## Algebraical Problems, Producing Simple and Quadratic Equations, with Their Solutions; Designed as an Introduction to the Higher Branches of Analytics: to which is Added an Appendix, Containing a Collection of Problems on the Nature and Solution of Equations of Higher Dimensions |

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Page 420

... equation of five dimensions by the solution of a simple equation . ax2 bx 19.

... equation of five dimensions by the solution of a simple equation . ax2 bx 19.

**Transform the equation**a3- + + 0 , m n into one whose coefficients shall be integral . — 20.**Transform the equation**y3 - 2py ' - 33p'y + 14p = 0 , into one ... Page 421

... equation . - 3x + 4 = 0 , into 27.

... equation . - 3x + 4 = 0 , into 27.

**Transform the equation**a 2x2 one whose roots shall be one - eighth of the roots of the given equation . 28. If a , b , c , & c . be the roots of the equation xn -1 - — -2 & c . = 0 , transform it ... Page 422

... equation whose roots are an arithmetic , a geo- metric , and a harmonic mean between a and b . - - 36.

... equation whose roots are an arithmetic , a geo- metric , and a harmonic mean between a and b . - - 36.

**Transform the equation**x3 2x2 + 2x 4 = 0 , into one whose roots are the squares of the roots of the original equation . 37.**Transform the**... Page 423

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**Transform**an**equation**into one whose roots shall be the squares of the differences of the roots of the original**equation**; and show by means of this**transformation**how the number of impossible roots in an**equation**of five dimensions may ...### Other editions - View all

### Common terms and phrases

3x²y addition answer the conditions arithmetic series arithmetical progression casks common difference completing the square containing cost cube digits distance Divide the number equal equation ³ equation of fractions equation x² extracting the root extracting the square find the values former gain geometric series geometrical progression Given 3x Given x Given x² greater guineas harmonic progression least common multiple length less Let 4x number of days number of gallons number of pounds number of shillings number of terms number of yards pence pieces problem proportion px² Quadratics received Required the number second equation sheep shil sold square root squaring both sides Substituting this value subtraction third three numbers Transform the equation transposition travelled unknown quantity values of x wheat whence whole number x²y x²y² xy² зу ху

### Popular passages

Page 24 - 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 251 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards ; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.

Page 378 - From two places at a distance of 320 miles, two persons, A and B, set out at the same time to meet each other. A travelled 8 miles a day more than B, and the number of days in which they met was equal to half the number of miles B went in a day. How many miles did each travel, and how far per day ? 20.

Page 2 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Page 371 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...

Page 231 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately 1 Ans.

Page 157 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together. What was the weight of the fish ? Let 2x = the weight of the body in pounds.

Page 375 - A gentleman bought two pieces of silk, which, together, measured 36 yards. Each of them cost as many shillings per yard as there were yards in the piece, and their whole prices were as 4 to 1. What were the lengths of the pieces ? Solution.

Page 365 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in...

Page 188 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.