A Practical System of Algebra in Theory and Practice in Two Parts: With a New Method of Solving Cubic Equations and Those of Higher Orders |
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Practical System of Algebra, in Theory and Practice, in Two Parts: With a ... John D. Williams No preview available - 2017 |
A Practical System of Algebra in Theory and Practice in Two Parts: With a ... John D. Williams No preview available - 2016 |
Practical System of Algebra, in Theory and Practice, in Two Parts: With a ... John D. Williams No preview available - 2017 |
Common terms and phrases
a²x² Algebra algebraic quantities arithmetical mean arithmetical progression arithmetical series assumed numbers ax² binomial bushels coefficients common denominator common difference common excess consequently cube root cubic equation denote the number divided dividend divisor dollars equa equal roots expressed find the four Find the square find the value formula four quantities four roots fraction geometrical progression geometrical series give Given 23 given equation greater Hence last term less means method miles mult multiplied negative number of terms permutations proportion proposed equation quadratic equation quan ratio reduced remainder required to find result RULE second equation second term side square root substituted subtracted surd taken Theo theorem third three roots tion tities transposing transposition trial unknown quantity value of x whence yards
Popular passages
Page 55 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Page 151 - Then, as the difference of these results is to the difference of the two assumed numbers, so is the difference between the true result, and either of the former, to the correction of the number belonging to the result used ; which correction...
Page 32 - Any quantity may be transposed from one side of an equation to the other, by changing its sign...
Page 35 - A person employed 4 workmen, to the first of whom he gave 2 shillings more than to the second ; to the second 3 shillings more than to the third ; and to the third 4 shillings more than to the fourth. Their wages amounted to 32 shillings. What did each receive ? Ans.
Page 35 - A cask, which held 146 gallons, was filled with a mixture of brandy, wine, and water. In it there were 15 gallons of wine more than there were of brandy, and as much water as both wine and brandy. What quantity was there of each...
Page 60 - 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 could each do it separately? Ans. A in 24, B in 48 days.
Page 112 - B gained a sum less by 40 dollars, than twice the sum that A had lost ; when it appeared that B had twice as much money as A. What money did each begin with ? Ans.
Page 138 - RULE. Take some new unknown quantity, and subjoin to it a third part of the coefficient of the second term of the equation with its sign changed ; then, if this sum, or difference...
Page 97 - 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 60 - В ; in order to which he found he must perform the journey in 28 hours less than the first did. Now the time in which the first travels 17 miles added to the time in which the second travels 56 miles is 13 hours and 40 minutes. How many miles does each go per hour ? Ans.