Elements of algebra, compiled from Garnier's French translation of L. Euler. To which are added, solutions of several miscellaneous problems1824 |
Inni boken
Resultat 1-5 av 49
Side 26
... assume a3 and b ± 2 . Then a + b = 5 and a - b1 . Moreover a2 = 9 , ab = 6 , b2 = 4 . Therefore a2 + ab + b2 = 19 , and a2 - ab + b2 = 7 . the product required is 5 × 19 × 1 × 7 , which is 665 . Now a6729 , and b664 . Therefore ao ...
... assume a3 and b ± 2 . Then a + b = 5 and a - b1 . Moreover a2 = 9 , ab = 6 , b2 = 4 . Therefore a2 + ab + b2 = 19 , and a2 - ab + b2 = 7 . the product required is 5 × 19 × 1 × 7 , which is 665 . Now a6729 , and b664 . Therefore ao ...
Side 37
... assumed as the value of the fraction , it is evident that this fraction is equal to what- ever be the value of m . α ma ть , 103. We have thus seen that every fraction may be ex- pressed in an infinity of ways , without altering its ...
... assumed as the value of the fraction , it is evident that this fraction is equal to what- ever be the value of m . α ma ть , 103. We have thus seen that every fraction may be ex- pressed in an infinity of ways , without altering its ...
Side 39
... assuming unity for the denominator ; for example 6 is the same as f , for 6 divided by 1 gives 6 , and moreover the same number 6 may be ex- pressed by the fractions 8 12 , 1 , 2 , 3 , 2 , & c . ad infinitum , and so of any other number ...
... assuming unity for the denominator ; for example 6 is the same as f , for 6 divided by 1 gives 6 , and moreover the same number 6 may be ex- pressed by the fractions 8 12 , 1 , 2 , 3 , 2 , & c . ad infinitum , and so of any other number ...
Side 83
... 1. Divide the number 7 into two such parts that the greater shall exceed the less by 3 . Assume the greater part . Then 7 - x the lesser . G 2 And And since the greater exceeds the less by 3 , ONE UNKNOWN QUANTITY . 83.
... 1. Divide the number 7 into two such parts that the greater shall exceed the less by 3 . Assume the greater part . Then 7 - x the lesser . G 2 And And since the greater exceeds the less by 3 , ONE UNKNOWN QUANTITY . 83.
Side 84
... Assume the greater part . ..a - x the lesser . •• a − x + b = x . ..2x = a + b , and a a + b the greater part , 2 a + b a - b and a - x = a . -- the lesser . 2 3. A father leaves 1600 crowns , to be divided among his 3 sons , in the ...
... Assume the greater part . ..a - x the lesser . •• a − x + b = x . ..2x = a + b , and a a + b the greater part , 2 a + b a - b and a - x = a . -- the lesser . 2 3. A father leaves 1600 crowns , to be divided among his 3 sons , in the ...
Innhold
1 | |
4 | |
8 | |
12 | |
16 | |
19 | |
22 | |
28 | |
101 | |
115 | |
133 | |
137 | |
138 | |
140 | |
142 | |
148 | |
32 | |
36 | |
40 | |
43 | |
46 | |
49 | |
50 | |
51 | |
52 | |
53 | |
64 | |
66 | |
69 | |
74 | |
76 | |
88 | |
152 | |
157 | |
167 | |
173 | |
183 | |
189 | |
195 | |
204 | |
249 | |
254 | |
269 | |
276 | |
298 | |
301 | |
305 | |
311 | |
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.