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affected algebraic quantities arithmetical arithmetical means arranged binomial co-efficient common difference common factor consequently contain continued fraction contrary signs cube root decimal deduce denominator divide dividend double product entire number enunciation equa equal equation becomes equation involving example extract the square figure Find the greatest find the values formula fourth fraction given number gives greater greatest common divisor greyhound Hence highest exponent inequality irreducible fraction last term least common multiple less logarithm manner method monomial multiplicand multiply necessary negative number of terms obtain operation perfect square positive roots preceding problem progression proposed equation proposed polynomials quotient reduced remainder required root result rule second degree second member second term square root substituted subtract suppose suppress take the equation tens third tion transformation transposing twice the product unity unknown quantity verified vulgar fraction whence whole number
Page 158 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 1 5| days, but B would have been 28 days in performing A's journey How far did each travel ? Ans.
Page 122 - 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 101 - A person bought a chaise, horse, and harness, • for £60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each?
Page 125 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 39 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend.
Page 76 - A fish was caught whose tail weighed 9Z6. ; his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together : what was the weight of the fish?
Page 31 - That is, 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 252 - That is : The first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one.