Hinton - The Fourth Dimension.pdf

CHAPTER V
THE SECOND CHAPTER IN THE HISTORY
OF FOUR SPACE
LOBATCHEWSKY, BOLYAI, AND GAUSS
BEFORE entering on a description of the word of
Lobatchewsky and Bolyai it will not be out of place
to give a brief account of them, the materials for which
are to be found in an article by Franz Schmidt in the
forty-second volume of the Mathematische Annalen,
and in Engel’s edition of Lobatchewsky.
Lobatchewsky was a man of the most complete and
wonderful talents. As a youth he was full of vivacity,
carrying his exuberance so far as to fall into serious
trouble for hazing a professor, and other freaks. Saved
by the good offices of the mathematician Bartels, who
appreciated his ability, he managed to restrain himself
within the bounds of prudence. Appointed professor at
his own University, Kasan, he entered on his duties under
the regime of a pietistic reactionary, who surrounded
himself with sycophants and hypocrites. Esteeming
probably the interests of his pupils as higher than any
attempt at a vain resistance, he made himself the tyrant’s
right-hand man, doing an incredible amount of teaching
and performing the most varied official duties. Amidst
all his activates he found time to make important contributions
to science. His theory of parallels is most
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