By Augustus De Morgan

From the EDITOR’S NOTE.

No apology is required for the booklet of the current new version of *The examine and problems of Mathematics*,—a attribute construction of 1 of the main eminent and luminous of English mathematical writers of the current century. De Morgan, notwithstanding taking larger rank as an unique inquirer than both Huxley or Tyndall, used to be the peer and lineal precursor of those nice expositors of technological know-how, and he utilized to his lifelong activity an historic gear and a mental perception that have now not but borne their complete academic fruit. And nowhere have those distinctive features been exhibited to better virtue than within the current paintings, which was once conceived and written with the whole ordinary freedom, and with the entire fireplace, of younger genius. For the contents and objective of the publication the reader should be spoke of the Author's Preface. The paintings nonetheless comprises issues (notable between them is its insistence at the learn of logic), that are insufficiently emphasised, or slurred, by way of straightforward treatises; whereas the freshness and naturalness of its perspective contrasts strongly with the mechanical personality of the typical text-books. common teachers and scholars can't fail to benefit by way of the final loftiness of its tone and the sound tenor of its directions.

the unique treatise, which was once released by way of the Society for the Diffusion of important wisdom and bears the date of 1831, is now virtually inaccessible, and is marred via various errata and typographical solecisms, from which, it truly is was hoping, the current variation is unfastened. References to the remainder mathematical textbooks of the Society for the Diffusion of necessary wisdom now out of print have both been passed over or supplemented by way of the point out of extra smooth works. The few notes that have been additional are normally bibliographical in personality, and refer, for example, to trendy treatises on common sense, algebra, the philosophy of arithmetic, and pangeometry. For the portrait and autograph signature of De Morgan, which graces the web page contrary the identify, The Open court docket Publishing corporation is indebted to the courtesy of vital David Eugene Smith, of the nation general college at Brockport, N. Y.

THOMAS J. MCCORMACK.

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**Example text**

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.