# Elementary Algebra: Embracing the First Principles of the Science

A.S. Barnes & Company, 1848 - Algebra
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Page 135 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 234 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 231 - Quantities are said to be in proportion by composition, when the sum of the antecedent and consequent is compared either with antecedent or consequent.
Page 145 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Page 38 - Divide the coefficient of the dividend by the coefficient of the divisor.
Page 137 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.
Page 141 - ... equal to the square root of the numerator divided by the square root of the denominator.
Page 116 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14JA days, B 17fa, and C 23JT.
Page 56 - To add fractional quantities together. RULE. Reduce the fractions, if necessary, to a common denominator ; then add the numerators together, and place their sum over the common denominator.