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 2
... evident from this , that all magnitudes can be ex- pressed by numbers , and that the foundation of all the sciences of mathematics must consist in a complete treatise on the science of numbers , and in a correct examination of the dif ...
... evident from this , that all magnitudes can be ex- pressed by numbers , and that the foundation of all the sciences of mathematics must consist in a complete treatise on the science of numbers , and in a correct examination of the dif ...
Page 5
... evident , that from the numbers repre- sented by a and d , to which the sign + is prefixed , are to be subtracted those which are represented by the remaining letters b , c , e , which are preceded by the sign B 3 - . 12. It 12. It is ...
... evident , that from the numbers repre- sented by a and d , to which the sign + is prefixed , are to be subtracted those which are represented by the remaining letters b , c , e , which are preceded by the sign B 3 - . 12. It 12. It is ...
Page 10
... evident , first , that , with respect to the letters , the product will be ab : but it is as yet uncertain whether the sign + or the sign is to be prefixed ; all that we know is , that it must be one or the other . Now I say that it ...
... evident , first , that , with respect to the letters , the product will be ab : but it is as yet uncertain whether the sign + or the sign is to be prefixed ; all that we know is , that it must be one or the other . Now I say that it ...
Page 13
... evident that the quotient will be b , because a being multiplied by b gives the dividend ab . It is equally 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 ...
... evident that the quotient will be b , because a being multiplied by b gives the dividend ab . It is equally 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 ...
Page 14
... evident from this , that the quotient must be more than 3 , and less than 4. In order therefore to determine it exactly , another species of numbers must be employed , called fractions , of which we shall treat in succeeding chapters ...
... evident from this , that the quotient must be more than 3 , and less than 4. In order therefore to determine it exactly , another species of numbers must be employed , called fractions , of which we shall treat in succeeding chapters ...
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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.