Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
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Resultat 1-5 av 39
Side
... preceding Rule is founded XXXIV . Of the Resolution of Fractions into Infinite Series XXXV . On the Expansion of Irrational Powers in Infinite Series · 167 · 173 183 · 187 · 189 191 195 XXXVI . Of the Expansion of Negative Powers XXXVII ...
... preceding Rule is founded XXXIV . Of the Resolution of Fractions into Infinite Series XXXV . On the Expansion of Irrational Powers in Infinite Series · 167 · 173 183 · 187 · 189 191 195 XXXVI . Of the Expansion of Negative Powers XXXVII ...
Side 56
... preceding chapter amounts principally to this , that the square root of a given number is a number such that its square is equal to the number pro- posed , and that we may prefix to such roots either a positive or a negative sign . 145 ...
... preceding chapter amounts principally to this , that the square root of a given number is a number such that its square is equal to the number pro- posed , and that we may prefix to such roots either a positive or a negative sign . 145 ...
Side 61
... preceding chapter , that all the numbers , of which it was proposed to extract the square roots , were positive . When therefore it is proposed to extract the square root of a negative number , there must arise a great difficulty , be ...
... preceding chapter , that all the numbers , of which it was proposed to extract the square roots , were positive . When therefore it is proposed to extract the square root of a negative number , there must arise a great difficulty , be ...
Side 64
... preceding chapter . Thus we know that the cube root of 8 is 2 ; of 27 , 3 ; of 64 , 4 , and so on ; and in like manner that the cube root of 27 is -3 ; and of -125 , -5 , & c . - 169. Again , if the number proposed be a fraction , as ...
... preceding chapter . Thus we know that the cube root of 8 is 2 ; of 27 , 3 ; of 64 , 4 , and so on ; and in like manner that the cube root of 27 is -3 ; and of -125 , -5 , & c . - 169. Again , if the number proposed be a fraction , as ...
Side 76
... preceding chapter , x + 8 = 15 , we found immediately x = 7 . And in general in the equation x + a = b , where where a and b signify any known numbers whatever , 76 ALGEBRAIC EQUATIONS . Of Simple Equations involving only one unknown ...
... preceding chapter , x + 8 = 15 , we found immediately x = 7 . And in general in the equation x + a = b , where where a and b signify any known numbers whatever , 76 ALGEBRAIC EQUATIONS . Of Simple Equations involving only one unknown ...
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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.