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

20

NON-EUCLIDEAN GEOMETRY

[ca. I.

praise myself. Indeed the whole contents of the work, the path
taken by your son, the results to which he is led, coincide
almost entirely with my meditations, which have occupied my
mind partly for the last thirty or thirty-five years. So I
remained quite stupefied. So far as my own work is concerned,
of which up till now I have put little on paper, my intention
was not to let it be published during my lifetime. Indeed the
majority of people have not clear ideas upon the questions of
which we are speaking, and I have found very few people who
could regard with any special interest what I communicated to
them on this subject. To be able to take such an interest one
must have felt very keenly what precisely is lacking, and about
that most men have very confused ideas. On the other hand,
it was my idea to write all this down later, so that at least it
should not perish with me. It is therefore a pleasant surprise
for me that I am spared this trouble, and I am very glad that
it is just the son of my old friend who takes the precedence of
me in such a remarkable manner..."
Wolfgang sent a copy of this- letter to his son with the
remark:
" Gauss's answer with regard to your work is very satisfactory, and redounds to the honour of our country and nation.
A good friend says, That's very satisfactory! " *
John Bolyai was the reverse of pleased. That he would
be disappointed at the news that Gauss had already reached
the same conclusions as himself was natural. But his chagrin
led him to doubs whether Gauss had really made these discoveries independently of his work. He conceived the absurd
idea that his father must have sent his papers to Gauss some
time earlier (they had been in his hands for several years),
and that Gauss had made use of them, jealous of being beaten
by this young Hungarian. In this he relied upon a remark
made by Gauss in 1804, in a letter to his father, when both
of them were trying to demonstrate the Parallel Postulate.
Wolfgang had sent him what he thought was a rigorous proof,
and Gauss replied that his demonstration was invalid, and that
he would try as clearly as possible to bring to light the stumbling* Cf. Stickel, "Die Entdeckung der nichteuklidischen Geometrie
durch Johann Bolyai," Math. u. Naturwcissenschafdliche Berichte aus
Ungarn, Bd. xvii. p. 17 (1901). Also by the same author in Engel u.
Stackel's Urkunden zur Geschichte der nichlteuklidischen Geometrie, II.,
Wolfgang u. Johann Bolyai, vol. i. p. 72 (Leipzig, 1913).