## University Algebra: Embracing a Logical Development of the Science: With Numerous Graded Examples |

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3x²y 4a²bc a²bc a²x² algebraic algebraic quantities Arithmetic ax² Binomial Formula Bourdon called changing the signs Clearing of fractions coefficients common difference contain cube root decimal denote the number distance Divide dividend divisible equal roots equation whose roots equivalent exponent expression extract the square Find the cube Find the greatest Find the least Find the product Find the square following RULE given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple logarithm minuend monomial Multiplying both members negative nth root number of terms positive preceding principle proportion quotient radical sign real roots Reduce second degree second member second term solved square root STURM'S THEOREM Substituting subtract subtrahend third Transform the equation travels unknown quantity Whence whole number write X₁

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Page 248 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 226 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.

Page 220 - In any proportion, the product of the means is equal to the product of the extremes.

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 29 - 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.

Page 245 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.

Page 71 - 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 226 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.

Page 81 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare ? Let x be the number of leaps taken by the hound.

Page 232 - To find the ratio, when the extremes and the number of terms are given. Divide the last term by the first, and extract that root of the quotient whose index is one less than the number of terms. To find the number of terms, when the ratio and the extremes are given.