[Extract from a paper presented to the Texas Academy of Science, 
December 22, iSp/.] 
THE INTRODUCTION TO LOBACHEVSKI’S NEW ELEMENTS 
OF GEOMETRY. 
Translated from the Russian by G-eorge Bruce Halsted. 
TRANSLATOR’S PREFACE. 
No part of Lobachevski’s largest work, “New Elements,” has 
ever before been published in any language but the original 
Russian. 
I gave an account of it in 1893 at the Mathematical Congress of 
the World’s Columbian Exposition, and promised then the publi- 
cation of my translation. (See Mathematical Papers of Chicago 
Congress, pp. 92-95.) 
This promise was delayed for a personal visit to Kazan, the 
home of Lobachevski, and Maros-Vasarhely, the home of Bolyai. 
The volume of Ucheniya zapiski in which the publication of 
Noviya nachala was begun is dated 1835, but Lobachevski himself 
gives as the dates 1836, 1837, 1838, in his “Geometrical Researches 
on the Theory of Parallels” (1840), the little book by which alone 
his ideas have heretofore been accessible to the world in' general. 
But it is preeminently in his “New Elements” that the great 
Russian allows free expression to his profound philosophic insight, 
which on the one hand shatters forever Kant’s doctrine of our ab- 
solute a -priori knowledge of all fundamental spatial properties, 
while on the other hand emphasizing the essential relativity of 
space. 
Lobachevski’s position is still after sixty years the final phi- 
losophy. 
No one has gone beyond it. 
Many still exhibit, like Professor Newcomb in his beautiful ad- 
dress on the Philosophy of Hyper Space (Science, January 7, 
1898), a marked naivete. He says: “Certain fundamental axioms 
are derived from experience, not alone individual experience, per- 
haps, but the experience of the race.” On the contrary, the 
hereditary geometry, the Euclidean, is underivable from real ex- 
