Elements of AlgebraHilliard, Gray, Little, and Wilkins, 1831 - 304 σελίδες |
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Σελίδα 6
... denominator , become 75 and 19. Now the second fraction is 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 ...
... denominator , become 75 and 19. Now the second fraction is 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 ...
Σελίδα 7
... denominator . For this purpose , multiply the two terms of the first fraction by b + m , and of the second by b . Now , to multiply a by bm is to take a as many times as there are units in b , and again as many times as there are units ...
... denominator . For this purpose , multiply the two terms of the first fraction by b + m , and of the second by b . Now , to multiply a by bm is to take a as many times as there are units in b , and again as many times as there are units ...
Σελίδα 36
... denominator ( this denominator being either a simple quantity or a polynomial ) , and as many of these parts are taken as there are units in the numerator . Hence , addition , subtraction , multiplication , and division of fractions ...
... denominator ( this denominator being either a simple quantity or a polynomial ) , and as many of these parts are taken as there are units in the numerator . Hence , addition , subtraction , multiplication , and division of fractions ...
Σελίδα 49
... denominator by the ordinary method , we have 40 x 60 45 12x = 11+ 60 60 ; and because ( 43 ) the two members of an equation may be multi- plied by the same number , let us multiply this by 60 , which is equivalent to suppressing the ...
... denominator by the ordinary method , we have 40 x 60 45 12x = 11+ 60 60 ; and because ( 43 ) the two members of an equation may be multi- plied by the same number , let us multiply this by 60 , which is equivalent to suppressing the ...
Σελίδα 50
... denominator , if we take care to multiply every whole term by that denominator . Take the equation 52 4 x 13 = 77 13 8 6 OC . 12 3 The denominators have evidently common factors , and the least common multiple of the denominators is 24 ...
... denominator , if we take care to multiply every whole term by that denominator . Take the equation 52 4 x 13 = 77 13 8 6 OC . 12 3 The denominators have evidently common factors , and the least common multiple of the denominators is 24 ...
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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.