The elements of algebraOliver & Boyd, 1857 - 95 σελίδες |
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Σελίδα 11
... descend- ing order , it is obvious that in the product the powers of the same quantity will ascend or descend in the same order . Hence the operations may be performed by means of the coefficients alone , annexing afterwards the proper ...
... descend- ing order , it is obvious that in the product the powers of the same quantity will ascend or descend in the same order . Hence the operations may be performed by means of the coefficients alone , annexing afterwards the proper ...
Σελίδα 13
... descend in the same or- der as in the divisor and dividend , the quotient therefore is 3x + 7 3x2 - x + 2 + The process may be still farther abridged , as follows : - Arrange the coeffi- cients as before , and find the first figure of ...
... descend in the same or- der as in the divisor and dividend , the quotient therefore is 3x + 7 3x2 - x + 2 + The process may be still farther abridged , as follows : - Arrange the coeffi- cients as before , and find the first figure of ...
Σελίδα 66
... descending one . Thus 1 , 3 , 5 , & c . is an ascending series , whose common difference is 2 ; and 12 , 9 , 6 , & c . is a descending one , whose common difference is 3 . 72. In every series , of whatever kind , the first and last ...
... descending one . Thus 1 , 3 , 5 , & c . is an ascending series , whose common difference is 2 ; and 12 , 9 , 6 , & c . is a descending one , whose common difference is 3 . 72. In every series , of whatever kind , the first and last ...
Σελίδα 69
... descend in 11 seconds ; it being known that it descends 16.1 feet in the first second , 48.3 in the next , 80-5 in the ... descending one whose common ratio is - - 77. Retaining the same notation as before , let us assume t1 , t2 , tz ...
... descend in 11 seconds ; it being known that it descends 16.1 feet in the first second , 48.3 in the next , 80-5 in the ... descending one whose common ratio is - - 77. Retaining the same notation as before , let us assume t1 , t2 , tz ...
Σελίδα 71
... descending series . 79. If r be less than unity , the quantity " becomes less and less as n increases ; and by taking n large enough , it may be made less than any quantity that can be assigned . Hence , if n be taken infinite ...
... descending series . 79. If r be less than unity , the quantity " becomes less and less as n increases ; and by taking n large enough , it may be made less than any quantity that can be assigned . Hence , if n be taken infinite ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
2ab+b² a+b+c a²+2ab+b² a²+2ax a²x² annex arithmetical series ax² binomial binomial theorem common denominator common difference common ratio compound quantity consecutive numbers cube root deno denote the number Divide divisor double equal equation contains EXERCISES expressed Extract the square factor Find a number find the Greatest Find the number Find the sum following quantities geometric means GEOMETRICAL PROGRESSION given quantity Greatest Common Measure Hence Least Common Multiple letters miles per hour mixed quantities multiplied negative number of balls number of combinations number of permutations number of terms numbers whose sum numerator and denominator Prove QUADRATIC EQUATIONS quotient remainder shillings sign changed simple quantity square root subtracting surd t₁ things taken third total number transposing travelled unknown quantity
Δημοφιλή αποσπάσματα
Σελίδα 59 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 86 - The fore-wheel of a carriage makes six 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 four revolutions more than the hind-wheel in going the same distance.
Σελίδα 58 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Σελίδα 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.
Σελίδα 42 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Σελίδα 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.
Σελίδα 64 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 39 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.
Σελίδα 42 - Take the root of the first term, for the first term of the required root...
Σελίδα 38 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...