4th power affigned affirmative alfo alſo anfwering arife arithmetical mean ax˛ co-efficient confequently cube numbers cube root cubic equation decimal diff Diophantus divided divifor equal EXAMPLES extracting the root fecond term fide figns fimple equations fince find the fum find the roots find the value find three numbers find two numbers find x firft term firſt fome fquare numbers fquare root fubftituted fubtract fum fhall fum required fuppofed furd quantities geometric mean geometrical feries given equation given number impoffible improper fraction increaſe infinite feries laft laſt leaft lefs logarithm metical moidores moſt multiplied natural numbers negative nth root number of terms number required orders of differences poffible pofitive PROBLEM propofed quadratic equation queſtion quotient Reduce refult remainder Required the fum root required RULE ſcience ſeries ſhall ſquare ſum thefe theſe thoſe unknown quantity uſeful Whence whole numbers
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 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.