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annex arithmetical arithmetical means arithmetical progression binomial binomial formula called changing the sign coefficient continued fraction contrary signs cube root decimal places deduce a rule denote the number derived polynomial Divide dividend epoch equa equation containing exactly divisible EXAMPLES exponent extract the square figures Find the square find the values following RULE formula given equation given number gives greater greatest common divisor Hence indeterminate indicated inequality infinite number irreducible fraction last term least common multiple less letters logarithm members of equation monomial multiplicand negative quantity number of terms operation ounces positive preceding principle problem proposed equation quan quotient radical sign real roots remainder required root result second degree second member second term simplest form simultaneous equations solved square root Sturm's theorem Substituting subtract supposition symbols taken third tion tity transformed Transposing unknown quantity whence whole number
Page 114 - A person bought a chaise, horse, and harness, for £60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each?
Page 249 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 102 - В contains 9 gallons of wine and 3 gallons of water; how many gallons must be drawn from each cask so as to produce by their mixture 7 gallons of wine and 7 gallons of water t 33.
Page 101 - J of what he then had ; and this done, found that he had but 12 shillings remaining : what had he at first ? Ans.
Page x - The words employed are signs of ideas. and are also one of the principal instruments or helps of thought; and any imperfection in the instrument, or in the mode of using it, will destroy all ground of confidence in the result. So, in the science of mathematics, the meaning of the terms employed are accurately defined, while the language...
Page 115 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans. 20 days.
Page 34 - Hence we see that the exponent of any letter in the product is equal to the sum of the exponents of this letter in the multiplicand and multiplier.
Page 190 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page x - Language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought ; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process, and destroy all ground of confidence in the result.