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 10
... example , -α by b . It is 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 ...
... example , -α by b . It is 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 ...
Page 12
... example , 12 is the dividend , 3 is the divisor , 4 is the quotient . 35. From hence it follows , that if we divide a number by 2 , or into two equal parts , one of the parts , or the quotient , taken twice , will exactly make the ...
... example , 12 is the dividend , 3 is the divisor , 4 is the quotient . 35. From hence it follows , that if we divide a number by 2 , or into two equal parts , one of the parts , or the quotient , taken twice , will exactly make the ...
Page 14
... example of the same nature ; 6 ) 34 ( 5 30 4 . that is to say ; the divisor is 6 , the dividend 34 , the quotient is 5 , and the remainder 4 . 43. We must observe , however , the following rule , in those instances where there is a ...
... example of the same nature ; 6 ) 34 ( 5 30 4 . that is to say ; the divisor is 6 , the dividend 34 , the quotient is 5 , and the remainder 4 . 43. We must observe , however , the following rule , in those instances where there is a ...
Page 16
... example , to add to- gether the formulas a + b + c and d + e + f we state the sum in this manner , ( a + b + c ) + ( d + e + f ) 48. It will be easily seen that this is not addition itself , but merely the sign of it . In order however ...
... example , to add to- gether the formulas a + b + c and d + e + f we state the sum in this manner , ( a + b + c ) + ( d + e + f ) 48. It will be easily seen that this is not addition itself , but merely the sign of it . In order however ...
Page 17
... example of pure numbers , proposing to add to the for- mula 12-8 , this other 15-6 . If we commence by adding 15 , we shall have 12-8 + 15 . Now we shall thus add too much , since we had only to add 15-6 , and it is evident that 6 is ...
... example of pure numbers , proposing to add to the for- mula 12-8 , this other 15-6 . If we commence by adding 15 , we shall have 12-8 + 15 . Now we shall thus add too much , since we had only to add 15-6 , and it is evident that 6 is ...
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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.