556 SCIENCE. 
deavors, at last obtained this correspond- 
ence from the Royal Society of Sciences at 
Gottingen, where Bolyai had sent the let- 
ters of Gauss at his death. The Correspond- 
ence is fitly edited by Schmidt and 
Staeckel. It gives us a romance of pure 
science. Gauss was the greater mathe- 
matician ; Bolyai the nobler soul and truer 
friend. On April 10, 1816, Bolyai wrote to 
Gauss giving a detailed account of his son 
Janos, then fourteen years old ; and unfold- 
ing a plan to send JAnos in two years to 
Gottingen, to study under Gauss. He 
asks if Gauss will take Janos into his house, 
of course for the usual remuneration, and 
what Janos shall study meanwhile. Gauss 
never answered this beautiful and pregnant 
letter, and never wrote again for sixteen 
years! Had Gauss answered that letter 
Gottingen might now perhaps have to boast 
a greater than Gauss, for in sheer genius, 
in magnificent nerve, Bolyai Janos was un- 
surpassable, as absolute as his science of 
space. But instead, he joined the Austrian 
army, and the mighty genius which should 
have enriched the transactions of the great- 
est of learned societies with discovery after 
discovery in accelerating quickness, preyed 
instead upon itself, printing nothing but a 
brief two dozen pages. 
Almost to accident the world owes the 
admirable volumes in which Staekel and 
Engel contribute such priceless treasures to 
the non-Euclidean geometry. An Italian 
Jesuit, P. Manganotti, discovered that one 
of his order, the Italian Jesuit Saccheri, 
had already in 1733 published a series of 
theorems which the world had been ascrib- 
ing to Bolyai. Thereupon, in 1889, E. 
Beltrami published in the Atti della Reale 
Accademia dei Lincei, Serie 4, Vol. V., pp. 
441-448, a note entitled ‘Un Precursore 
italiano di Legendre e di Lobatschewski,’ 
giving extracts from Saccheri’s book which 
abundantly proved the claim of Manga- 
notti. 
[N. S. Von. X. No. 251. 
In the same year, 1889, E. d’Ovidio, in 
the Torino Atti, XXIV., pp. 512-518, called 
attention to this note in another entitled, 
Cenno sulla Nota del prof. E. Beltrami: 
‘Un Precursore, etc.,’’ expressing the wish 
that P. Manganotti would by a more ample 
discussion rescue Saccheri’s work from un- 
merited oblivion. Staeckel says the thought 
then came to him, whether Saccheri’s work 
were not a link ina chain of evolution, the 
genesis of the non-Euclidean geometry. 
In 1893, at the International Mathemat- 
ical Congress at Chicago, in the discussion 
which followed my lecture, ‘Some Salient 
Points in the History of Non-Euclidean 
and Hyper-Spaces,’ wherein I gave an ac- 
count of Saccheri with description of his 
book and extracts from it, Professor Klein, 
who had never before heard of Saccheri, and 
Professor Study, of Marburg, mentioned 
that there had recently been brought to light 
an old paper of Lambert’s anticipating in 
points the non-Euclidean geometry, and 
named in connection therewith Dr. Staeckel. 
I at once wrote to him and published in the 
Bulletin of the New York Math. Soc., Vol. III., 
pp. 79-80, 1893, a note on Lambert’s non- 
Euclidean geometry, mentioning Staeckel’s 
purpose to republish Lambert’s paper in the 
Abhandlungen of the Leipziger Gesellschaft 
der Wissenschaften. But after this, in 
January, 1894, Staeckel formed the plan 
to make of Saccheri and Lambert a book, 
and associating with him his friend Fried- 
rich Engel, they gave the world in 1895, 
‘ Die Theorie der Parallellinien, eine Urkun- 
densammlung zur Vorgeschichte der nicht- 
euklidischen Geometric.’ Strengthened by 
the universal success of this book, they 
planned two volumes in continuation. 
Staeckel takes the volume devoted to Bolyai 
Janos and his father. It is to begin with a 
more complete life of the two than has yet 
appeared, of course from material furnished 
largely by Franz Schmidt. 
Then follows the ‘ Theoria parallelarum ” 
