Abstract
PROF. HENRICI, in NATURE, vol. xxix. p. 453, considers Hamilton's proof of Euclid I. 32 invalid; and asserts that from his reasoning it would follow that the sum of the three angles of a spherical triangle equals two light angles. I venture to differ from him for the following reason:—The only thing which Hamilton requires to be granted is that when a moving straight line slides along a fixed straight line its direction is unchanged. This axiom will, I suppose, be granted by every one. Of course it is not true that in every case rotation is independent of translation. But Hamilton's proof does not require it to be true in every case, but only in the case of a straight line. Hence I maintain that Hamilton's reasoning is perfectly correct, and his proof valid.
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GEOGHEGAN, E. “The Axioms of Geometry”. Nature 29, 551 (1884). https://doi.org/10.1038/029551c0
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DOI: https://doi.org/10.1038/029551c0
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