# Explain Johann Bernoulli's postulate: "A quantity which is increased or decreased by an infinitely small quantity is neither increased nor...

Johann Bernoulli's postulate is simple: it says that a value does not change if an infinitesimally small value is added to it or subtracted from it. An infinitesimally small value *essentially* takes the value zero as in comparison to the value to which it is added/subtracted it is so small it may as well be zero.

In Newton's *Quadrature of Curves* (1704) he uses this idea as a mathematical trick/tool to differentiate `x^3` (giving of course `3x^2)`. This is a key idea in the theory of calculus, that the gradient of a function `f(x)` at ```x` can be calculated as the ratio of the strut and base of a very tiny triangle at `(x,f(x))` of widthÂ `o` and height `f'(x) times o`. Taking a very small section of the curve at the point `x` the curve can be theoretically defined as straight and as the hypotenuse of the tiny triangle described. The area under a curve (the integral) is conceived of in a similar way in the theory of calculus. Calculus dates back to Archimedes (200BC), at least.

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What is Ivan's transformation in the beginning of Master and Margarita?

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2019-06-11 09:41:26