Elements of AlgebraHilliard, Gray, Little, and Wilkins, 1831 - 304 σελίδες |
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Σελίδα 3
... evidently regard algebra as a species of language formed of a number of signs , by the aid of which the connexion of ideas is perceived with great facility in the reasoning which it is necessary to adopt , either to demonstrate the ...
... evidently regard algebra as a species of language formed of a number of signs , by the aid of which the connexion of ideas is perceived with great facility in the reasoning which it is necessary to adopt , either to demonstrate the ...
Σελίδα 6
... evidently greater than the first . 6 To ascertain whether this theorem is true , whatever be the pro- a posed fraction , let us designate this fraction by , supposing a < b . Let m be the number to be added to both terms of the fraction ...
... evidently greater than the first . 6 To ascertain whether this theorem is true , whatever be the pro- a posed fraction , let us designate this fraction by , supposing a < b . Let m be the number to be added to both terms of the fraction ...
Σελίδα 8
... evidently depends on the particular values which are given to the letters , and gener- ally varies with them . Thus 2 a3 has for its numerical value 54 , when a is made equal to 3 , for the cube of 3 is 27 , and twice 27 is 54. The ...
... evidently depends on the particular values which are given to the letters , and gener- ally varies with them . Thus 2 a3 has for its numerical value 54 , when a is made equal to 3 , for the cube of 3 is 27 , and twice 27 is 54. The ...
Σελίδα 10
... evidently 2 a2b ; 7a2c - 3 a2c is 4 a3 c . Then the polynomial itself becomes 2ab + 4a2c + 9 a c2 — 6 b3 . Let there be in any polynomial the terms +2 a3 b c2 , -4 a3 b c2 , + 6 a3 b c2 , — 8 a3 b c2 , + 11 a3 b c2 . First , the sum of ...
... evidently 2 a2b ; 7a2c - 3 a2c is 4 a3 c . Then the polynomial itself becomes 2ab + 4a2c + 9 a c2 — 6 b3 . Let there be in any polynomial the terms +2 a3 b c2 , -4 a3 b c2 , + 6 a3 b c2 , — 8 a3 b c2 , + 11 a3 b c2 . First , the sum of ...
Σελίδα 15
... evidently to take ab as many times as there are units in c , and to subtract from it a - b , taken as many times as there are units in d , in other words , we are to multiply abby c , and to subtract ab , multiplied by d . But ( a - b ) ...
... evidently to take ab as many times as there are units in c , and to subtract from it a - b , taken as many times as there are units in d , in other words , we are to multiply abby c , and to subtract ab , multiplied by d . But ( a - b ) ...
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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.