Elements of Algebra
Hilliard and Metcalf, 1825 - 276 pages
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according admit algebraic answers applied arising arrangements arrive becomes binomial coefficient common divisor consequently considered consists contains corresponding cube deduce denominator denoted determine divide dividend division divisor double employed enunciation equa equal evident example exponent expression extract factors figures follows formula four fourth fraction francs furnished given gives greater greatest indicated involving known less letters logarithm manner means method multiplied namely necessary negative observed obtain operation particular performed positive preceding present problem proposed equation question quotient radical sign raised reasoning reduced reference remainder render represent resolve respect result rule second degree second term simple solution sought square root substitute subtract successively suppose taken tens term third tion units unity unknown quantity whence whole write zero
Page 91 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 23 - RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 125 - Adding to the trial-divisor 3 ab, that is, three times the product of the first term of the root by the second, and...
Page 258 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 258 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Page 235 - From what has preceded, we perceive that the value of a fraction is the quotient arising from the division of the numerator by the denominator, or from the expression of this division.
Page 258 - 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.
Page 112 - Therefore, in the third and fourth forms, when q is greater than p2, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, both values of the unknown quantity are impossible.
Page 98 - This process, founded upon what was laid down in article 96, that the square of a fraction is expressed by the square of the numerator divided by the square of the denominator, may evidently be applied to any kind of fraction whatever, and more readily to decimals than to others.
Page 258 - A man has a lease for 99 years ; and being asked how much of it was already expired, answered, that two thirds of the time past was equal to four fifths of the time to come. Required the time past, and the time to come.