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 46
Side 9
... factors . 27. As yet we have only considered positive numbers , and it is impossible to doubt that the products so formed must be themselves positive : i . e . that + a multiplied by + b must ne- cessarily produce + ab . It will be ...
... factors . 27. As yet we have only considered positive numbers , and it is impossible to doubt that the products so formed must be themselves positive : i . e . that + a multiplied by + b must ne- cessarily produce + ab . It will be ...
Side 13
... factors is equal to the divisor , and the other factor to the quotient . So that if 63 be to be divided by 7 , we must seek such a product as , taking 7 for one of its factors , the other factor multiplied by it will give exactly 63 ...
... factors is equal to the divisor , and the other factor to the quotient . So that if 63 be to be divided by 7 , we must seek such a product as , taking 7 for one of its factors , the other factor multiplied by it will give exactly 63 ...
Side 14
... 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 , and less than 4. In order therefore to ...
... 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 , and less than 4. In order therefore to ...
Side 22
... factors those products are composed . -- 65. In order however to show how multiplication is actually performed , we must first observe that to multiply , for example , the formula a b + c by 2 , we must multiply each term separately by ...
... factors those products are composed . -- 65. In order however to show how multiplication is actually performed , we must first observe that to multiply , for example , the formula a b + c by 2 , we must multiply each term separately by ...
Side 24
... factors , which are therefore not divisible by any other numbers without remainder . This theorem however is not universally true , although it has but one single exception , viz . , where the difference between two numbers is only 1 ...
... factors , which are therefore not divisible by any other numbers without remainder . This theorem however is not universally true , although it has but one single exception , viz . , where the difference between two numbers is only 1 ...
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.