The Philosophy of Mathematics
The Philosophy of Mathematics
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In our eReader you can find the full English version of the book. Read The Philosophy of Mathematics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Philosophy of Mathematics
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Having thus summarily, though perhaps too briefly, considered the chief points in the differential calculus, I now proceed to an equally rapid exposition of a syste- matic outline of the Integral Calculus, properly so called, that is, the abstract subject of integration.
THE INTEGRAL CALCULUS. j^ 3 5 THE INTEGRAL CALCULUS.
Its Fundamental Division. The fundamental divi- sion of the Integral Calculus is founded on the same prin- ciple as that of the Differential Calculus, in distinguishing the i...ntegration of explicit differential formulas, and the integration of implicit differentials or of differential equa- tions. The separation of these two cases is even much more profound in relation to integration than to differen- tiation. In the differential calculus, in fact, this dis- tinction rests, as we have seen, only on the extreme im- perfection of ordinary analysis. But, on the other hand, it is easy to see that, even though all equations could be algebraically resolved, differential equations w^ould none the less constitute a case of integration quite distinct from that presented by the explicit differential formulas ; for, limiting ourselves, for the sake of simplicity, to the first order, and to a single function y oi a.
What to read after The Philosophy of Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Auguste Comte to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Having thus summarily, though perhaps too briefly, considered the chief points in the differential calculus, I now proceed to an equally rapid exposition of a syste- matic outline of the Integral Calculus, properly so called, that is, the abstract subject of integration.
THE INTEGRAL CALCULUS. j^ 3 5 THE INTEGRAL CALCULUS.
Its Fundamental Division. The fundamental divi- sion of the Integral Calculus is founded on the same prin- ciple as that of the Differential Calculus, in distinguishing the i...ntegration of explicit differential formulas, and the integration of implicit differentials or of differential equa- tions. The separation of these two cases is even much more profound in relation to integration than to differen- tiation. In the differential calculus, in fact, this dis- tinction rests, as we have seen, only on the extreme im- perfection of ordinary analysis. But, on the other hand, it is easy to see that, even though all equations could be algebraically resolved, differential equations w^ould none the less constitute a case of integration quite distinct from that presented by the explicit differential formulas ; for, limiting ourselves, for the sake of simplicity, to the first order, and to a single function y oi a.
What to read after The Philosophy of Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Auguste Comte to read onlineMoreLess
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