## New Elementary Algebra: Embracing the First Principles of the Science |

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algebraic quantities ANALYSIS.-Let x denote antecedent arithmetical arithmetical means binomial called Charles Clearing of fractions coefficient common difference complete equation completing the square contains contrary signs cost cube DAVIES denominator denote the number Divide dividend division dollars equal number equal to 12 equation whose roots EXAMPLES exponent extracting the square factors Find the square Find the sum following RULE formula Give the rule given number greater greatest common divisor hence indicated John last term least common multiple lemons Let x denote logarithm minuend minus monomial Multiply negative number added number is equal number of apples number of terms operation perfect square polynomial progression proportion quan quotient radical ratio Reduce remainder second degree second member second term simultaneous equations square root Substituting this value subtract tity transposing trinomial twice unknown quantity VERIFICATION

### Popular passages

Page 72 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...

Page 270 - 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 71 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 146 - Two travellers set out at the same time from London and York, whose distance apart is 150 miles; one of them goes 8 miles a day, and the other 7 ; in what time will they meet ? Ans, In 10 days. 10. At a certain election, 375 persons voted for two candidates, and the candidate chosen had a majority of 91; how many voted for each 1 Ans.

Page 146 - A person has two horses, and a saddle worth £50. Now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first. What is the value of each horse ? Ans.

Page 270 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order.

Page 76 - 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 175 - 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 271 - Quantities are said to be in proportion by inversion, or inversely, when the consequents are made the antecedents and the antecedents the consequents.

Page 118 - A fish was caught whose tail weighed 9lb., 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 ? Let 2a;= the weight of the body.