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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Page 6
... amounts to 100-50 , or what is the same thing , + 100-50 , i . e . +50 . 1 14. Now since negative numbers may be considered as debts , in the same manner as positive numbers signify actual property , it may be said that negative numbers ...
... amounts to 100-50 , or what is the same thing , + 100-50 , i . e . +50 . 1 14. Now since negative numbers may be considered as debts , in the same manner as positive numbers signify actual property , it may be said that negative numbers ...
Page 19
... amount or value of such debt . 59. Now 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 ...
... amount or value of such debt . 59. Now 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 ...
Page 56
... 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. Thus , when a ...
... 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. Thus , when a ...
Page 62
... amount to 0 , or nothing , it is evident that the square root of a negative number cannot be ranked among possible numbers , and therefore that every such root must be termed an impos- sible or imaginary number , so called , because it ...
... amount to 0 , or nothing , it is evident that the square root of a negative number cannot be ranked among possible numbers , and therefore that every such root must be termed an impos- sible or imaginary number , so called , because it ...
Page 64
... since we have already seen that the cube of 3 amounts only to 27 ; and also that it must be less than 4 , since the cube of 4 is 64. We know therefore that that the cube root sought must be some intermediate num- ( 64 ) from them.
... since we have already seen that the cube of 3 amounts only to 27 ; and also that it must be less than 4 , since the cube of 4 is 64. We know therefore that that the cube root sought must be some intermediate num- ( 64 ) from them.
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Page 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 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.
Page 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Page 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
Page 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.
Page 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.