A Practical System of Algebra: Designed for the Use of Schools and Private StudentsBaldwin and Cradock, 1831 - 309 σελίδες |
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Σελίδα 31
... number of terms be found in the quotient , as will law by which it may be continued at pleasure . ( 1 ) Divide 1 by 1 - a . a6 & c . This is sufficient to shew that the index of each succeeding term would increase by 1 to any length we ...
... number of terms be found in the quotient , as will law by which it may be continued at pleasure . ( 1 ) Divide 1 by 1 - a . a6 & c . This is sufficient to shew that the index of each succeeding term would increase by 1 to any length we ...
Σελίδα 61
... terms as follows : n ( u + x ) " = a " ++ an − 1x + + & c . ( a — x ' ) " = a " —— a " −1x + n ( n - 1 ) 1.2 ¿ n ... number of terms , viz . 2 , counting from the beginning we have 10 , the next coefficient , and so the others may be ...
... terms as follows : n ( u + x ) " = a " ++ an − 1x + + & c . ( a — x ' ) " = a " —— a " −1x + n ( n - 1 ) 1.2 ¿ n ... number of terms , viz . 2 , counting from the beginning we have 10 , the next coefficient , and so the others may be ...
Σελίδα 79
... terms , successively , by the denominators of those fractions , or by multiplying both sides by the product of all the denominators , or by any quantity ... number that is divisible by 2 , 3 , and 4 , without a remainder , is 12 . Whence ...
... terms , successively , by the denominators of those fractions , or by multiplying both sides by the product of all the denominators , or by any quantity ... number that is divisible by 2 , 3 , and 4 , without a remainder , is 12 . Whence ...
Σελίδα 98
... value of x will readily be found . RULE II . Multiply , or divide , each of the equations by such numbers , or quantities , as will make one of the terms the same in all the equations , unless one of the terms is already so ; then ...
... value of x will readily be found . RULE II . Multiply , or divide , each of the equations by such numbers , or quantities , as will make one of the terms the same in all the equations , unless one of the terms is already so ; then ...
Σελίδα 132
... terms by a geome- trical series , beginning the first term , if the second be even , with unity for the numerator ... number . EXAMPLES . ( 1 ) Given the general equation axpx = q to find the value of x . Multg . by the series ; and ...
... terms by a geome- trical series , beginning the first term , if the second be even , with unity for the numerator ... number . EXAMPLES . ( 1 ) Given the general equation axpx = q to find the value of x . Multg . by the series ; and ...
Συχνά εμφανιζόμενοι όροι και φράσεις
1st eq 2nd eq absolute number added Algebra arithmetical progression binomial biquadratic change of signs coefficient common denominator common difference compound quantity cube root cubic equation Divide the number dividend divisor equa equal quantities EXAMPLES FOR PRACTICE expressed Extg Extracting the roots Find a number Find the sum find the value Find two numbers find x geometrical progression Given the common greatest common measure hence highest power improper fraction infinite series last term 41 less method Multg Multiply nth root number of terms operation original equation proposed equation quadratic equation ques Reduce remainder Required the cube Required the numbers RULE second term side simple equations square root substituting subtract successive sums surd terms 20 third term trans transformed equation unknown quantity Whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 154 - What two numbers are those, whose difference is to the greater as 2 to 9, and the difference of whose squares is 128 1 Prob.
Σελίδα 68 - ... the square of the two terms of the root already obtained, the remainder will be equal to twice the first two terms of the root multiplied by the third plus the square of the third. Dividing this remainder, therefore, by twice the terms of the root already found, or which is the same thing, dividing the first term of the remainder by twice the first term of the root, we shall obtain the third term sought. Subtracting from the first remainder twice the product of the first two terms of the root...
Σελίδα 302 - J of the first, \ of the second, and \ of the third, may be all equal to each other. Ans. 8, 12, and 16.
Σελίδα 120 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
Σελίδα 53 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 305 - The sum of the first and second of four numbers in geometrical progression is 15, and the sum of the third and fourth is 60. Required the numbers.
Σελίδα 33 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Σελίδα 308 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 307 - Find four numbers in arithmetical progression such that the sum of the first and third shall be 22, and the sum of the second and fourth 36.