## Elements of Algebra: Including Sturms' Theorem |

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### Common terms and phrases

affected algebraic quantities arithmetical arithmetical progression arrangements binomial binomial theorem called co-efficient common difference consequently continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa example exponent extract the square figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner method monomial multiplicand multiply number of terms obtain operation ounces perfect power perfect square permutations positive roots preceding problem progression proposed equation quan quotient radical sign real roots Reduce remainder required to find resolved result rule satisfy second degree second member second term simplest form square root substituted subtract superior limit suppose supposition taken third tion total number transformed unity unknown quantity whence whole number

### Popular passages

Page 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.

Page 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.

Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 69 - Ibs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and t.ail together : what was the weight of the fish ? Let 2x = the weight of the body, in pounds.

Page 41 - ... 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 179 - Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.

Page 208 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.

Page 110 - 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 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.

Page 91 - 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.