The elements of non-Euclidean plane geometry and trigonometry, by H. S. Carslaw.

26

NON-EUCLIDEAN GEOMETRY [nc. I. 12]

The Notes on Parallels,* found among his papers, probably
belong to this period. Some use of them will be made below in
the formal development of the Geometry of Bolyai and
Lobatschewsky.
However his plans were changed when, in February, 1832,
Bolyai's work reached his hands. He saw that it was now
unnecessary for him to proceed with this work. The enthusiasm with which he read the Appendix we have already seen.
I have entered at some length into this story, partly because
of its intrinsic interest; partly because of the unfortunate
claim made by some mathematicians that to Gauss should
be ascribed the discovery of the Non-Euclidean Geometry;
partly, also, because it has been suggested that the work of
Bolyai and Lobatschewsky had been inspired by the investigations of Gauss.
The claim and the suggestion we now know to be unfounded.
The wonderful discovery, which revolutionised the science of
Geometry, must always be associated with the names of Bolyai
and Lobatschewsky, who, independently and without any
knowledge of the work of Gauss, fully developed the new
Geometry. While the glory of the discovery is theirs, we must
not forget the advance which Gauss, and also Schweikart, had
made along the same lines.
* Cf. Gauss, Werke, vol. viii. p. 202; also Bonola, loc. cit. p. 67.