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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Resultat 1-5 av 48
Side 6
... less than nothing . Thus when a man possesses nothing and owes 50 crowns , it is 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 ...
... less than nothing . Thus when a man possesses nothing and owes 50 crowns , it is 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 ...
Side 7
... less than nothing . -- 10 17. All these numbers , whether positive or negative , are known by the name of integers , and are so called to distinguish them from broken or fractional numbers , and from many other kinds of numbers , of ...
... less than nothing . -- 10 17. All these numbers , whether positive or negative , are known by the name of integers , and are so called to distinguish them from broken or fractional numbers , and from many other kinds of numbers , of ...
Side 14
... 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 determine it exactly , another species of numbers must be ...
... 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 determine it exactly , another species of numbers must be ...
Side 33
... less than their denominators , have a value less than unity . For if we have a number which is to be divided by another number greater than itself , the quotient must evidently be less than 1 . For example , if a line of two feet long ...
... less than their denominators , have a value less than unity . For if we have a number which is to be divided by another number greater than itself , the quotient must evidently be less than 1 . For example , if a line of two feet long ...
Side 34
... less than its denomi- nator . These fractions are called improper fractions , to dis- tinguish them from real fractions , or fractions properly so called , which having a numerator less than their denominator are less than unity or ...
... less than its denomi- nator . These fractions are called improper fractions , to dis- tinguish them from real fractions , or fractions properly so called , which having a numerator less than their denominator are less than unity or ...
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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.