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acres added arithmetical progression arithmetical series biquadrate BIQUADRATIC EQUATIONS cambric circumscribing circle co-efficient common difference completing the square cube root cubic equation denominator diameter digits Divide divisor equal evolution EXAMPLES Find the least Find the square Find the sum find the value Find three numbers Find two numbers find x fraction geometrical progression Given x Given x2 hypotenuse inscribed circle last remainder last term least value least whole number miles an hour minus Multiply number of terms numbers in arithmetical prob quadratic quotient ratio represent the required required number required square required the number Required the square right-angled triangle root of x2 RULE second term sides solved square number square root substituted subtraction taken any number taken at pleasure THEOREM third transposing travelled unknown letter unknown quantity Whence x y f x2 f yards
Page 20 - ... or minus multiplied by minus, gives plus. Plus multiplied by minus, or minus multiplied by plus, gives minus.
Page 105 - Two persons, A and B, can perform a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 and B in 48 days.
Page 61 - In every proportion the product of the extremes is equal to the product of the means. Thus, in the proportion 3 : 5 : : 6 : 10 we have 3 X 10 = 5 X 6.
Page 93 - ... then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
Page 69 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Page 137 - But, if we add the square of half the coefficient of the second term to the first member to make it a complete square, we must add it to the second member to preserve the equality of the members. Having extracted the square root of each member, these roots are equal, since like roots of equals are equal. Now, since the first...
Page 42 - In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2.
Page 95 - Find the. value of one of the unknown quantities in each of the equations, and form a new equation by making one of these values equal to the other.