## Treatise on Algebra, for the Use of Schools and Colleges |

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added algebraic arrangements becomes binomial called coefficient consisting contain continued decimal denominator determine difference divide dividend division divisor entire number equal equation evident example exponent expression extracting factors figure find the values formula four fourth fraction functions given gives greater greatest common divisor hand indicated interest least less letters limit logarithm manner means multiplied necessary negative obtain operation perfect performed polynomials positive preceding principles problem progression proportion proposed question quotient radical raised ratio received reduced remainder represent Resolving respectively result rule satisfy second term shillings sides simple solution sought square root substitution subtract successively taken tens term third third power tion transformed twice units unity unknown quantity values of x variations whence whole yards

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Page 117 - 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 242 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 19 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...

Page 258 - VARIATIONS of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of variations of the signs, p the number of permanences ; we shall have m=n+p. Moreover, let n' denote the number of positive roots, and p...

Page 100 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 9 - 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.

Page 98 - If both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed.

Page 217 - ... exponent of which is one less than the number, which marks the place of this term. Let L "designate any term whatever of the progression, and let n represent the number of this term; from what has been said, we have This is called the general term of the progression.

Page 67 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14ff days, B 17ff, and C 23J y . 21.

Page 38 - 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.