# Download Analyse convexe et optimisation by Michel Willem PDF

By Michel Willem

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213. The ond |JJJ. 420 a is f to a ^ : Suppose first it of these required to divide is f J 2, an d the sec quotient of these by the ordinary rule or 6420. This fraction must now be reduced decimal on the principles of the last article, by the rule usually given, either exactly, or by approxi mation, according to the nature of the factors in the denominator. When mon the decimal fraction corresponding to a fraction cannot be exactly found, com always hap pens that the series of decimals which approximates to it, contains the same number repeated again and in the Thus, again.

Any two or more numbers be multiplied to indifferent in what order they are multi it is plied, the result is the same. Thus, 10X6X4X3 = 3X10X4XG = 6X10X-X3, VI. In dividing one number by another, for etc. ex ample 156 by 12, we may break up divide each of parts by the divisor, and then add the results. its We may this is expressed thus 156 T2~ the dividend, and part 156 into 72, 60, and 24 : _ 72 + == 12 60 12 + 24 12 ; ELEMENTARY RULES OF ARITHMETIC. The same thing cannot be done with 25 the divisor.

We need not, therefore, write the denominator, we put some mark upon the numerator, by which we may know the number of cyphers in the denominator. This mark is for our own selection. The method which is followed is to point provided, in its stead, from the numerator as many figures as there are 7 3 3 cyphers in the denominator. 229. 334; 3 229 3 pleased, have represented them thus, 17334 or thus, 17334 3 229 3 or in any way by which we ^^ , , , might choose to agree tor is 1 followed by to recollect that the 3 cyphers.

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