## 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 |

### From inside the book

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**quotients**will be equal . ( 15. ) If the same quantity be added to and subtracted from another , the value of the latter will not be altered . ( 16. ) If a quantity be both multiplied and divided by another , its value will not be ... Page 2

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**quotients**will be equal . ( 15. ) If the same quantity be added to and subtracted from another , the value of the latter will not be altered . ( 16. ) If a quantity be both multiplied and divided by another , its value will not be ... Page 162

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**quotient**may be 7 . Let x = the greater ; .. 91 x = the less , and X 2x - 91 = 7 ; ..x = 14X - 637 ; by transposition , 637 = 13x ; and ... 49 = x ; ... the parts are 49 and 42 . 55. From each of 16 coins an artist filed the worth of ... Page 198

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**quotient**and a remainder of 3 ; when divided by 9 gives another**quotient**and a remainder of 8. 198 Examples of the Solution of Problems. Page 199

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**quotient**which was got when the number was divided by 9 ; and the other digit is equalth of the**quotient**got when the num- ber was divided by 4. Required the number . Let x and y = the digits in order ; then 10x + y = the number ...### 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 quantities 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 multiplying every term number of days number of gallons number of shillings number of terms number of yards pence pieces problem proportion px² quotient 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 ах зу ху

### Popular passages

Page 22 - 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 249 - 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 376 - 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 369 - 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 229 - 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 155 - 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 373 - 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 363 - 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 186 - 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.