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subtilize    
v. 使稀薄;使精细;细微区别

使稀薄;使精细;细微区别

subtilize
v 1: mark fine distinctions and subtleties, as among words
2: make more subtle or refined [synonym: {rarefy}, {sublimate},
{subtilize}]
3: make (senses) more keen [synonym: {subtilize}, {subtilise}]

Subtilize \Sub"til*ize\, v. t. [imp. & p. p. {Subtilized}; p.
pr. & vb. n. {Subtilizing}.] [L. subtiliser.]
1. To make thin or fine; to make less gross or coarse.
[1913 Webster]

2. To refine; to spin into niceties; as, to subtilize
arguments.
[1913 Webster]

Nor as yet have we subtilized ourselves into
savages. --Burke.
[1913 Webster]


Subtilize \Sub"til*ize\, v. i.
To refine in argument; to make very nice distinctions.
--Milner.
[1913 Webster]


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  • 3. 10 Linear Approximations and Differentials
    Differentials are useful when the value of a quantity is unimportant, only the approximate change in the quantity in response to a change in input is desired As long as the change dx in input x is very small, the differential dy will be a good approximation to the expected change in the output y
  • 4. 2 Linear approximations and differentials
    Suppose that the edge of a cube was measured to be 20 in, with a possible measurement error of 1 in Use differentials to estimate the maximum possible error, the relative error and the percentage error in calculating the volume of the cube
  • Linear Approximations and Differentials
    One important use of differentials and linearization in experimental science is estimating the effect of error in measuring one quantity on the error in some other quantity computed from the measured value
  • 3. 10: Linear Approximations and Differentials
    Linear approximations may be used in estimating roots and powers In the next example, we find the linear approximation for f (x) = (1 + x) n at x = 0, which can be used to estimate roots and powers for real numbers near 1





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