Elements of AlgebraHilliard and Metcalf, 1825 - 276 pages |
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Page ix
... obtain any power whatever of a simple quantity To extract the root of any power whatever of a simple quantity 138 To simplify radical expressions containing one term Of imaginary roots in general · · 139 ib . · 140 141 142 ib . Of ...
... obtain any power whatever of a simple quantity To extract the root of any power whatever of a simple quantity 138 To simplify radical expressions containing one term Of imaginary roots in general · · 139 ib . · 140 141 142 ib . Of ...
Page xi
... obtain the equation , the roots of which are the differ- 202 ences between one of the roots of the proposed equation ... obtained Inconvenience of this method when the roots differ but little ib . 220 221 222 Of the changes which a ...
... obtain the equation , the roots of which are the differ- 202 ences between one of the roots of the proposed equation ... obtained Inconvenience of this method when the roots differ but little ib . 220 221 222 Of the changes which a ...
Page xiv
... obtain the parts sought it is sufficient to perform operations purely arith- metical upon the given numbers . If , for example , the number to be divided were 9 , and the excess of the greater above the less 5 , the less part would be ...
... obtain the parts sought it is sufficient to perform operations purely arith- metical upon the given numbers . If , for example , the number to be divided were 9 , and the excess of the greater above the less 5 , the less part would be ...
Page xv
... obtain any power whatever of a simple quantity 136 137 ib . To extract the root of any power whatever of a simple quantity 138 To simplify radical expressions containing one term Of imaginary roots in general Of fractional exponents ...
... obtain any power whatever of a simple quantity 136 137 ib . To extract the root of any power whatever of a simple quantity 138 To simplify radical expressions containing one term Of imaginary roots in general Of fractional exponents ...
Page xv
... obtain the equation , the roots of which are the differ- ences between one of the roots of the proposed equation and ... obtained Inconvenience of this method when the roots differ but little 219 ib . 220 221 222 Note - respecting equal ...
... obtain the equation , the roots of which are the differ- ences between one of the roots of the proposed equation and ... obtained Inconvenience of this method when the roots differ but little 219 ib . 220 221 222 Note - respecting equal ...
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Common terms and phrases
a² b³ algebraic Algebraic Quantities Arith arithmetic becomes binomial coefficient common divisor consequently cube root deduce denominator denoted divided dividend division double the product employed entire number enunciation equa equal to zero evident example exponent extract the root extract the square figures follows formula fraction given in art given number gives greater greatest common divisor last term letters logarithm method multiplicand multiplied negative number of arrangements number of factors observed obtain operation perfect square proposed equation proposed number proposed quantity quan question quotient radical quantities radical sign reduced remainder represent resolve result rule given second degree second term simple quantities square root subtract suppose tens terms involving tion tities units unity unknown quantity vulgar fractions whence whole numbers
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.