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 13
... coefficients are severally 3 , 4 , and 7 ; when no number is prefixed , as is the case when the quantity is to be taken but once , we say that the coefficient is unity ; the quantities xy , abc , yz , & c . are in fact the same as 1xy ...
... coefficients are severally 3 , 4 , and 7 ; when no number is prefixed , as is the case when the quantity is to be taken but once , we say that the coefficient is unity ; the quantities xy , abc , yz , & c . are in fact the same as 1xy ...
Σελίδα 17
... coefficients are literal instead of numeral , they are to be collected in a similar way ; but here their several sums will have a compound form , as in the following examples : 1 ax + by2 cdx + ady bx - cy2 2 * ADDITION . 17.
... coefficients are literal instead of numeral , they are to be collected in a similar way ; but here their several sums will have a compound form , as in the following examples : 1 ax + by2 cdx + ady bx - cy2 2 * ADDITION . 17.
Σελίδα 20
... coefficients . 1 . From ax2 + mxy + nx + b Take sx2 · рxy + qx . с - ( as ) x2 + ( m + p ) xy + ( n − q ) x + b + c - 2 . From pxy + qxz —rz2 + s Take mxy - pqxz ― -nz2 + a 3 . From a ( xy ) + bxy + c ( a + x ) 2 Take ( xy ) -bxy + ( a ...
... coefficients . 1 . From ax2 + mxy + nx + b Take sx2 · рxy + qx . с - ( as ) x2 + ( m + p ) xy + ( n − q ) x + b + c - 2 . From pxy + qxz —rz2 + s Take mxy - pqxz ― -nz2 + a 3 . From a ( xy ) + bxy + c ( a + x ) 2 Take ( xy ) -bxy + ( a ...
Σελίδα 21
... coefficients annex the product of the letters , and it will be the whole product . Thus , if it be required to multiply 6ax by 4b , we have 24 for the product of the coefficients , and abx for the product of the letters ; consequently ...
... coefficients annex the product of the letters , and it will be the whole product . Thus , if it be required to multiply 6ax by 4b , we have 24 for the product of the coefficients , and abx for the product of the letters ; consequently ...
Σελίδα 25
... coefficients annex the quotient of the let- ters , and it will be the whole quotient . * NOTE . The rule for the signs must be observed here , as well as in multiplication . 1. Divide 12ax by 3a . EXAMPLES . 2. Divide 24xy by 3xy . 12ax ...
... coefficients annex the quotient of the let- ters , and it will be the whole quotient . * NOTE . The rule for the signs must be observed here , as well as in multiplication . 1. Divide 12ax by 3a . EXAMPLES . 2. Divide 24xy by 3xy . 12ax ...
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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
Δημοφιλή αποσπάσματα
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.