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 11
... means of letters and signs the letters being employed to represent quantities , and the signs to represent the operations performed on them . ( 2. ) The sign + ( plus ) denotes addition . — ( minus ) denotes subtraction . Thus , a + b ...
... means of letters and signs the letters being employed to represent quantities , and the signs to represent the operations performed on them . ( 2. ) The sign + ( plus ) denotes addition . — ( minus ) denotes subtraction . Thus , a + b ...
Σελίδα 14
... means of connecting the quantity to which it belongs to one which precedes . Thus , in the first exam- ple , below , the positive quantities 6ax and 7ax would be understood to be positive even if the + before them were omitted ; the ...
... means of connecting the quantity to which it belongs to one which precedes . Thus , in the first exam- ple , below , the positive quantities 6ax and 7ax would be understood to be positive even if the + before them were omitted ; the ...
Σελίδα 44
... means of fractional indices ; for the cube root of a2 is a and the cube root of a or a1 is a3 ; also the fourth root of ab3 is aba , 1 T " & c . It likewise appears that , since the division of the powers of the same quantity is ...
... means of fractional indices ; for the cube root of a2 is a and the cube root of a or a1 is a3 ; also the fourth root of ab3 is aba , 1 T " & c . It likewise appears that , since the division of the powers of the same quantity is ...
Σελίδα 45
... means of ex- ponents or indices . NOTE . Since the even powers of all quantities , whether positive or negative , are alike positive , ( Art . 36 , NOTE , ) it follows that the even roots of all positive quantities may be either ...
... means of ex- ponents or indices . NOTE . Since the even powers of all quantities , whether positive or negative , are alike positive , ( Art . 36 , NOTE , ) it follows that the even roots of all positive quantities may be either ...
Σελίδα 85
... means geometrical ratio . Also , to avoid the too frequent repetition of the term , two dots are usually placed between the quantities to represent their ratio ; thus , ab signifies the ratio of a to b ; and a and b are called the terms ...
... means geometrical ratio . Also , to avoid the too frequent repetition of the term , two dots are usually placed between the quantities to represent their ratio ; thus , ab signifies the ratio of a to b ; and a and b are called the terms ...
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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.