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adding Algebra arithmetical Article assumed cent clearing of fractions coŽfficients combinations completing CONTAINING cost cube denominator difference digits distance dividing divisible divisor easily equal errors evidently example expression extracting the square factors find the number find the values formula four fractions given equation gives greater greatest common divisor hence integral Last term leave less Let x letters logarithms manner means method miles Multiplying nearly NOTE obtained omitting operation perform polynomial powers preceding prime PROBLEM pupil quantities question Quotients ratio readily find reducing remainder render represent the numbers respectively result scale second equation sides signs similar solution solved square root substituting substituting the value subtracting taken third tion transposing traveled trial true unknown quantities value of x whence whole number
Page 329 - It is required to find three numbers in arithmetical progression, such, that the sum of every two of them may be a square.
Page 341 - Calcutta by the payment of £5025 16s. 8d. in London ? 2. Show why it follows from our system of notation, that a number when divided by 9 leaves the same remainder as the sum of its digits will leave when divided by 9. Write down all the numbers that can be composed of the four digits 3, 4, 5, 6, which will each be exactly divisible by 11. 3. At what rate per cent. simple interest will £7433 6s. 8d. amount to £9942 Is. 8d. in 7£ years ? 4. Show that the rule for dividing...
Page 6 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 246 - The coefficient of the second term of any equation is equal to the sum of all the roots with their signs changed. 2. The coefficient of the third term is equal to the sum of the products of all the roots taken two and two. 3. The coefficient of the fourth term is equal to the sum of the products of all the roots taken three and three, with their signs changed.
Page 159 - ... and each boy got as many nuts as there were boys in his company. Moreover all the boys in the larger company got 225 nuts more than all the boys in the smaller company ; and the whole number collected was 1025. How many boys were there ? Ans.
Page 320 - Divide a line into two parts, such that the sum of their squares shall be double the square on another line.
Page 288 - E, represent the errors which result from these substitutions. "We assume that the errors of the results are proportional to the errors of the assumed numbers. This supposition is not entirely correct ; but if we employ numbers near to the true values, the error of this supposition is generally not very great, and the error becomes less and less the further we carry the approximation. We have then E:E'::xr:xr'. ~Whence, Art. 305, EE...
Page 221 - It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 331 - Problems, the first of which finds "three square numbers, such that the sum of every two of them may be a square number;" the second determines " values for the sides of a triangle in whole numbers, such that the lengths of the three lines from the angles to the middle of the opposite sides may be expressed by rational whole numbers ;