Henderson — Foundations of Geometry. 
13 
what exaggeratedly characterized as the most remarkable two 
dozen pages in the history of thought. When this work at last 
reached Gauss, he wrote to his pupil and friend, Gerling: “I 
hold this young geometer von Bolyai to be a genius of the 
first magnitude.” Bolyai called his work, The Science Abso- 
lute of Space, independent of the truth or falsity of Euclid's 
Axiom XI ( which can never be decided a priori). And later, 
we read on the title page of the elder Bolyai’s Kurzer Grund- 
riss: “the question, whether two straight lines , cut by a third, 
if the sum of the interior angles does not equal two right 
angles, intersect or not? no one on the earth can answer with- 
out assuming an axiom (as Euclid the eleventh).” The work 
of Bolyai, the younger, which makes all preceding space only 
a special case, only a species under a genus, and requiring a 
descriptive adjective Euclidian, was rescued from oblivion, 
after thirty years, by Professor Richard Baltzer, of Dresden; 
and J. Hoiiel, of Bordeaux, following in the steps of Baltzer, 
inserted extracts from Bolyai’s book in his Essai Critique sur 
les principes fondamentaux de la Geometrie elementaire. 
Indeed, this scientist mastered the principal European lan- 
guages in order to make known to his contemporaries the 
most celebrated mathematical works. 
There is another name which deserves to become conspic- 
uous in the history of non-Euclidian geometry; but not until 
1900 were the facts in connection with his independent dis- 
covery accurately known. In a letter to the elder Bolyai, 
written October 31, 1851, Gerling, a scholar of Gauss and 
Professor of Astronomy at Marburg, wrote as follows: “We 
had here about this time (1819) a law professor Schweikart, 
who had attained to similar ideas, since without help 
of the Euclidian axiom he developed in its beginnings a geom- 
etry which he called Astralgeometry. What he communi- 
cated to me thereon I sent to Gauss, who then informed me 
how much farther already had been attained on this way, and 
later also expressed himself about the acquisition, which is 
offered to the few expert judges in the Appendix to your 
