"Archimedes' Book of Lemmas"

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“The centre of gravity of any hemisphere is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.”

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“Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.”

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“Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.”

“The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.”

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