Elements of Algebra: Including Sturms' Theorem
A. S. Barnes, 1848 - Algebra - 368 pages
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added addition affected algebraic apply arithmetical arranged becomes binomial called cents changing co-efficient common divisor consequently considered contain contrary corresponding cube denominator denote determine difference divide dividend division divisor entire enunciation equa equal equation example exponent expression extract factors figure formula four fourth fraction given gives greater greatest hence indicated involving known leaps least less letter limit logarithm manner means method monomial multiplied necessary negative observe obtain operation ounces perfect square performed polynomial positive preceding principle problem progression proportion proposed question quotient radical Reduce reference remainder represent resolved result rule satisfy second degree second term similar square root substituted subtract suppose taken tens term third tion transformed true units unity unknown quantity whence write
Page 259 - 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 163 - 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 163 - 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 192 - 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 96 - 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 164 - 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 77 - 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.