/p<?7] Henderson — Foundations of Geometry. 
21 
general geometry contains many propositions common to all 
the systems, which should be enumerated in the same terms 
in each of these. Sometimes a modification in the form of 
statement, veiling the special property of the figure in the 
particular type of space, would result from a generalization 
of the theorems for the general geometry, in which case such 
special properties should be clearly indicated. Thus, to state 
an illustration cited by M. Barbarin,* that of the convex quad- 
rilateral inscribed in a circle, in Euclidian geometry, the sum 
of two opposite angles is constant and equal to two right angles', 
in non-Euclidian geometry, this sum is variable. Notwith- 
standing this, the two forms may be reconciled, since in 
both cases the sum of two opposite angles equals that of the 
other two , and this is sufficient for a convex quadrilateral to 
be inscriptible. Such generalizations often lead to a com- 
plete redistribution of values, and so clarify the processes of 
Euclidian geometry in the most distinctive way. Professor 
E. Study has said : 
“The conception of geometry as an experimental science is only 
one among many possible, and the standpoint of the empiric is as 
regards geometry by no means the richest in outlook. For he will 
not, in his one-sidedness, justly appreciate the fact that in mani- 
fold, and often surprising ways the mathematical sciences are in- 
tertwined with one another, that in truth they form an indivisible 
whole. 
“Although it is possible and indeed highly desirable that each sep- 
arate part or theory be developed independently from the others and 
with the instrumentalities peculiar to it, yet whoever should disre- 
gard the manifold interdependence of the different parts, would de- 
prive himself of one of the most powerful instruments of research. 
“This truth, really self-evident yet often not taken to heart, ap- 
plied to Euclidian and non-Euclidian geometry, leads to the some- 
what paradoxical result that, among conditions to a more profound 
understanding of even elementary parts of the Euclidian geometry, 
the knowledge of the non-Euclidian geometry cannot be dispensed 
with. 
*On the Utility of Studying non-Euclidian Geometry , 1 . c. 
t Ueber Nicht-Euklidische und Linien-Geometrie, Greifswald, 1900. 
