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The idea of slicing by parallel planes was rediscovered in China, and a simpler proof that the volume of a sphere is two-thirds the volume of its circumscribing cylinder, using areas alone, was given by Liu Hui in ad 263.
A simpler proof was found by Jones.
In one case, it discovered a simpler proof than Principia's.
See also [7] for a simpler proof of this result.
Due to this new description a considerably simpler proof is enabled.
In this paper, we give a more direct and much simpler proof of this result.
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The results presented therein involve simpler proofs than those of[92].
In Section 3, we review some existing results and offer simpler proofs for some of them.
Old age has at last freed him to make an incontrovertible, utterly simple proof of mastery.
A simple proof of this theorem was attributed to the Pythagoreans.
But there is one quite simple proof here, which is that you can, for the money, have a civilised life.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com