## Elements of AlgebraHilliard and Metcalf, 1825 - 276 pages |

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### Common terms and phrases

a² b³ algebraic Algebraic Quantities Arith arithmetic becomes binomial changing the signs coefficient common divisor consequently courier cube root decimal deduce denominator denoted divided dividend division double the product employed entire numbers enunciation equa evident example exponent extract the root extract the square factor x figures find a number follows formula fraction given in art given number gives greater greatest common divisor letters logarithm method multiplicand multiplied negative number of arrangements number of factors observed obtain operation perfect square preceding article proposed equation proposed number proposed quantity quan question quotient radical quantities radical sign reduced remainder represented resolve result rule given second degree second member second term simple quantities square root subtract suppose taken tens third tion tities units unity unknown quantity vulgar fractions whence whole numbers α²

### Popular passages

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 256 - 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 256 - 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 233 - 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 256 - 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 256 - 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.