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 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 tities transposing trinomial twice unknown quantity VERIFICATION
Popular passages
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 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 158 - 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 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 175 - 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 127 - 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 77 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. Thus, (a — 6)* = (a — b) (a — 6)=a2— 2a6 + 6'.
Page 95 - RULE. — Multiply each numerator by all the denominators except its own, for the new numerators; and all the denominators together for a common denominator. NOTE 1.
Page 105 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.