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
... 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 please , as , a5 + 1 = a® ; a © + 1 = a1 & c . ( 3 ) Divide 1 + ax + bx2 + ...
... 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 please , as , a5 + 1 = a® ; a © + 1 = a1 & c . ( 3 ) Divide 1 + ax + bx2 + ...
Σελίδα 69
... root is to be extracted , has no exact root , the work may be continued at pleasure , or as far as till the law of the series becomes obvious . [ V. Ex . 3 , p . 60. ] ( 4 ) Required the cube root of a3 - EVOLUTION . 69.
... root is to be extracted , has no exact root , the work may be continued at pleasure , or as far as till the law of the series becomes obvious . [ V. Ex . 3 , p . 60. ] ( 4 ) Required the cube root of a3 - EVOLUTION . 69.
Σελίδα 106
... continued pro- portion , Then xy :: y : z Whence xz = y2 . It is sometimes easier to employ fewer letters than there are unknown quantities . Thus , the solution becomes more easy and elegant . There are some examples of this kind of ...
... continued pro- portion , Then xy :: y : z Whence xz = y2 . It is sometimes easier to employ fewer letters than there are unknown quantities . Thus , the solution becomes more easy and elegant . There are some examples of this kind of ...
Σελίδα 151
... continued proportion , which being added together , the sum is 126 , but when mul- tiplied together , the product is 13824. Required the num- bers ? Let x , y , and z represent the three numbers . Then by continued proportion xy :: y ...
... continued proportion , which being added together , the sum is 126 , but when mul- tiplied together , the product is 13824. Required the num- bers ? Let x , y , and z represent the three numbers . Then by continued proportion xy :: y ...
Σελίδα 155
... continued geometrical pro- portion ; the sum of the first and second is 10 , and the differ- ence of the second and third is 24. Required the numbers ? Ans . The numbers are 2 , 8 , and 32 , or 25 , -15 , and 9 . ( 41 ) The 4th part of ...
... continued geometrical pro- portion ; the sum of the first and second is 10 , and the differ- ence of the second and third is 24. Required the numbers ? Ans . The numbers are 2 , 8 , and 32 , or 25 , -15 , and 9 . ( 41 ) The 4th part of ...
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.