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

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### Common terms and phrases

3abc algebraic quantities arithmetical means arithmetical progression binomial Binomial Theorem called cents common denominator common difference complete equation completing the square contain contrary sign cube decimal denotes dividend division divisor dollars double product enunciation equation gives equation involving EXAMPLES exponent extracting the square fifth power figure find a number Find the square Find the sum Find the values following RULE fourth power geometrical progression Give the rule given number greater greyhound Hence last term leaps least common multiple minus mixed quantity monomial Multiply negative number expressed number of terms obtain ounces of silver perfect square polynomial question quotient radical sign ratio Reduce remainder second degree second power second term simplest form square root Substituting this value subtract take the equation tens third three terms tion transposing trinomial twice the product unknown quantity values of x Verification whence 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.