Finally, it is on the whole in keeping with Mill's presuppositions to admit even in the case of the method of difference that in practice it is approximative and instructive, while the theoretical formula, to which it aims at approaching asymptotically as limit, if exact, is in some sense sterile.

It is much to be deplored that Leonardo does not give the least intimation how he found his approximative value, outrunning by this result more than three centuries.

Such a formula is approximative, in that it is known that the result of its application will only be approximately correct; it differs from an approximative formula of the kind mentioned in (i) (b) above, in that it is adopted of necessity, not by choice.

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The following are instances of the application of approximative formulae to the calculation of the volumes of solids.