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

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algebraic quantities Analysis.—Let x denote arithmetical arithmetical means binomial called Charles Clearing of fractions coefficient common difference complete equation completing the square contains contrary signs cost cube 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 geometrical progression Give the rule given number greater greatest common divisor hence indicated John John,s last term least common multiple lemons Let x denote logarithm miles minuend minus monomial Multiply negative number added number equal number of apples number of terms perfect square polynomial progression proportion quan quotient radical ratio Reduce remainder result second degree second member second term simultaneous equations square root Substituting this value subtract subtrahend tity tlhe transposing trinomial twice units unknown quantity VERIFICATION whence write

### Popular passages

Page 73 - 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 177 - The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units.

Page 160 - 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 155 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Page 148 - 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 148 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.

Page 279 - In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the square of the middle term when there is an uneven number of terms.

Page 74 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.

Page 129 - A person goes to a tavern with a certain sum of money in his pocket, where he spends 2 shillings ; he then borrows as much money as he had left, and going to another tavern, he there spends 2 shillings also ; then borrowing again as much money as was left, he went to a third tavern, where likewise he spent two shillings and borrowed as much as he had left ; and again spending 2 shillings at a fourth tavern, he then had nothing remaining.

Page 80 - 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.