The Mathesis universalis, a more elementary work, contains copious dissertations on fundamental points of algebra, arithmetic and geometry, and critical remarks.

Of 1903); earlier formulations of the bases of arithmetic are given by him in the editions of 1898 and of 1901.

Some writers have attempted unification by treating algebra as concerned with functions, and Comte accordingly defined algebra as the calculus of functions, arithmetic being regarded as the calculus of values.

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John heaved a sigh at this, and his wife stared with arms a-kimbo, and both appeared to be wondering if they had capital enough to begin such a course with, or arithmetic enough to carry it through.

He showed at an early age wellmarked mathematical powers, and his progress was so rapid in arithmetic and geometry that he was soon beyond the guidance not only of his father but of schoolmaster Schulz, who assisted in the mathematical department of his training.

Thus, while arithmetic may be defined as that branch of deductive reasoning concerning classes and relations which is concerned with the establishment of propositions concerning cardinal numbers, it must be added that the introduction of cardinal numbers makes no great break in this general science.

Algebraic treatment consists in replacing either of the terms A or B by an expression which we know from the laws of arithmetic to be equivalent to it.

I see what a good and useful study it is, though I must confess my mind wanders from it sometimes! for, nice and useful as arithmetic is, it is not as interesting as a beautiful poem or a lovely story.

The measure of the area of a rectangle is thus presented as the product of the measures of the sides, and arithmetic and mensuration are developed concurrently.

The graphic method may therefore be used in arithmetic for comparing two particular magnitudes of the same kind by comparing the corresponding lengths P and Q measured along a single line OX from the same point O.