Elements of AlgebraHilliard, Gray, Little, and Wilkins, 1831 - 304 σελίδες |
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Σελίδα 4
... tion 2x + 19 = 67 . Now , if 2x augmented by 19 gives 67 , 2x is less than 67 by 19 , or 2 x 67 19 48 . Therefore x is half of 48 ; that is , x = 48 24 ; and as the less number is 24 , the greater , which is x + 19 , is 24+ 19 , or 43 ...
... tion 2x + 19 = 67 . Now , if 2x augmented by 19 gives 67 , 2x is less than 67 by 19 , or 2 x 67 19 48 . Therefore x is half of 48 ; that is , x = 48 24 ; and as the less number is 24 , the greater , which is x + 19 , is 24+ 19 , or 43 ...
Σελίδα 15
... tion of two binomials , such as a b , c d , where a denotes the sum of the positive terms , and — b of the negative terms of the mul- tiplicand , and c and d stand for the same things in the multiplier . We can now effect the ...
... tion of two binomials , such as a b , c d , where a denotes the sum of the positive terms , and — b of the negative terms of the mul- tiplicand , and c and d stand for the same things in the multiplier . We can now effect the ...
Σελίδα 23
... products arising from multiplying each term of the divisor by each term of the quotient sought . If then we can discover in the dividend , a term which arose , without reduc- tion , from the multiplication of one of the terms Division . 23.
... products arising from multiplying each term of the divisor by each term of the quotient sought . If then we can discover in the dividend , a term which arose , without reduc- tion , from the multiplication of one of the terms Division . 23.
Σελίδα 24
Bourdon (M., Louis Pierre Marie). tion , from the multiplication of one of the terms of the divisor by one of the terms of the quotient , then , by dividing the term of the dividend by that of the divisor , we may be certain of obtaining ...
Bourdon (M., Louis Pierre Marie). tion , from the multiplication of one of the terms of the divisor by one of the terms of the quotient , then , by dividing the term of the dividend by that of the divisor , we may be certain of obtaining ...
Σελίδα 47
... tion , are rather vague , we shall begin with the second part , in which they are fixed and invariable . From the definition of an equation , it is composed of two parts , separated from one another by the sign . The part on the left is ...
... tion , are rather vague , we shall begin with the second part , in which they are fixed and invariable . From the definition of an equation , it is composed of two parts , separated from one another by the sign . The part on the left is ...
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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.