Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
Inni boken
Resultat 1-5 av 35
Side 18
... Suppose that it were required to add together the formulas , a + b and a - b . Our rule would give a + b + a - b . Now a + a = 2a , and b - b - 0 . The sum is therefore 2a . 56. Consequently , if we have to add together the sum and ...
... Suppose that it were required to add together the formulas , a + b and a - b . Our rule would give a + b + a - b . Now a + a = 2a , and b - b - 0 . The sum is therefore 2a . 56. Consequently , if we have to add together the sum and ...
Side 19
... suppose that it were required to subtract from the formula a ― e the formula b - d , we should first subtract b , which will give a - c - b . Now it is clear that we have sub- tracted too much by d , for it was required to subtract from ...
... suppose that it were required to subtract from the formula a ― e the formula b - d , we should first subtract b , which will give a - c - b . Now it is clear that we have sub- tracted too much by d , for it was required to subtract from ...
Side 20
... Suppose we had to subtract the formula 6−2 + 4 from 9-3 +2 we shall obtain by our rule 9-3 + 2-6 + 2-4 = 0 . Now this is evident , for 9-3 + 2 = 8 and 6-2 + 4 = 8 and 8 ― 8 = 0 . 62. All difficulty in the operation of subtraction being ...
... Suppose we had to subtract the formula 6−2 + 4 from 9-3 +2 we shall obtain by our rule 9-3 + 2-6 + 2-4 = 0 . Now this is evident , for 9-3 + 2 = 8 and 6-2 + 4 = 8 and 8 ― 8 = 0 . 62. All difficulty in the operation of subtraction being ...
Side 23
... suppose that A is to be multiplied by 73 ; now it is evident that the product will be four times A. For we must first take A 7 times , and then subtract 3 times A from the product . - 69. In general then , if it be required to multiply ...
... suppose that A is to be multiplied by 73 ; now it is evident that the product will be four times A. For we must first take A 7 times , and then subtract 3 times A from the product . - 69. In general then , if it be required to multiply ...
Side 29
... Suppose , for example , it were required to divide the quantity ac bc by a ―b , the quotient , as we have before shown , must be such , that being multiplied by the divisor a - b , it will produce the dividend ac - bc . Now we can ...
... Suppose , for example , it were required to divide the quantity ac bc by a ―b , the quotient , as we have before shown , must be such , that being multiplied by the divisor a - b , it will produce the dividend ac - bc . Now we can ...
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Vanlige uttrykk og setninger
already seen arithmetic means arithmetic series arithmetical progression assume binomial cent CHAP coefficient common difference Completing the square consequently consider contains cube root decimal determine divided dividend divisible equal equation evident example exponent expressed Extracting the root factors find the greatest Find the sum find the values formula four roots fourth term geometric means geometrical progression given number gives greater number greatest common divisor greatest common measure Hence infinite series infinitum instance integer irrational last term less letters logarithm manner method multiplied negative numbers number of permutations number of terms obtain quadratic surds quotient radical sign ratio reduced remainder represented required to find rule second degree second term square root subtracted suppose third degree three numbers tion transposition unity unknown quantity whence whole number
Populære avsnitt
Side 46 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Side 24 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 228 - There are three numbers in geometrical progression ; the sum of the first and second of which is 9, and the sum of the first and third is 15.
Side 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Side 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Side 58 - We call this new species of numbers, irrational numbers ; they occur whenever we endeavour to find the square root of a number which is not a square. Thus, 2 not being a perfect square, the square root of 2, or the number which, multiplied by itself, would produce 2, is an irrational quantity. These numbers are also called surd quantities, or incommensurables.
Side 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Side 77 - any quantity may be transferred from "one side of the equation to the other, by changing its sign ;" and and it is founded upon the axiom, that " if equals be added to " or subtracted from equals, the sums or remainders will be
Side 113 - Ans. 3 and 7 8. The difference of two numbers is 2, and the difference of their cubes is 98; required the numbers. Ans. 5 and 3 9.
Side 37 - If the numerator and denominator are both, multiplied or both divided by the same number, the value of the fraction will not be altered.