Elements of AlgebraHilliard, Gray, Little, and Wilkins, 1831 - 304 σελίδες |
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Σελίδα
... Negative Results . Theory of Negative Quantities • • Discussion of Problems of the First Degree , containing One or more Unknown Quantities . General Investigation of Equations and Problems of the First Degree . 1 7 11 12 14 20 36 37 45 ...
... Negative Results . Theory of Negative Quantities • • Discussion of Problems of the First Degree , containing One or more Unknown Quantities . General Investigation of Equations and Problems of the First Degree . 1 7 11 12 14 20 36 37 45 ...
Σελίδα 9
... negative terms . These denominations are improper , but custom has sanctioned them . The first term of a polynomial is not usually preceded by any sign , and then it is supposed to have the sign + . 11. Each of the literal factors which ...
... negative terms . These denominations are improper , but custom has sanctioned them . The first term of a polynomial is not usually preceded by any sign , and then it is supposed to have the sign + . 11. Each of the literal factors which ...
Σελίδα 10
... negative terms is greater than that of the positive . In this case , subtract the positive coefficient from the negative one , and place the sign before the result . Thus , if 5 a2 b be the sum of the positive terms , and -8a2b of the ...
... negative terms is greater than that of the positive . In this case , subtract the positive coefficient from the negative one , and place the sign before the result . Thus , if 5 a2 b be the sum of the positive terms , and -8a2b of the ...
Σελίδα 13
... negative ones . α We first take away 5a + 3bc , which gives 8 a2 - 2 ab - 5 a2 - 3bc ; but as this result is necessarily too little by 4 a b + b2 , we must add this last quantity ; it thus becomes or 8a2-2ab5a23bc4ab + b2 , 8a2-2ab ...
... negative ones . α We first take away 5a + 3bc , which gives 8 a2 - 2 ab - 5 a2 - 3bc ; but as this result is necessarily too little by 4 a b + b2 , we must add this last quantity ; it thus becomes or 8a2-2ab5a23bc4ab + b2 , 8a2-2ab ...
Σελίδα 15
... negative as well as positive terms this factor expresses the difference between the number of units in the sum of its positive terms and the sum of its negative ones . And the same holds true of the multiplier . It follows that the ...
... negative as well as positive terms this factor expresses the difference between the number of units in the sum of its positive terms and the sum of its negative ones . And the same holds true of the multiplier . It follows that the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a² b³ a³ b² absolute numbers algebraical algebraical quantities arithmetical binomial Bour coefficient common factor contains continued fraction contrary signs cube root denominator determine divide dividend entire and positive entire function entire numbers entire value enunciation equa equal evidently example exponent expression extract formulas given number gives greater greatest common divisor indeterminate inequality Let us designate letters logarithms method multiply negative nth root number of terms obtain operations perfect square performing the division polynomial preceding principle problem proposed equation question quotient radical sign reduced remainder resolved result rule satisfy second degree second member second term simple quantity solution square root subtract third tions trinomial unity unknown quantities value of x verified whence we deduce whole number
Δημοφιλή αποσπάσματα
Σελίδα 26 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 53 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Σελίδα 106 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Σελίδα 26 - Arrange the dividend and divisor with reference to a certain letter, and then divide the first term on the left of the dividend by the first term on the left of the divisor, the result...
Σελίδα 21 - To this result annex all the letters of the dividend, giving to each an exponent equal to the excess of its exponent in the dividend above that in the divisor.
Σελίδα 271 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 5 - ... the product multiply the number of tens by one more than itself for the hundreds, and place the product of the units at the right of this product, for the tens and units. Thus...
Σελίδα 127 - The algebraic sum of the two roots is equal to the coefficient of the second term taken with the contrary sign.
Σελίδα 248 - ... to the sum of the extremes multiplied by half the number of terms. Rule. — Add the extremes together, and multiply their sum by half the number of terms ; the product will be the sum of the series.
Σελίδα 26 - Though there is some analogy between arithmetical and algebraical division, with respect to the manner in which the operations are disposed and performed, yet there is this essential difference between them, that in arithmetical division the figures of the quotient are obtained by trial, while in algebraical division the quotient obtained by dividing the first term of the partial dividend by the first term of the divisor is always one of the terms of the quotient sought.