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affected algebraic quantities approximating arithmetical arithmetical means arrangements binomial called co-efficient common difference common factor consequently contain continued fraction contrary signs cube root decimal deduce denominator denote derived polynomial determine divide dividend division entire number enunciation equa equal equation becomes equation involving example extract the cube extract the square figure find the values formula fourth fraction given number gives greatest common divisor Hence hypothesis indeterminate inequality last term least common multiple less letters taken logarithm manner method monomial multiplicand multiplied number of terms obtain operation perfect square positive roots preceding problem progression proportion proposed equation proposed polynomials quotient real root reduced remainder required root resolved result satisfy second degree second member second term square root substituted subtract suppose take the equation tens third tion total number transformed equation transposing units unity unknown quantity whence whole number
Page 181 - C' then A is said to have the same ratio to B that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
Page 122 - These expressions may sometimes be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square roots of these factors; or, in algebraic language, V'abed . . . = i/a.
Page 181 - 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 114 - ... the entire part of the root sought. For example, if it were required to extract the square root of 665, we should find 25 for the entire part of the root, and a remainder of 40, which shows that 665 is not a perfect square. But is the square of 25 the greatest perfect square contained in 665 ? that is, is 25 the entire part of the root ? To prove this, we will first show that, the difference between the squares of two consecutive numbers, is equal to twice the less number augmented by unity.
Page 28 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 33 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Page 267 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 146 - 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 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.