ipoy ] Henderson — Foundations of Geometry. 19 
more definite shape, and my conviction that we cannot thoroughly 
demonstrate geometry a priori is, if possible, more strongly con- 
firmed than ever. But it will take a long time for me to bring my- 
self to the point of working out and making public my very exten- 
sive investigations on this subject, and possibly this will not be done 
during my life, inasmuch as I stand in dread of the clamor of the 
Boeotians, which would be certain to arise if I should ever give free 
expression to my views.” 
As that wayward Irishman, Bernard Shaw, has said, the 
prime and indispensible quality of the pioneer must be his 
willingness to make a fool of himself — at first! And it mat- 
ters not in what sphere, whether art, literature or science, the 
great thing, as Henrik Ibsen says, is not to allow one’s self to 
be frightened by the venerableness of the institution. 
Now that the truth in regard to many of the mooted ques- 
tions which pertain to the foundations of geometry has at 
last been daringly disclosed, the first question that naturally 
arises is : Has Euclid’s fame suffered by the discovery ? One 
might be led to think so if dependence were to be placed in 
Clifford’s characterization of Lobatchevsky’s celebrated mon- 
ograph as “Euclid without the vicious assumption.” Such a 
remark is not only misleading: it displays a fundamental mis- 
apprehension in regard to the Euclidian and non-Euclidian 
geometries. The real truth of the matter is that Euclid’s 
genius today shines forth more resplendently than ever ; the 
almost flawless perfection of his work is only thrown into 
clearer perspective and higher relief. From the purely philo- 
sophical, the metaphysical point of view, the discovery of the 
non-Euclidian geometry is of vast interest ; for it gives rise 
to endless speculations in regard to the character of space — 
even of inter-stellar space. Are the three angles of a trian- 
gle equal to two right angles if the sides of the triangle are 
the distances from the earth to the remotest fixed star ? In 
the realization that Euclidian geometry is only a chapter in a 
more general geometry, fitly entitled Pan-Geometry, and the 
consequent almost infinite extension of the domain of research 
consists the great value of the discovery to the mathemati- 
