## A University Algebra: Comprising a Compendious, Yet Complete and Thorough Course in Elementary Algebra, and an Advanced Course in Algebra Sufficiently Extended to Meet the Wants of Our Universities, Colleges, and Schools of Science |

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### Common terms and phrases

added affected applied arithmetical base becomes called coefficients common considered constant containing corresponding decimal denominator determine develop difference differential distance dividend dividing division divisor equal equation evident EXAMPLES exponent expression Extract factors figure formula fraction function given gives greater Hence imaginary increases increment indicated infinitesimal integral interest involved known less letters logarithm manner means method miles multiplied negative observe obtain operation passes polynomial positive preceding problem progression Prop proportion quadratic quotient radical ratio reduced relation remainder represented resolved result root rule satisfy Show simple solution solve square square root substituted Subtracting taken term third tion transformed unknown quantity variable whence write

### Popular passages

Page 26 - 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 127 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.

Page 8 - To raise a whole number or a decimal to any power, use it as a factor as many times as there are units in the exponent.

Page 30 - The Greatest Common Divisor of two or more numbers is the greatest number that will exactly divide each of them. Thu4, 18 is the greatest, common divisor of 36 and 54, since it is the greatest number that will divide each of them without a remainder.

Page 21 - The square of the sum of two quantities is equal to the SQuare of the first, plus twice the product of the first by the second, plus the square of the second.

Page 21 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.

Page 125 - One variable number is said to vary directly as a second and inversely as a third, when it varies jointly as the second and the reciprocal of the third. Thus...

Page 37 - A common divisor of two numbers is a divisor of their sum and also of their difference.

Page 158 - COR. — The differential of a fraction having a constant numerator and a, variable denominator is the product of the numerator with its sign changed into the differential of the denominator, divided by the square of the denominator. Let...