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

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according added affirmative alſo Anſ anſwering approximation ariſe arithmetical changes co-efficient common completing conſequently continued cube denominator determined difference divided diviſor equal equation EXAMPLES extracting feries fide figns find the ſum find the value find three find x firſt term fought four fraction geometrical give Given given number greater greateſt indices infinite ſeries involved known laſt leaſt leſs letters logarithm manner mean method moſt multiplied muſt natural nearly negative Note numbers ſuch poſitive PRACTICE PROBLEM progreſſion proportion propoſed quadratic equation queſtion quotient ratio Reduce remainder Required the ſum RULE ſame ſecond term ſeries ſhall ſide ſigns ſome Square ſquare number ſquare root ſubſtituted ſubtract ſum Suppoſe taken theſe third thoſe three numbers tion unknown quantity uſe Whence whole numbers whoſe

### Popular passages

Page 76 - 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 23 - 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 167 - ... 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 73 - 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 28 - 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 28 - ... and the product be divided :by the number of terms to that place, it will give the coefficient of the term next following.

Page 75 - 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 69 - 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 15 - 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.