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added algebraic quantities arithmetical arithmetical means binomial called coefficient common divisor sought Completing the square compound interest continued fraction decimal deduce divide the number dividend division entire number enunciation equal evident example exponent expression extract the root factor figure find a number find the greatest find the number find the square find the values following rule formula Freeing from denominators geometrical progression given number gives greater greatest common divisor less manner monomial multiplied number corresponding number of days number of letters number of terms obtain operations perfect square performed polynomials problem progression by difference progression by quotient proportion question radical sign ratio reduced remainder Required the number required to divide resolve the equation result root sought second degree second power second term shillings solution square root subtract third power third root tion unity unknown quantities values of x vulgar fraction whence yards
Page 242 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 31 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 149 - A square court yard has a rectangular gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the gravel walk ; and the number of square yards in the walk exceeds the number of yards in the periphery of the court by 164. Required the area of the court ? All equations of the second degree may be reduced to one of the following forms.
Page 100 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 9 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Page 217 - Therefore, any term of the progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term.
Page 98 - If both terms of a fraction be multiplied by the same number, the value of the fraction will not be changed.
Page 215 - A number consisting of three digits which are in arithmetical progression, being divided by the sum of its digits, gives a quotient 48 ; and if 198 be subtracted from the number, the digits will be inverted.
Page 67 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14ff days, B 17ff, and C 23J y . 21.