## A Treatise on Algebra ... |

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added algebraic already approximate arithmetical arrangements becomes binomial called coefficient consisting contain continued decimal denominator determine difference divide dividend division divisor easy entire number equal equation evident example exponent expression extract factors figure find the values formula four fourth fraction given gives greater greatest common divisor indicated 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 quantities variations whence whole

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Page 240 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 115 - 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 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 280 - 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 276 - Every equation of an odd degree has at least one real root ; and if there be but one, that root must necessarily have a contrary sign to that of the last term. 4°.

Page 98 - ... 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 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.

Page 215 - ... exponent of which is one less than the number, which marks the place of this term. Let...

Page 237 - The logarithm of a number, is, therefore, the exponent of the power, to which it is necessary to raise a given or invariable number, in order to produce the proposed number. Thus in the equation a...