New Elementary Algebra: Embracing the First Principles of the Science |
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algebraic expression algebraic quantities ANALYSIS.-Let x denote antecedent arithmetical arithmetical means binomial called cents Charles Clearing of fractions coefficient common difference complete equation completing the square contains contrary signs cost cube denote the number dividend division dollars equal number equal to 12 equation whose roots EXAMPLES exponent extracting the square Find the square Find the sum following RULE Give the rule given number greater greatest common divisor hence indicates John last term least common multiple lemons Let x denote logarithm minuend minus monomial Multiply negative number added number of apples number of terms ounces 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 tity transposing trinomial twice unknown quantity VERIFICATION Write written yards
Popular passages
Page 63 - 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 167 - The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units.
Page 150 - 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 145 - 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 138 - 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 138 - 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 269 - 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 64 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Page 119 - 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 70 - 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.