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abc2 affected algebraic expression algebraic quantities arithmetical arithmetical progression arrangements becomes binomial binomial theorem called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend and divisor division entire number enunciation equa equal equation involving example figure formula fourth given equation given number gives greatest common divisor hence highest exponent inequality last term least common multiple less logarithm manner merator method monomial multiplicand and multiplier nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient radical sign real roots remainder result second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing trinomial unity unknown quantity whence whole number
Page 279 - 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 183 - 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 183 - 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 212 - 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 184 - 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.