## An Introduction to Algebra: With Notes and Observations: Designed for the Use of Schools, and Places of Public Education |

### From inside the book

Page 78

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**can perform a piece of work in 8 days ; A and C**together in 9 days ; and B and C in 10 days : How many days will it take each perfon to perform the same work alone ? Ans . A 1434 days , 49 B1723 , and C 237 . 41 31 QUADRATIC EQUATIONS ...### Other editions - View all

An Introduction to Algebra: With Notes and Observations: Designed for the ... John Bonnycastle,James Ryan, Fra No preview available - 2016 |

### Common terms and phrases

४८ 4th power affirmative alſo anſwering ariſe arithmetical becauſe co-efficient completing the Square confequently cube numbers cube root cubic equation decimal diff Diophantus divided diviſor equal EXAMPLES extracting the root fame feries fide figns fimple equation fince find the roots find the ſum find the value find three numbers find two numbers find x firſt term fractional quantities fubtract fuch fum required furd quantities geometric mean given equation given number improper fraction increaſed infinite ſeries laſt leaſt leſs Let the number logarithm metical moſt multiplied natural numbers negative nth root number of terms number required obſerved orders of differences poſitive poſſible PROBLEM progreſſion propoſed quadratic equation quotient Reduce Required the ſum reſpectively reſult root required RULE ſame ſcience ſecond term ſigns ſimple ſome ſquare numbers ſquare root ſubſtituted ſum ſhall ſuppoſe theſe thoſe unknown quantity uſe Whence whole numbers whoſe

### Popular passages

Page 78 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Page 25 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.

Page 169 - ... if the logarithm of any number be multiplied by the index of its power, the product will be equal to the logarithm of that power.

Page 3 - If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value...

Page 75 - There is a fish whoso tail weighs 9 pounds, his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail ; what is the whole weight of the fish ? Ans. 72 pounds.

Page 30 - Note. The whole number of terms will be one more than the index of the given power ; and when both terms of the root are +, all the terms of the power will be...

Page 30 - ... and the product be divided :by the number of terms to that place, it will give the coefficient of the term next following.

Page 77 - There is an island 73 miles in circumference, and 3 footmen all start together to travel the same way about it ; A goes 5 miles a day, B 8, and C 10 ; when will they all come together again ? Ans. 73 days.

Page 71 - It is required to find how many days he worked, and how many he was idle ? Let x be the days worked, and y the days idled.

Page 17 - To reduce an improper fraction to a whole or mixed quantity. RULE. Divide the numerator by the denominator, for the integral part, and place the remainder, if any, over the denominator, for the fractional part ; then the two, joined together, with the proper sign between them, will give the mixed quantity required.