product, and difference of their squares, shall be all equal.
Σελίδα 145 - The fore-wheel of a carriage makes 6 revolutions more than the hind- wheel in going 120 yards; but if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind-wheel in the same distance.