The Nature of Mathematics
The Nature of Mathematics
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In our eReader you can find the full English version of the book. Read The Nature 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 Nature of Mathematics
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Dx = xz, and so on. More fully, from d(x 3 ) = 3cc 2 . Dx, we conclude, not that fx 2 . Dx = $x 3, but that fx 2 . Dx = $x 3 + c, where <: c " de- notes some constant depending on the fixed value for x from which the integration starts. Consideraparabola?/ 2 = a#; then 2y. Dy a. Dx, or dx = ' . a tf) O j Thus the area from the origin to the point x is j^L-l ? + c ; 8 2ty 3 ^i/ 2 cfo/ 2V 3 but d- = y ' y ; thus the area is - + c, or, since y 2 ax, 3ct a on %x . Y + c. To determine c when we measure the area from to x, we have the area zero when x = ; hence the above equation gives c = 0. This whole result, now quite simple to us, is one of the greatest discoveries of Archimedes. Let us now make a few short reflections on the infinitesimal calculus. First, the extraordinary power of it in dealing with complicated questions lies in that the question is split up into an infinity of simpler ones which can all be dealt with at once, thanks to the wonderfully economical fashion in which the calculus, like analytical geometry, deals with variables.
What to read after The Nature of Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Philip E B Philip Edward Bertrand Jourdain to read online
To quickly assess the difficulty of the text, read a short excerpt:
Dx = xz, and so on. More fully, from d(x 3 ) = 3cc 2 . Dx, we conclude, not that fx 2 . Dx = $x 3, but that fx 2 . Dx = $x 3 + c, where <: c " de- notes some constant depending on the fixed value for x from which the integration starts. Consideraparabola?/ 2 = a#; then 2y. Dy a. Dx, or dx = ' . a tf) O j Thus the area from the origin to the point x is j^L-l ? + c ; 8 2ty 3 ^i/ 2 cfo/ 2V 3 but d- = y ' y ; thus the area is - + c, or, since y 2 ax, 3ct a on %x . Y + c. To determine c when we measure the area from to x, we have the area zero when x = ; hence the above equation gives c = 0. This whole result, now quite simple to us, is one of the greatest discoveries of Archimedes. Let us now make a few short reflections on the infinitesimal calculus. First, the extraordinary power of it in dealing with complicated questions lies in that the question is split up into an infinity of simpler ones which can all be dealt with at once, thanks to the wonderfully economical fashion in which the calculus, like analytical geometry, deals with variables.
What to read after The Nature of Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Philip E B Philip Edward Bertrand Jourdain to read online
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