The Method of Mechanical Theorems - Other Propositions in The Palimpsest

Other Propositions in The Palimpsest

A series of propositions of geometry are proved in the palimpsest by similar arguments. One theorem is that the location of a center of gravity of a hemisphere is located 5/8 of the way from the pole to the center of the sphere. This problem is notable, because it is evaluating a cubic integral.

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    We want in every man a long logic; we cannot pardon the absence of it, but it must not be spoken. Logic is the procession or proportionate unfolding of the intuition; but its virtue is as silent method; the moment it would appear as propositions and have a separate value, it is worthless.
    Ralph Waldo Emerson (1803–1882)