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1st eq 2nd eq a-Ha absolute number added 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 geometrical progression geometrical series Given the common greatest common measure hence highest power improper fraction infinite series last term 41 less method Multg Multiply nth root number of factors number of terms operation original equation preceding proposed equation quadratic equation ques Reduce remainder Required the cube Required the numbers Required the square RULE second term side simple equations square root substituting subtract successive sums surd terms 20 third term tion trans transformed equation unknown quantity Whence whole number
Page 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.
Page 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...
Page 302 - J of the first, \ of the second, and \ of the third, may be all equal to each other. Ans. 8, 12, and 16.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.