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
... clear that he has less than nothing by 50 crowns ; for if any one were to present him with 50 crowns for the purpose of paying his debts , he would still be in the actual possession of nothing , though he would be in fact richer than ...
... clear that he has less than nothing by 50 crowns ; for if any one were to present him with 50 crowns for the purpose of paying his debts , he would still be in the actual possession of nothing , though he would be in fact richer than ...
Page 9
... clear , that if we take this debt 3 times it will be 3 times as great , and conse- quently that the product sought is -3a . In like manner therefore , if we multiply -a a by + b , we shall obtain ab . We arrive therefore at this ...
... clear , that if we take this debt 3 times it will be 3 times as great , and conse- quently that the product sought is -3a . In like manner therefore , if we multiply -a a by + b , we shall obtain ab . We arrive therefore at this ...
Page 13
... clear that if ab be divided by b , the quotient will be a . And in general in all the instances of division , if the divi- dend be divided by the quotient , we shall obtain again the divisor ; the same as 24 divided by 4 gives 6 , and ...
... clear that if ab be divided by b , the quotient will be a . And in general in all the instances of division , if the divi- dend be divided by the quotient , we shall obtain again the divisor ; the same as 24 divided by 4 gives 6 , and ...
Page 14
... clear at first sight that the number 7 is not a factor of 24 , for 7 times 3 only gives 21 , which is less ; and 7 times 4 gives 28 , which is greater than 24. But it is at least evident from this , that the quotient must be more than 3 ...
... clear at first sight that the number 7 is not a factor of 24 , for 7 times 3 only gives 21 , which is less ; and 7 times 4 gives 28 , which is greater than 24. But it is at least evident from this , that the quotient must be more than 3 ...
Page 16
... clear that this must be done by first adding to it + d then + e and then + f ; which gives the sum a + b + c + d + e + f . 49. We should proceed in the same way if any of the - terms were affected by the sign - : we should join them one ...
... clear that this must be done by first adding to it + d then + e and then + f ; which gives the sum a + b + c + d + e + f . 49. We should proceed in the same way if any of the - terms were affected by the sign - : we should join them one ...
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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.