Elements of the Differential And Integral Calculus: By a New Method, Founded ...
Elements of the Differential And Integral Calculus: By a New Method, Founded ...
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In our eReader you can find the full English version of the book. Read Elements of the Differential And Integral Calculus: By a New Method, Founded ... 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 Elements of the Differential And Integral Calculus: By a New Method, Founded ...
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Now Dc* and De' are each equal to xdx^, and hence the rate of increase of D/ is equal to 2xdx^. But the differential of the cube is represented by three such solids as Df and the rate of increase of the whole, or the differential of the differential x^ is 6xdx^.
Again th"e solid D(f ox xdx^ tends to increase in the direc- tion Dd' at such a rate as would generate the suppositive increment Dd"*, equal to dx^ in the same unit of time and Digitized by Google SUCCESSIVE DIFFERENTIALS. 83 in a unifo...rm manner. Hence d{xdx^) is equal to dx^, and, therefore, d{6xdx*) is equal to 6ilx^, (22) It must always be remembered that the solids rep- resented in the figure are not the actual increments of the cube, but the symbols which represent its rate of increase and the successive rates of that rate at the instant that x is equal to AB; that is, they are the increments that would take place in the cube, and in the increments themselves if made uni- formly. The la7V which governs the increase of the cube, contains within itself not only the rate at which the cube is, at any instant increasing, but also the law of change in that rate, and the law to which that law is subject ; and these symbols represent the development of that law which was actually operating at the instant the cube attained the value of AB^ or x^y and before any farther increase had taken place.
What to read after Elements of the Differential And Integral Calculus: By a New Method, Founded ...?
You can find similar books in the "Read Also" column, or choose other free books by Catherinus Putnam Buckingham to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Now Dc* and De' are each equal to xdx^, and hence the rate of increase of D/ is equal to 2xdx^. But the differential of the cube is represented by three such solids as Df and the rate of increase of the whole, or the differential of the differential x^ is 6xdx^.
Again th"e solid D(f ox xdx^ tends to increase in the direc- tion Dd' at such a rate as would generate the suppositive increment Dd"*, equal to dx^ in the same unit of time and Digitized by Google SUCCESSIVE DIFFERENTIALS. 83 in a unifo...rm manner. Hence d{xdx^) is equal to dx^, and, therefore, d{6xdx*) is equal to 6ilx^, (22) It must always be remembered that the solids rep- resented in the figure are not the actual increments of the cube, but the symbols which represent its rate of increase and the successive rates of that rate at the instant that x is equal to AB; that is, they are the increments that would take place in the cube, and in the increments themselves if made uni- formly. The la7V which governs the increase of the cube, contains within itself not only the rate at which the cube is, at any instant increasing, but also the law of change in that rate, and the law to which that law is subject ; and these symbols represent the development of that law which was actually operating at the instant the cube attained the value of AB^ or x^y and before any farther increase had taken place.
What to read after Elements of the Differential And Integral Calculus: By a New Method, Founded ...?
You can find similar books in the "Read Also" column, or choose other free books by Catherinus Putnam Buckingham to read onlineMoreLess
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