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2nd power 3x²y 3xy² 4th power algebraic arithmetical arithmetical mean arithmetical progression coefficient denominator difference Divide x² dividend equation whose roots equation x³ EXAMPLES exponent expression figure Find the 5th Find the equation Find the greatest Find the least Find the number Find the product Find the roots Find the value find x fractions geometrical mean geometrical progression given equation Given x² greatest common divisor last term least common multiple letters mantissa miles minuend mixed quantity monomials Multiply negative number of terms Operation problem Prop proportion px² quotient Reduce remainder root of x³ second member Simplify Solution Solve the equation square root subtract take the square transposed unknown quantity Va² Vide Def whence x²y x²y² x³y xy² xy³ y² x²
Page 122 - A banker has two kinds of money ; it takes a pieces of the first to make a crown, and b of the second to make the same sum. Some one offers him a crown for c pieces. How many of each kind must the banker give him ? Ans.
Page 226 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 40 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 57 - Divide the greater number by the less, the divisor by the remainder, and thus continue to divide the last divisor by the last remainder until there is no remainder ; the last divisor will be the greatest common divisor.
Page 239 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 195 - A man travelled 105 miles, and then found that if he had not travelled so fast by 2 miles an hour, he should have been 6 hours longer in performing the journey.
Page 117 - C in ten days ; how many days would it take each to perform the same work alone ? Ans.
Page 223 - If the means of a proportion are equal, either mean is called a Mean Proportional between the first and last terms, and the last term is called a Third Proportional to the first and second terms.