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Page 132 - If the product of two numbers is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Page 29 - Thus the product of the sum and difference of two numbers is equal to the difference of their squares.
Page 97 - If the degree of the numerator is equal to, or greater than, that of the denominator, the preceding methods are inapplicable.
Page 381 - The sum of the products of the roots taken two at a time is equal to the coefficient of the third term.
Page 29 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 66 - A trinomial belongs to this type, ie it is a perfect square, when two of its terms are perfect squares, and the remaining term is equal to twice the product of the square roots of these terms.
Page 430 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 167 - Find the number. 13. If a certain number is divided by the sum of its three digits, the quotient is 43. The sum of the first two digits is equal to the third digit, and if 99 be added to the number, the first and last digits will be interchanged. Find the number. 14. If a certain number is divided by the sum of its two digits, the quotient is 4 and the remainder 3. Three times the first digit exceeds the second digit by 3. Find the number. 15.
Page 84 - To reduce fractions to their lowest terms. A fraction is in its lowest terms when its numerator and denominator are prime to each other; that is, when both terms have no common divisor.
Page 29 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.