271 



Concerning Spheric Geometry, 



By David A. Roth rock. 



(Al)stract.) 



In this paper is devolopod a system of analytic geometry upon the 

 surface of a sphere, in wliicli tlie axes of reference are great circles and 

 tlie coordinates of a point are arcs of great circles. With a jn-oper choice 

 of axes, the equations of the loci known as spheric straight line, spheric 

 circle, spheric ellipse, spheric hyperbohi, spheric parabola defined metri- 

 cally as in plane analytics, appear in a form analogous to their equations 

 in the plane. 



The paper also investigates other loci of more complex character, to- 

 gether with a discussion of the notion of spheric pole and polar, radical 

 axis, etc. A sunnnavy of the literature upon this system of geometry is 

 also included. 

 lUoomington, Indiana, 

 Norcmber 30, 1911. 



