## First Lessons in Algebra: Embracing the Elements of the Science |

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added addition affected algebraic antecedent arithmetical becomes binomial called cents changing coefficient common difference completing composed consequent considered contains cube denominator denotes difference Divide dividend division divisor dollars double elimination entire equal equation equation 22 EXAMPLES exponent expression extracting the square extremes factors fifth power figure Find the square Find the values following RULE four fourth power fraction gives greater half Hence indicated interest known last term less letter manner means method monomial multiplied negative number of terms obtain operations perfect square periods person polynomial positive pound progression proportion question quotient radical raise ratio receive Reduce remainder represent result second degree second term similar simplest form square root Substituting subtract taken tens third tion transposing twice units unknown quantity values of x Verification whence write yards

### Popular passages

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 89 - 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 175 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...

Page 231 - Quantities are said to be in proportion by inversion, or inversely, when the consequents are made the antecedents and the antecedents the consequents.

Page 35 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.

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.

Page 136 - The square of a number composed of tens and units is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.

Page 79 - A fish was caught whose tail weighed 9Z6. ; his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together : what was the weight of the fish?

Page 231 - Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.