Abstract

1926] ORIGINS OF FOURTH DIMENSION CO~CEPTS 397 Near the origin a cubical parabola and a lemniscate are two approximations; for large distances from the origin a lituus is a good approximation. 6. Mr. Barr's paper was a continuation of a study presented at the last meeting of the Indiana section. The data were collected from a study of 1000 semester examination papers written under twenty instructors. The results indicated that probably too much time was being given to re-mastering material of high school grade and too little time to actual mastery of algebra of college grade. The time and place of the next meeting were left to be decided by the executive committee. H. T. DAVIS, Secretary-Treasurer. ORIGIXS OF FOURTH DIMENSION CONCEPTS By FLORI:\.N C:\]ORI, University of California 1. From Aristotle to Henry More. Inquiries into the possibility of a fourth dimension of space reach as far back as Greek philosophy. Nevertheless, for 2000 years no one dared to proclaim the existence of such a space. Thus Aristotle in his Heaven says that a solid has mag~tude "in three ways and beyond these there is no other magnitude because the three are all." This is the record of man's